Solutions Manual for Managerial Economics and Strategy 3rd edition By Jeffrey M. Perloff, James A. B

Managerial Economics and Strategy 3e Jeffrey Perloff, James Brander (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) All Chapters Solutions Manual Supplement files download link at the end of this file. Chapter 1 Has No Solutions Manual

CHAPTER 2 SUPPLY AND DEMAND SOLUTIONS TO END-OF-CHAPTER QUESTIONS Demand 1.1

1.2

When the price of coffee changes, the change in the quantity demanded reflects a movement along the demand curve. When other variables that affect demand change, the entire demand curve shifts. For example, when income changes, this causes coffee demand to shift.

Q = 0.1. Y An increase in Y shifts the demand curve to the right, from D1 to D2.

1.3

The relationship between the quantity of coffee (𝑄) and the price of sugar (𝑝𝑠 ) is defined by the coefficient on the 𝑝𝑠 term in the equation. Since this coefficient is negative (it’s value is −0.3), an increase in the price of sugar (𝑝𝑠 ) will decrease the quantity of coffee. This is the definition of a complementary good. More

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specifically, if the price of sugar goes up by $1.00 per pound, then the demand for coffee will fall by 300,000 tons.

1.4

The market demand curve is the sum of the quantity demanded by individual consumers at a given price. Graphically, the market demand curve is the horizontal sum of individual demand curves.

1.5 a. The inverse demand curve for other town residents is p = 200 − 0.5Qr. b. At a price of $300, college students demand 100 units of firewood, and other residents demand no firewood. Other residents will demand zero units of firewood if the price is greater than or equal to $200. c. The market demand curve is the horizontal sum of individual demand curves, as illustrated below.

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Supply 2.1

The effect of a change in pf on Q is Q = −20pf p f Q = −20(1.10) p f Q = −22 units. p f

Thus, an increase in the price of fertilizer will shift the avocado supply curve to the left by 22 units at every price (i.e., a parallel shift to the left).

2.2

When the price of avocados changes, the change in the quantity supplied reflects a movement along the supply curve. When costs or other variables that affect supply change, the entire supply curve shifts. For example, the price of fertilizer represents a key factor of avocado production, which affects the cost of avocado production, shifting the avocado supply curve. This is because avocado prices are measured on a graph axis. Other factors that affect supply are not measured by a graph axis.

2.3

Given the supply function, Q = 58 + 15p–20pf, The effect of a change in p on Q is Q = 15p. p To change quantity by 60, price would need to change by 60 = 15p p = $4.00.

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2.4

The market supply curve is the sum of the quantity supplied by individual producers at a given price. Graphically, the market supply curve is the horizontal sum of individual supply curves.

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Market Equilibrium 3.1

The supply curve is upward sloping and intersects the vertical price axis at $6. The demand curve is downward sloping and intersects the vertical price axis at $4.

When all market participants are able to buy or sell as much as they want, we say that the market is in equilibrium: a situation in which no participant wants to change its behavior. Graphically, a market equilibrium occurs where supply equals demand. An equilibrium does not occur at a positive quantity because supply does not equal demand at any price.

3.2

The equilibrium price is p = $300, and the equilibrium quantity is Q = 2000.

3.3

Given that ps = $0.20, pc = $5, and Y = $55,000 (note Y is measured in thousands, so the value to use here is 55), the demand for coffee can be rewritten as Q = 14 − p and the supply of coffee can be rewritten as Q = 8.6 + 0.5p.

When all market participants are able to buy or sell as much as they want, we say that the market is in equilibrium: a situation in which no participant wants to change its behavior. Graphically, a market equilibrium occurs where supply equals demand. Thus, the equilibrium price is D=S 14 − p = 8.6 + 0.5p 5.4 = 1.5p p = $3.60.

Find the equilibrium quantity by substituting this price into either the supply or demand function. For example, using the supply function, the equilibrium quantity is

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Q = 8.6 + 0.5p Q = 8.6 + 0.5(3.60) Q = 8.6 + 1.8 Q = 10.4 units.

3.4 If Y = $55,000, ps = 0.20, pc = $5, and p = 4, the quantity demanded is Q = 8.56 − 4 − 0.3(0.2) + 0.1(55) = 10. The quantity supplied is Q = 9.6 + 0.5(4) − 0.2(5) = 10.6.

There is an excess supply equal to 10.6 − 10.0 = 0.6 in this case. Because of the excess supply, firms unable to sell at the price of $4 would lower their prices, forcing the market price down. Price would fall until the equilibrium price was reached.

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Shocks to the Equilibrium 4.1

a. The new equilibrium with the horizontal supply curve is where the new demand curve intersects the horizontal supply curve. The new equilibrium price is unchanged. See figure. b. The new equilibrium with the vertical supply curve is where the new demand curve intersects the vertical supply curve. The new equilibrium price is higher.

See figure. c. The new equilibrium with the upward-sloping supply curve is where the new demand curve intersects the upward-sloping supply curve. The new equilibrium price is higher. See figure.

4.2 a. Health benefits from drinking coffee shift the demand curve for coffee to the right because more coffee is now demanded at each price. The new market equilibrium is where the original supply curve intersects the new coffee demand curve, at a higher price and larger quantity.

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b. An increase in the usefulness of cocoa will increase demand for cocoa. This will drive up the equilibrium price of cocoa. Since cocoa and coffee are likely substitutes, this will increase the demand for coffee. The new market equilibrium is where the original supply curve intersects the new coffee demand curve, at a higher price and higher quantity.

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c. A recession shifts the demand curve for coffee to the left because less coffee is now demanded at each price. The new market equilibrium is where the original supply curve intersects the new coffee demand curve, at a lower price and lower quantity.

d. New technologies increasing yields shift the supply curve for coffee to the right because more coffee is now supplied at each price. The new market equilibrium is where the original demand curve intersects the new avocado supply curve, at a lower price and higher quantity.

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4.3

Outsourcing shifts the labor demand curve to the right because more Indian workers are demanded at each wage. The new market equilibrium is where the original supply curve intersects the new labor demand curve.

4.4

Given that pt = $0.80, the demand for avocados can be rewritten as Q = 160 − 40p and the supply of avocados can be rewritten as Q = 50 + 15p.

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When all market participants are able to buy or sell as much as they want, we say that the market is in equilibrium: a situation in which no participant wants to change its behavior. Graphically, a market equilibrium occurs where supply equals demand. Thus, the equilibrium price is D=S 160 − 40p = 50 + 15p 110 = 55p p = $2.00.

Find the equilibrium quantity by substituting this price into either the supply or demand function. For example, using the supply function, the equilibrium quantity is Q = 50 + 15p Q = 50 + 15(2.00) Q = 50 + 30 Q = 80 units.

When the price of tomatoes increases to $1.35, the demand curve for avocados shifts out to Q = 171 − 40p The supply of avocados is unchanged. The new equilibrium is found where D=S 171 − 40p = 50 + 15p 121 = 55p p = $2.20.

The equilibrium quantity is found as before Q = 50 + 15p Q = 50 + 15(2.20) Q = 50 + 33 Q = 83 units.

4.5 A leftward shift in the labor supply curve will drive up wages and reduce employment. The size of these effects will depend on the relative slopes of the supply and demand curves for labor.

4.6

The damage reduces the supply of oranges, increasing the equilibrium price and decreasing the equilibrium quantity of orange juice.

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The demand for grapefruit juice increases as the price of orange juice increases because grapefruit juice is a substitute. As the demand for grapefruit juice increases, the equilibrium price and quantity of grapefruit juice increase.

4.7

The increased use of corn for producing ethanol will shift the demand curve for corn to the right. This increases the price of corn overall, reducing the consumption of corn as food.

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4.8

Suppose supply is initially S1, but it decreases by a small amount to S2 after the BP oil spill. When all market participants are able to buy or sell as much as they want, we say that the market is in equilibrium: a situation in which no participant wants to change its behavior. Graphically, a market equilibrium occurs where supply equals demand. The original market equilibrium is where the original demand curve intersects the original supply curve (e1). The new market equilibrium is where the original demand curve intersects the new supply curve (e2). When the supply curve shifts by a relatively small amount, the change in the equilibrium price is likely to be small.

4.9 Concerns about botulism caused the demand curve for baby formula to shift in. (A lower quantity was demanded at any given price.) This demand curve shift would put downward pressure on price and quantity. The removal of production permits caused the supply curve to shift in. (A lower quantity was supplied at any given price.) This supply curve shift would put upward pressure on price and downward pressure on quantity. Overall, the price could rise or fall depending on the relative size of the demand curve and supply curve shifts. However, quantity would have to fall.

p2 p1

Q2

Q1

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4.10 An increase in petroleum prices shifts the aluminum supply curve to the left because the cost of producing aluminum is more expensive at each price. An increase in the cost of petroleum also shifts the demand curve for aluminum to the right because the petroleum price increase makes a substitute, plastic, more expensive (by making the cost of plastic production higher). The new equilibrium is where the new aluminum supply curve intersects the new aluminum demand curve.

When the supply curve shifts to the left, the new equilibrium price is higher and the new equilibrium quantity is lower. When the demand curve shifts to the right, the new equilibrium price is higher and the new equilibrium quantity is higher. When both curves shift, the new equilibrium price is higher, but the new equilibrium quantity could be higher, lower, or unchanged.

4.11 The cartoon seems to show a bumper harvest of lobsters. A large increase in the catch will shift the supply curve to the right (from S1 to S2) which will cause price to fall from p1 to p2.

4.12 When drilling increases in response to the rising price of crude oil, the demand for bentonite increases as well. The demand curve will shift to the right and cause the equilibrium price and quantity of bentonite to increase. This is illustrated in the picture below:

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Effects of Government Interventions 5.1 The effect of vendor licensing is to reduce the number of street vendors relative to the undistorted market equilibrium. Therefore, the number of handbags (and other products) offered for sale by street vendors is less than it would be without licensing (with free entry). As a result, the supply curve for handbags available from street vendors has shifted in compared with what it would be without licensing. The diagram representing the street vendor handbag market is therefore similar to the diagram in Q&A 2.2. The market price is higher and the quantity sold is lower than it would be without mandatory licensing.

5.2

In the absence of price controls, the leftward shift of the supply curve as a result of Hurricane Katrina would push market prices up from p0 to p1 and reduce quantity from q0 to q1. At a government imposed maximum price of p2, consumers would want to purchase qd units, but producers would only be willing to sell qs units. The resulting shortage would impose search costs on consumers making them worse off.

The reduced quantity and price also reduced firms’ profits.

5.3

With a binding price ceiling, such as a ceiling on the rate that can be charged on loans, some consumers who demand loans at the rate ceiling will be unable to obtain them. This is because the demand for bank loans is greater than the supply of bank loans to low-income households with the usury law.

5.4

With the binding rent ceiling, the quantity of rental dwellings demanded is that quantity where the rent ceiling intersects the demand curve (QD). The quantity of rental dwellings supplied is that quantity where the rent ceiling intersects the supply

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its behavior. Graphically, a market equilibrium occurs where supply equals demand. Thus, the equilibrium price is D=S 160 − 40p = 50 + 15p 110 = 55p p = $2.00.

Find the equilibrium quantity by substituting this price into either the supply or demand function. For example, using the supply function, the equilibrium quantity is Q = 50 + 15p Q = 50 + 15(2.0) Q = 50 + 30 Q = 80 units.

If a $0.55 tax is imposed, the demand curve can be rewritten to account for the tax.

First, the demand curve can be rewritten as inverse demand by solving for p Q = 160 − 40p p = 4 − 0.025Q. The tax is subtracted from inverse demand to give p = 3.45 − 0.025Q and then this inverse demand curve can be turned back into a demand curve Q = 138 − 40p.

Setting supply equal to demand, the new equilibrium (pretax) price is D=S 138 − 40p = 50 + 15p 88 = 55p p = $1.60.

The after-tax price is $2.15.

Using the supply function, the equilibrium quantity is Q = 50 + 15p Q = 50 + 15(1.60) Q = 50 + 24 Q = 74 units.

5.7 a. If demand is vertical and supply is upward sloping, then all the tax burden is paid by consumers because they are not price sensitive. b. If demand is horizontal and supply is upward sloping, then all the tax burden is paid by producers because consumers are infinitely price sensitive.

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c. If demand is downward sloping and supply is horizontal, then all the tax burden is paid by consumers because producers are infinitely price sensitive.

5.8 If instead of the tax being levied on producers it is collected from consumers, then the effect will be a decrease in demand. The demand curve will shift left until the vertical distance between the original demand curve and the new one is equal to the tax of $2.40. This new demand curve, call it D2, will intersect the original supply curve (S1) at a price of $5.60 and a quantity of 11.6. In addition to the price of $5.60 per bushel, buyers will also have to pay the $2.40 tax for a total, after-tax price of $8.00. The seller will receive the $5.60 per bushel, and the government will collect $27.84 billion in tax revenue (the $2.40 tax multiplied by the 11.6 billion bushels of corn traded in the new equilibrium).

This equilibrium is not the same as the case in Q&A 2.3 because in that problem the supply curve is perfectly elastic, while in this case it is not. In Q&A 2.3, the seller passes on the entire tax to consumers, while here, the tax is split with $0.80 being paid by consumers and $1.60 paid by producers.

5.9 A tax on consumers will undoubtedly shift the demand curve down by an amount equal to the size of the tax. The new equilibrium price and quantity with the tax will be where the new demand curve intersects the original supply curve. The decrease in quantity will be larger (and tax revenue smaller) the more horizontal the supply curve is. Just the opposite is true if the supply curve is more vertical—quantity effects will be small, and revenue generation from the tax will be large.

When to Use the Supply-and-Demand Model 6.1

The supply-and-demand model is accurate in perfectly competitive markets, which are markets in which all firms and consumers are price takers: no market participant can affect the market price. If there is only one seller of a good or service—a monopoly—that seller is a price taker and can affect the market price. Firms are also price setters in an oligopoly—a market with only a small number of firms.

Experience has shown that the supply-and-demand model is reliable in a wide range of markets, such as those for agriculture, financial products, labor, construction, many services, real estate, wholesale trade, and retail trade.

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Managerial Problem 7.1

A tax paid by consumers shifts the demand curve down by an amount equal to the size of the tax. Just the opposite, suspending a tax on consumers should raise the demand curve by an amount equal to the size of the suspended tax. Although fuel supply is more likely to be vertical in the short run than in the long run, equilibrium fuel prices will increase when the demand curve shifts up whether the supply curve is vertical or upward sloping.

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SOLUTIONS TO SPREADSHEET EXERCISES Solutions Available on MyLab Economics

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CHAPTER 3 EMPIRICAL METHODS FOR DEMAND ANALYSIS SOLUTIONS TO END-OF-CHAPTER QUESTIONS Elasticity 1.1 Elasticity of demand for prenatal smoking is inelastic:

   %Q/%P  2.65/21  0.1262.

1.2

An arc price elasticity is an elasticity that uses the average price and average quantity as the denominator for percentage calculations. For example, let Q be the average quantity and p be the average price. The arc price elasticity is Q p  ε= Q p Q  p   .

Q  p  The change in price is $0.30 and the change in quantity is –2,994. Average price is $1.14 and average quantity is 21,189. Thus, the arc elasticity of demand is  2,994  1.14  ε=   = –0.537.

21,189  0.30 

ε=

1.3

The elasticity of demand is the percentage change in quantity divided by the percentage change in price: Q p  ε= Q p ε= From the demand equation,

Q  p   . p  Q 

Q is –2, so p  10  ε =  2  .  80  ε = –0.250.

1.4 Differentiating the demand function Q = Apε, we find that dQ/dp = εApε–1.

Substituting that expression into the point elasticity definition, <LINK>Equation 139

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3.8</LINK>, we learn that the elasticity is

dQ p p p = eAp e -1 = eAp e -1 e = e. dp Q Q Ap Because the elasticity is a constant, it does not depend on a particular value of p or Q and is therefore the same at every point along the demand curve.

1.5 The elasticity of demand is the percentage change in quantity divided by the percentage change in price: ∆𝑄 ⁄𝑄 𝜀= ∆𝑝⁄ 𝑝 or ∆𝑄 𝑝 𝜀= ( ) ∆𝑝 𝑄 or using calculus this expression can be written as 𝑑𝑄 𝑝 𝜀= ( ) 𝑑𝑝 𝑄 𝑑𝑄 From the demand equation, = −8𝑝 so 𝑑𝑝

5

200

𝜀 = −8(5) ( ) = − = −0.5.

400 400 Since the elasticity coefficient is less than 1 (in absolute value) this is an example of relatively inelastic demand at this price and quantity.

1.6

The figure below refers to the graph of a linear inverse demand curve. Demand is elastic for all quantities to the left of the midpoint. At the midpoint, elasticity equals –1. Finally, demand is inelastic for all quantities to the right of the midpoint.

1.7

According to Equation 3.1, the elasticity of demand is   (percentage change in quantity demanded ÷ percentage change in price)  3.8%  10%  0.38, which is inelastic.

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Calculated similarly,

Q is 16.2, so the cross-price elasticity of demand with p p

respect to the price of palm oil is

 31  ε = 16.2   1,275  ε = 0.394.

1.10 The income elasticity of demand is the percentage change in quantity divided by the percentage change in income: ∆𝑄 ⁄𝑄 𝜀= ∆𝑌⁄ 𝑌 or 𝜀=

∆𝑄 𝑌 ( ) ∆𝑌 𝑄

∆𝑄

From the demand equation, is 0.2. Plugging in 45 cents for p, 31 cents for pp, and ∆𝑌 1,275 for Q and then solving for Y, Y = $1.5. So, the income elasticity of demand is 𝜀 = 1.5 0.2 (1275)=0.0002. Since the income elasticity coefficient is positive we can conclude coconut oil is a normal good (i.e as income increases so does the demand for coconut oil).

1.11 The connection between these two events is the complementary relationship between smoking and alcohol consumption discussed in the mini-case. As mentioned there, the value of the cross-price elasticity between cigarettes and alcoholic beverages is roughly -1.0. When a tax is placed on cigarettes this shifts the supply curve left (assuming the producers remit the tax, though the same result occurs if buyers do so) and drives up the equilibrium price of cigarettes. As the price of cigarettes rises, the demand for alcoholic beverages falls. This results in a smaller equilibrium quantity in the market for alcoholic beverages as shown in the figure below.

1.12 The mini-case describes a good, Google Play apps, with very elastic demand (estimated coefficient of -3.7). If the price of these apps increases by 5% then the quantity demanded will fall (as evidenced by the negative sign) by 5  3.7 = 18.5%.

Revenue in this case will fall. To calculate the percentage change in revenue, consider first the amount of revenue the firm earns before the price change (R1 = P  Q) and compare to the revenue earned after the price change which is given by R2 = P(1 + 0.05)  Q(1 – 0.185) = PQ  0.88575 = R1  0.88575. This means that revenue falls by roughly 14% as a result of this price change.

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Regression Analysis 2.1

Assume the first day, the supply of cod is S1. The next day, the supply of cod is S2.

A market equilibrium occurs where supply equals demand. In this case, the equilibrium is where the vertical supply curve intersects the downward-sloping demand curve.

The demand curve shows the quantity demanded at various prices. The demand curve is identified from frequent changes in supply because the demand curve is assumed not to shift from day to day. As a result, each market equilibrium price and quantity of cod reveals a point along the demand curve.

2.2

A demand function with price as the only explanatory variable defines a demand curve: Q = a + bp.

Quantity is a function of price in a demand function, while price is a function of quantity in an inverse demand function. We can use algebra to rearrange a linear demand equation so that price is on the left-hand side and quantity on the right-hand side to generate the inverse demand curve: p = –(a/b) + (1/b)Q. Asking how many customers would buy a proposed new menu item at various prices can be used to estimate the demand curve, and the inverse demand curve can be calculated from it. .

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A demand function with price and income as explanatory variables can be generated from the focus group by also asking for their level of income. Essentially, a regression with the quantity demanded as the dependent variable and price and income as the explanatory variables could be estimated if each member of the focus group is asked their level of income.

2.3

If p = $2.00, then the predicted quantity is Q = 130 – 3.5p Q = 130 – 3.5(2.00) Q = 130 – 7 Q = 123 units.

In this case, the residual would be the difference in the predicted quantity and the actual quantity 129 – 123 = 6.

Included in the error term is any factor that would affect the quantity of popsicles demanded but that is not directly included in the demand equation. Factors that affect the demand for popsicles include consumer income, the prices of substitutes and complements, the weather, and temperature.

2.4

A demand function with price as the only explanatory variable defines a demand curve: Q = a + bp.

Quantity is a function of price in a demand function. Using Excel, the equation for this demand function is Q = 92.429 – 0.6857p.

The R2 statistic is the share of the dependent variable’s variation that is “explained by the regression”--that is, accounted for by the explanatory variables in the estimated regression equation. Using Excel, the statistic is 0.9749.

2.5 Recall the estimated demand equation: 𝐸 = 2400 − 25𝑝 + 84𝐹 a. If the price is $0.08 per KWH and the average monthly temp is 80 degrees then the estimated demand for electricity is 𝐸 = 2400 − 25(8) + 84(80) = 8920. b. A one cent decline in price will raise electricity demand by 25 GWH while a one degree fall in temperature will actually decrease demand by 84 GWH. If, instead, temperature were to rise by one degree then the increase in demand would be greater from the temperature change than from the price change. c. If the primary driver of electricity use as it relates to temperature is heating in winter and cooling in summer, then we might expect a negative sign on the temperature variable in cooler climates. As temperature rises from cold (say 30 degrees Fahrenheit) to slightly less cold (maybe 50 degrees Fahrenheit) then individuals using electricity to directly heat their homes (or to run the blowers on

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the natural gas furnaces that heat their homes) would use less electricity. Chance are, however, that in both northern and southern climates the relationship between temperature and electricity use is nonlinear (high use at very low and very high temperatures with more moderate use when temperatures require less heating / cooling).

2.6

Mai should focus her efforts on the data shown in panel (b) (the one with the lower R2). The fit in panel (a) is already very good, so any costly attempt to improve her estimate would not yield much additional precision in panel (a).

Panel (b), however, has more room for improvement and spending additional money to gather temperature and sunshine data will be more valuable in that case.

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Properties and Statistical Significance of Estimated Coefficients 3.1

Using Excel, the equation for this demand function is Q = 12.533 – 6.2496p.

3.2

This question has multiple parts. Each part is answered below. a) Using Excel, the equation for the demand function with 2.0 as the quantity in the first row is Q = 12.140 – 5.8546p. b) Using Excel, the equation for the demand function with 2.7 as the quantity in the second row is Q = 12.493 – 6.1545p.

3.3

Q is –1.438, so the effect of an increase in price on p the quantity of Camry’s demanded is ΔQ = –1.438(Δp) ΔQ = –1.438(1) ΔQ = –1.438 thousand.

From the demand equation,

From the demand equation, if the price is $20 thousand, then demand is Q = 53.857–1.438p Q = 53.857–1.438(20) Q = 25.097 thousand The elasticity of demand is the percentage change in quantity divided by the percentage change in price:

Q p  Q p Q  p   . ε= p  Q 

ε=

From the demand equation,

3.4

Q is –1.438, so p  20  ε =  1.438 .  25.097  ε = –1.146.

According to Excel, the price coefficient’s standard error is 0.0549, and the corresponding t-statistic is –12.477. Statistically, an explanatory variable’s coefficient is significantly different than zero at the 0.05 level if its t-statistic is larger than 1.96 in absolute value. In this example, the t-statistic is 12.477, so the price coefficient is statistically significant.

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Regression Specification 4.1

An explanatory variable's coefficient is statistically significantly different than zero at the 0.05 level if its t-statistic is larger than 1.96 in absolute value. In this example, the t-statistic is 4.25, so the price coefficient is statistically significant.

A year of experience raises CEO compensation by 36.10 thousand dollars, which seems economically significant.

4.2

To find the log-linear demand equation, take the log of both sides and simplify:

ln(Q)  ln( A)   ln( p)  u .

You can estimate this in Excel using an OLS regression of the form Y    X

by converting your quantity and price data to logs. In the resulting regression, α will be an estimate of ln(A) and β will be an estimate of ε.

4.3

Revenue (R) is defined as the price of the good (p) multiplied by the quantity of the good sold (Q): R = pQ. As such, revenue is not linear in price, so using the linear function form would be a misspecification. Since the relationship between price and quantity is linear, the linear functional form could be used to estimate quantity with price as an explanatory variable.

4.4 The trouble with this specification is that the demand for alcohol is partially determined by a subjects current health status, not the other way around (as indicated here). Once liver failure sets in (a low value for L) then alcohol consumption is curtailed. It does not follow that drinking lots of alcohol will help fight off the onset of liver failure.

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Forecasting 5.1

Fresh foods are substitutes for Heinz prepared foods. Since fresh fruits and vegetables are in greater supply in May, June, and July, and their corresponding prices are likely lower, consumers demand less of Heinz prepared foods, decreasing Heinz’s second-quarter revenues.

5.2

The estimated relationship on the second quarter explanatory variable (S) is 0.452, indicating a positive relationship between revenue and the second quarter. The key to understanding the comparison to other quarters is to note that the missing quarter is fall. That means that the coefficient for each of the other quarterly dummy variables measures the difference relative to the fall quarter. So, the 0.452 means that revenue is $452 million higher in spring than fall. Furthermore, spring has higher revenue than winter but lower revenue than summer.

5.3

Revenue is determined in large part by the consumers' demand curve. We know that consumer demand is affected by variables such as income, population, and advertising. Forecasts based on extrapolation (pure time series analysis) ignores these structural, causal variables. The role of such variables may be implicit in an extrapolation. For example, one reason why revenue may have grown smoothly over time is that population increased smoothly over this period. An alternative to extrapolation uses economic theory to derive the causal relationships between economic variables. Forecasts based on a regression specification that incorporates underlying causal factors is called theory-based econometric forecasting. With theory-based econometric forecasting, we predict the dependent variable based on underlying factors, not just on the time series pattern of the dependent variable. We need theory-based methods to forecast revenues for companies such as FedEx and Sony because demand for their products is affected by structural variables and does not smoothly follow a time trend.

5.4

a. Using the regression tool in Excel generates the following trendline for revenue for Amazon and Walmart. In each of these equations t is a time variable that is 1 in 2008, 2 in 2009, etc. This makes 2021 (the year we want to forecast) t=14.

Amazon’s revenue is given by: 𝑅𝑒𝑣𝑒𝑛𝑢𝑒𝐴𝑚𝑎𝑧𝑜𝑛 = −13.73 + 16.50𝑡 and Walmart’s revenue is given by: 𝑅𝑒𝑣𝑒𝑛𝑢𝑒𝑊𝑎𝑙𝑚𝑎𝑟𝑡 = 395.52 + 10.95𝑡 Using these equations we can forecast Amazon’s revenue in 2021 as −13.73 + 16.50(14) = 217.27. Walmart’s forecast for 2021 is 395.52 + 10.95(14) = 548.82.

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a. Using the equations from part (a) Amazon’s revenue will equal that of Walmart when −13.73 + 16.50𝑡 = 395.52 + 10.95𝑡 which implies 5.55𝑡 = 409.25.

Solving for t gives t=73.7. If 2021 is t=14 then it will take around 60 more years – so about 2081 for Amazon’s revenue to equal Walmart’s. b. It certainly seems reasonable that Amazon’s high rate of growth in the past few years has come at the expense of Walmart since both retailers aim to be a ‘we have everything’ kind of shopping experience – albeit with very different business models.

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Managerial Problem 6.1

This question has multiple parts. Each part is answered below. a) A t-statistic equals the coefficient divided by the standard error, so the standard error equals the coefficient divided by the t-statistic: –413/–12.8 = 32.266. b) The new standard error would be 322.66. An explanatory variable's coefficient is statistically significantly different than zero at the 0.05 level if its t-statistic is larger than 1.96 in absolute value. In this example, the t-statistic is –1.28, from –413/322.66, so the price coefficient is not statistically significant.

6.2

Using Excel, the equation for this demand function is Q = 1,023.92 – 412.82p.

The statistic is the share of the dependent variable's variation that is "explained by the regression"--that is, accounted for by the explanatory variables in the estimated regression equation. Using Excel, the statistic is 0960.

The standard error is a measure of how much each estimated coefficient would vary if we re-estimated the underlying true demand relation with many different random samples of observations. The standard error on the intercept is 33.78 and the standard error on the price coefficient is 32.70.

A t-statistic for a regression variable can be calculated as the estimated coefficient divided by the coefficient's standard error. For the intercept, this is 30.311, from a coefficient of 1,023.92 divided by 33.78. For the price variable, this is –12.624, from –412.82 divided by 32.70.

An explanatory variable's coefficient is statistically significantly different than zero at the 0.05 level if its t-statistic is larger than 1.96 in absolute value. In this example, the t-statistic for the intercept is 30.311, so it is statistically significantly different than zero. The t-statistic for the price variable is 012.624, so it is statistically significantly different than zero.

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SOLUTIONS TO SPREADSHEET EXERCISES Solutions Available on MyLab Economics

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CHAPTER 4 CONSUMER CHOICE SOLUTIONS TO END-OF-CHAPTER QUESTIONS Consumer Preferences

1.1

If consumers receive more of any product, even if they have as much of that product as they need for now, they can save the product for future use, sell the product for money, or exchange it for other goods. Under the “free disposal” assumption, economists assume that there is no cost to getting rid of unwanted goods—hence, people are no worse off (weakly better off) with more goods.

1.2

If the neutral product is on the vertical axis, the indifference curves are parallel vertical lines.

1.3

a. If an indifference curve is thick then it violates the “more is better” assumption because there could be two bundles on the same “thick” indifference curve where one bundle has slightly more of both goods than the other—but is not considered better by the indifference curve. b. If an indifference curve bend backward, then it violates the “more is better” assumption because there will be two bundles that have the same amount of one good but less of the other on the same indifference curve. c. Finally, indifference curves cannot intersect because you can have three bundles—A, B, and C—where A and B are on one indifference curve and B and C are on another and the two indifference curves intersect at B. Since A and C are not on the same indifference curve, one must be preferred to the other, but by transitivity, they must be the same.

1.4

This question has multiple parts. Each part is answered below. a. b. c. d.

1.5

Imperfect substitutes Complements Independent (neither complements nor substitutes) Perfect substitutes for many consumers

An indifference curve is the set of all bundles of goods that a consumer views as being equally desirable. Indifference curves are convex to the origin, which means they are “bowed in.” This is due to consumers having a diminishing marginal rate of substitution, where consumers are willing to give up more of one good to obtain another unit of a second good the more of the first good they have. Convex indifference curves show that a consumer views two goods as imperfect substitutes, which is common, instead of perfect complements or perfect substitutes, both of which are rare, special cases.

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Utility 2.1

William’s indifference curves are right angles (as in panel b of Figure 4.4). His utility function is U = min(H, W), where min means the minimum of the two arguments, H is the number of units of hot dogs, and W is the number of units of mustard.

2.2

The marginal rate of substitution (MRS) shows the rate at which a consumer can substitute one good for another while remaining on the same indifference curve. Graphically, MRS is the slope of the indifference curve. If soda is measured on the horizontal axis, then Porsha’s 1 MRS is −3 (and if juice is measured on the horizontal axis, then her MRS is − 3).

2.3

He will prefer the bundle with four pizzas and four boxes of graham crackers because if MRS = −1 at this point, and the indifference curve is convex, he will be unwilling to trade down to any lower quantity of graham crackers at a one-for-one ratio. At the point where he has five pizzas and one box of graham crackers, his indifference curve will have a slope of less than −1. Thus, if forced to trade one for one, his utility level would fall.

2.4

If Sanghoon prefers consumption bundle b to consumption bundle c, it must be the case that the value of his utility function is higher at b than at c. It follows that the square of his utility at b must exceed the square of his utility at c. Therefore, Linh’s utility, which is the square of Sanghoon’s utility, must also be higher at b than at c. For any two consumption bundles, the one preferred by Sanghoon is also preferred by Linh. As they have exactly the same ordering of consumption bundles, Sanghoon and Linh have the same ordinal preferences.

2.5

Andy’s marginal utility of apples divided by its price is 23  1.5. The marginal utility for kumquats is 45  1.2. That is, a dollar spent on apples gives him more extra utils than a dollar spent on kumquats. Thus, he maximizes his utility by spending all his money on apples and buying 402  20 of apples.

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The Budget Constraint 3.1

See figure below. Let’s denote mangos by “C” and oranges by “O.” It is given: C = 4, O = 3, PC = $2, PO = $1.

The most he can spend on these goods, Y = 4  2  3  1 = 8  3 = $11.

The budget constraint: 2C  1O = 11  2C  O = 11.

3.2

The marginal rate of transformation between B (burritos) and Z (pizza) is p 10  Z    2 pB 5 .

3.3

A budget line or budget constraint shows the bundles of goods that can be bought if the entire budget is spent on those goods at given prices. The opportunity set is all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint. Income doubles to $100, and the price of pizza doubles to $2. The maximum amount of pizza Lisa can obtain is unchanged because income and the price of pizza both double. However, Lisa can now obtain 50 burritos, from income of $100 divided by the $2 price of burritos. Unless Lisa consumed all pizza and no burritos before the income and price change, she is better off. However, if Lisa maximized utility by consuming only pizza before the changes, then it is possible that she is equally well off (e.g., no better off).

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3.4

A budget line or budget constraint shows the bundles of goods that can be bought if the entire budget is spent on those goods at given prices. The opportunity set is all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint. A 25 percent income tax reduces income by 25 percent, which reduces the maximum quantity of opera concerts and the maximum quantity of ice hockey games Dale can attend by 25 percent, shifting the budget line inward. Consequently, Dale’s opportunity set has shrunk.

3.5

The opportunity set is all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint. In this case, Sophia can obtain a maximum of 40 apps (and have the 2 pounds of gummy worms her parents give her) or a maximum of 42 pounds of gummy worms per month (including the 2 pounds of worms her parents give her). Without the possibility of selling the gummy worms, her opportunity set looks like this:

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If she can sell the gummy worm, then the opportunity set would extend up to 42 apps on the vertical axis as indicated by the dashed line in the diagram.

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Constrained Consumer Choice 4.1

There are multiple parts to this problem. Each part is answered below. a. 50S  50T = 500  S  T = 10 b. MRS = −MUS /MUT = −2T/2S = −T/S c. At the optimal, the budget constraint and the indifference curve should be tangent; therefore, we should have −MRS = PS /PT  T/S = 50/50 = 1  T * = S *. The optimal must also be affordable; thus, S *  T * = 10. Substitution gives us S * = T * = 5.

4.2

There are multiple parts to this problem. Each part is answered below. a. Setting MUR/pR = MUC/pC yields 20RC/10 = 10R2R2/5 or 2C = 2R. Therefore, R = C. We then substitute R = C into the budget equation to obtain: 10C + 5C = 90 or C = 6 (and R = 6). The diagram looks like Figure 4.8 with only the middle indifference curve shown and with R and C on the axes. b. Using the same method as in part (a), the new solution is R = 6, C = 3. In this case, the budget line from part (a) has the same intercept on the R axis, but the intercept on the C axis falls by half, so the budget line pivots inward.

4.3

See figure below. e1 will be the same as e2 if the tangent point of the indifference curve and the budget line is on the solid region of the budget line; that is, if the water restriction does not “bite.” If the tangent point is on the dashed region, e2 will be different than e1, a corner solution, with less water.

4.4

If the U.S. price of gasoline changes from being below the Canadian price to going above, then a utility-maximizing Canadian who lives equally close to gas stations on both sides of the border would shift from buying gas in the United States (where indifference curve I2 touches budget line L1 on the U.S. gas axis) to buying gas in Canada (where indifference curve I1 touches budget line L2 on the Canadian gas axis). In the diagram, the two goods on the axes are Canadian gas and U.S. gas. They are perfect substitutes, so the indifference

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curves are straight lines. The consumer will consume on one axis or the other depending on which price is lower.

4.5

E-books are relatively more expensive in Germany than in the United States, so the budget line for Germany is steeper. If Max and Bob have identical indifference curves, then Max will consume relatively more printed books than Bob does because printed books in Germany are relatively less expensive in terms of e-books compared to the United States.

However, since the indifference curves are convex, we cannot say without additional information the exact quantities of each type of book that Max and Bob will consume (or whether Bob or Max will consume more total books) when maximizing utility.

If Bob’s budget line goes through Max’s optimal bundle, then we can say that Bob will be on a higher indifference curve than Max, but he may or may not consume more e-books than Bob.

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4.6

See figure below. Suppose the number of pizza/day is on the horizontal axis and number of cola/day on the vertical axis and that the indifference curves are negatively sloped and strictly convex.

The original budget constraint passes through the bundle (1 pizza, 2 colas). As this bundle is the optimum, the indifference curve and the budget constraint will be tangent at this point. After the special, because pizza becomes cheaper, the budget constraint becomes less steep after 1 pizza, and there will be a kink in the budget constraint. As a result, Ralph will buy more pizza and less cola.

4.7

Amazon sales are not initially taxed. When Amazon sales are taxed, this raises the Amazon price, pivoting the budget line inward along the Amazon axis. The new tangency point where consumers maximize utility has more purchases from Best Buy. This is because goods from Best Buy and Amazon are substitutes, and goods from Best Buy have become relatively less expensive (now that Amazon goods are taxed).

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4.8

See figure below. Assume the budget is $100. Compare e1 and e2. We know that you would go to the pool fewer times if you did not purchase the membership.

4.9

The budget line identifies the bundles of goods that can be bought if the entire budget is spent on those goods at given prices. The half-price promotion is the same as the BOGO promotion for the first two nights stay and for four or more nights of stay. With the halfprice promotion, the cost of the third and fourth nights is half-price, so the slope of the half-price budget constraint is half its slope between two and four nights. An equilibrium consumption bundle is the one on the budget constraint that gives the highest level of pleasure. The shape of Angela’s indifference curves determine whether she stays at the resort three or four nights when behaving optimally. For example, if her preferences are represented by indifference curve I1, then her optimal bundle contains a four-night stay at the resort. If her preferences are represented by indifference curve I2, then her optimal bundle contains a three-night stay.

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Deriving Demand Curves 5.1

In what follows it is assumed we have the number of $12 shoes on the vertical axis and the number of $3 shoes on the horizontal axis. After the tariff, the $3 shoes cost 3  1.67 = 5.01 and the $12 shoes cost 12  1.37 = 16.44. The slope of budget constraint before the tariff is −3/12 = −0.25 and after the tariff it becomes = −5.01/16.44 = −0.305. Note that before the tariff, Laura had to give up 0.25 unit of expensive shoe to get a cheap shoe, but after the tariff, this rate increases to 0.3. This means that after the tariff, cheap shoes have become relatively more expensive. Assuming Laura’s nominal income is fixed, as a result of the tariff, the budget constraint shifts inward and becomes steeper. Since as a result of tariffs, the real income (the purchasing power) has decreased, Laura will buy fewer of both types of shoes, but because $3 shoes are now relatively more expensive, there will be some substitution away from $3 shoes to $12 shoes, so Laura will end up buying relatively more expensive shoes.

5.2

As the price of tracks rises, if the amount of live music Jack buys rises, then tracks and live music are substitutes. However, if the amount of live music Jack buys falls, then tracks and live music are complements.

In the first figure, the quantity of live music increases when the price of tracks increases. In the second, the quantity of live music decreases.

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5.3

A demand curve shows the quantity demanded at each possible price, holding constant other factors that influence purchases. Pie and ice cream are complements. Therefore, assume Olivia will eat pie, qp, and ice cream, qic, in fixed proportion, where qp = qic = q. Let the price of pie be pp and the price of ice cream be pic. With a budget of Y, the relation of demand and price can be expressed as Y = ppqp + picqic Y = ppq + picq Y = (pp + pic)q q = Y / (pp + pic).

Thus, the resulting demand curve for pie is downward sloping and asymptotically approaches zero:

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5.4

As income rises, consumption of all goods will increase given normal, convex indifference curves. The figure below shows a case where at incomes of $25,000 or less, a person would not buy any savings (in this case a corner solution), but would clearly do so with an income of $100,000.

5.5

The diagram below illustrates this scenario. Florencia is originally consuming at a corner point (point A), but when the price of live concerts drops (and the budget line swings out to the dotted one), her best point moves to B where she consumes some of each good. Ajay initially consumes some of each at point C and when the budget line shifts, he consumes at a new point, point D, that is one a higher indifference curve.

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Behavioral Economics 6.1

Suppose that the restaurant always offers two specials chosen from three possibilities: a chicken special, a fish special, and a vegetarian special. Initially, the menu ordering is chicken, then fish. As Professor Cerf always picks the second item, he picks the fish special. Later the restaurant changes its offerings to fish (listed first) and vegetarian. In this case, Professor Cerf again chooses the second special, vegetarian. As Professor Cerf chooses fish over chicken and vegetarian over fish, transitivity of preferences would imply that he would choose vegetarian over chicken. But if the restaurant later lists vegetarian and chicken in that order as its two specials, Professor Cerf chooses chicken over vegetarian, as chicken is the second item. Thus, his choices are not transitive.

6.2

See figure below. Suppose you are at point O. Assume you are willing to accept AD units of Y in order to give up OA units of X. On the other hand, to buy OB units of X(OA = OB), you are willing to pay BC units of Y. Therefore, you value the same unit of X differently, depending on whether you want to give it up or you want to buy it. The indifference curve would be DOC and has a kink at the endowment point. The graph shows different budget constraints at three different relative prices for X. As you can see, the optimum does not change for small changes of relative price. Therefore, for a range of prices, the demand curve for X will be vertical.

6.2

If a store’s posted price includes the sales tax, consumers observe a change in the price as the tax rises. On the other hand, if a store posts the pretax price and collects the tax at the cash register, consumers are less likely to note that the post-tax price has increased when the tax rate increases. One explanation for the lack of an effect of a tax on consumer behavior is consumer ignorance. An alternative explanation for ignoring taxes is bounded rationality: People have a limited capacity to anticipate, solve complex problems, or enumerate all options. Another explanation is that people incur a cost, such as the time taken or the mental strain, in making calculations and that deciding whether to incur this cost is part of their rational decision-making process. In contrast, inattention due to lack of salience is not rational.

Quoting salaries after deducting income taxes rather than in pretax form could have an effect on job applications to due worker ignorance and bounded rationality. Reasons why it might not have a large effect are that people are more likely to pay attention to taxes when making large, one-time transactions, and accepting a job is an important, infrequent event. .

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Furthermore, that a worker would need to pay income taxes is obvious, and many workers believe income taxes to be relatively high. The extent to which workers will pay attention to income taxes increases as labor supply becomes more elastic (when workers are sensitive to wages).

Managerial Problem 7.1

The technological progress is not neutral. Because of the technology progress, less labor was required to spin the same amount of cotton in order to produce the same amount of product.

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Spreadsheet Exercises Solutions Available on MyLab Economics

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CHAPTER 5 PRODUCTION SOLUTIONS TO END-OF-CHAPTER QUESTIONS

PRODUCTION FUNCTIONS 1.1 Candy production requires giant vats, heaters, coolers, and barrels. The manufacturing of many candies starts with workers combining flour, sugar or corn syrup, and a variety of other ingredients to form a slurry in giant vats. Flavors are introduced and dye is added for color. Next, the mixture is drained from the vats into barrels or molds and is cut and shaped into the final product. Other machines are then used by workers to sort, package, and label the candy. All of this work is overseen by managers, and the candy company is supported by office staff, accountants, truck drivers, and marketers.

1.2

The production function shows only the maximum amount of output that can be produced from given levels of labor and capital because the production function includes only efficient production processes. A firm engages in efficient production if it cannot produce its current level of output with fewer inputs, given existing knowledge about technology and the organization of production. The combination q = 10, L = 3, and K = 6 cannot be a point on the production function with point q = 10, L = 3, and K = 5 because it would not be efficient.

1.3

Yes, this is clearly possible. Since we know that L = 3 and K = 5 yield q=10, then adding a bit of one of the inputs could increase output. So, it is possible that going from K = 5 to K = 6 will increase output from q = 10 to q = 11. This would be shown by moving to a higher isoquant.

1.4

The more time a firm has to adjust its inputs, the more factors of production it can alter.

The short run is a period of time so brief that at least one factor of production cannot be varied practically. The long run is a lengthy enough period of time that all relevant inputs can be varied. The long run is longest for Boeing because aircraft production requires large, specialized machines that take time to produce and shortest for Wacky Jack’s because providing singing telegrams requires primarily easy-to-adjust labor.

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2.6

There are three main factors that may increase undernourishment even if agricultural output per acre (yield) rises. First, a decrease in the total amount of land used for food production may partially offset increases in yield. Second, population growth may exceed the increase in food production. Third, political failures, particularly those resulting in wars and other violent conflicts, may disrupt food distribution systems. This third factor was by far the most important reason for increasing undernourishment in the 2014–2016 period.

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LONG-RUN PRODUCTION 3.1 If an isoquant were thick, it would imply that the addition of both capital and labor from a point on the inside edge of an isoquant to the outer edge of the same isoquant would not increase output.

3.2

Recall the difference between the short run and the long run. The short run is defined as the period of time for which at least one of the firm’s inputs is fixed and cannot be changed. The long run begins at some point in the future when all inputs become adjustable. Therefore, a list of short-run inputs for Sweeps might include the workers they hire (or worker hours), some tools and supplies that can be easily adjusted, etc. but not the time and expertise of the firm’s leadership or its office space (assuming they’ve signed a lease for a fixed period of time for their current office). In the long run, all of Sweeps inputs become adjustable and so anything that is used in producing their product (labor, tools and supplies, managerial expertise, office space, etc.) would be part of the list of long-run inputs.

3.3

3.4 When the amount of labor used is reduced from 4 to 3, the amount of capital must be increased in order to stay on the 20 unit isoquant. At L = 3, there is not a specific value given for output = 20, with K = 1 output is equal to 17 and with K = 2 output is equal to 24. A value of K between 1 and 2 (maybe 1.5 or so) should produce output = 20 .

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when L = 3. If L is reduced by one more unit to L = 2, then Table 5.2 (and the corresponding isoquant) shows that K = 2 will produce 20 units of output.

3.5 a.The isoquants are right angles as the firm must have one disk and one hour of recording time (capital) to make a recording. Increasing one input without increasing the other results in no increase in output. b. The MRTS is 0 along the horizontal portion of an isoquant and is negative infinity along the vertical portion. It is undefined at the corner point. c. If labor is less than capital, then the total product curve is increasing in the labor input up to point where labor equals capital, after which it is constant. The average product of labor is positive and constant if labor is less than capital and declining if labor exceeds capital. The marginal product of labor is one if labor is less than capital and drops to zero if labor exceeds or equals capital.

3.6 a. See figure.

b. See figure. Assume the number of copy machines K is fixed at 1. Then production function is Q = 1000 * min(L, 3). For L  3, Q = 1000L; for L > 3, Q = 3000.

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3.7

This question continues the discussion from Question 3.3. In that question, we added a third technology (the Assisted Truck) that lay between the Self-Driving Truck technology and the Traditional Truck technology. What we saw in that case was that the isoquant developed another kink. In this diagram, we add in two more intermediate technologies at Point A and Point B and add in two more kinks. As we consider more and more intermediate technologies, more and more kinks will be added to the diagram and the curve will start to approximate a smooth line.

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3.8 The isoquants are straight lines. The marginal product of B is one. If we put B on vertical axis, the MRTS (the slope of the isoquant) is −½.

3.9

We know that the marginal rate of technical substitution is MRTS  MPL / MPK  23 .

3.10 The production function is q = 10L0.5K0.5. The marginal product of labor is ∂q/∂L = (0.5)(10)L-0.5K0.5. At L = 16 and K = 25, the marginal product is (0.5)(10)(5)/4 = 6.25. The marginal product of capital is ∂q/∂K = 0.5(10)L0.5K-0.5 = 0.5(10)(4)/5 = 4.0.

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output become smaller (diminish). To exhibit diminishing returns to labor, labor must increase by more than 1 unit, holding capital constant, to increase production from 1 to 2. Similarly, to exhibit diminishing returns to capital, capital must increase by more than 1 unit, holding labor constant, to increase production from 1 to 2.

4.6 For Cobb-Douglas production function 𝑸 = 𝑨𝑳𝒂 𝑲𝒃 , there is constant returns to scale when 𝑎 + 𝑏 = 1, increasing returns to scale when 𝑎 + 𝑏 > 1, and decreasing returns to scale when 𝑎 + 𝑏 < 1. In addition, we know that 𝑀𝑃𝐿 = 𝑎𝐴𝐿𝑎−1 𝐾 𝑏 and 𝑀𝑃𝐾 = 𝑏𝐴𝐿𝑎 𝐾 𝑏−1 .

In this case, the Crocs production function is 𝑞 = 22.7𝐿0.88 𝐾 0.48. This production function exhibits increasing returns to scale since 0.88 + 0.48 = 1.36 > 1 and diminishing marginal productivity for both L and K since 𝑀𝑃𝐿 = 19.976𝐿−0.12 𝐾 0.48 and 𝑀𝑃𝐾 = 10.896𝐿0.88 𝐾 −0.52 .

4.7 We can determine returns to scale for Cobb-Douglas production functions by adding the exponents. If the sum exceeds one, there are increasing returns to scale. If the sum equals one, there are constant returns; if the sum is less than one, there are decreasing returns. In this case, Crocs production has increasing returns to scale, U.S. housing has constant returns to scale, and U.K. supermarkets have almost constant but slightly decreasing returns to scale.

4.8 The first worker increases output by 25 and the second by 10. That is, the marginal productivity of the first worker is 25, and the marginal productivity of the second worker is 10. This is an illustration of diminishing marginal returns to labor. This diminishing return to extra labor may be due to too many workers sharing too few machines or to crowding. It is possible (but unknown) that adding a second kiln and more materials along with the second worker would double the output to 50, or constant returns to scale.

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4.9 We do not have enough information to determine which company is more productive, as Firm 1 may use more capital input than Firm 2. If that is the case, it is possible that with the same capital/labor mix as Firm 2, Firm 1 would produce less than Firm 2.

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INNOVATION 5.1 The replacement of floppy disks by USB drive is an example of a product innovation (something new has been created). The flatter organizational structures that have become popular are an example of an organizational innovation (a change in the way the firm is structured). Finally, the increase in oil production due to fracking is a process innovation (a new way of producing and existing product).

5.2 The marginal product of labor of Firm 1 is only 90 percent of the marginal product of labor of Firm 2 for a particular level of inputs. Using calculus, we find that the MPL of Firm 1 is 1q1/L = 0.9f(L, K)/L = 0.92q2/L. 5.3 In the short run, the marginal product of the first few workers will be greater, as they are now able to produce more than they could with the old machine on a per-person basis. However, given that the number of workers needed to correctly operate the machine has been reduced, marginal labor productivity will fall sooner than with the old machine. In order to determine the precise changes in the shapes of the curves, more information is needed about how much labor is saved and how much more each worker can produce. This is partly dependent on the technology (i.e., how the workers interact with the machine). Returns to scale will also depend on the technology.

5.4 The technological progress is not neutral. Because of the technology progress, less labor was required to spin the same amount of cotton in order to produce the same amount of product.

5.5 Given the production function 𝑞 = 10𝐿 + 12𝐾, we know that that marginal product of 𝜕𝑞 labor is 𝑀𝑃𝐿 = 𝜕𝐿 = 10. The change the firm makes doubles the marginal product of labor (to 20) but does not affect capital. The new production function is 𝑞 ′ = 20𝐿 + 12𝐾.

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MANAGERIAL PROBLEM 6.1 The marginal product of labor will increase if the firm experiences falling output and reduces its work force. If the work force remained constant and less output were produced, marginal product would fall.

6.2 Not enough information is given to answer this question. If we assume that Japanese and American firms have identical production functions and produce using the same ratio of factors during good times, Japanese firms will have a lower average product of labor during recessions because they are less likely to lay off workers. However, it is not clear how Japanese and American firms expand output during good times (do they hire the same number of extra workers?). As a result, we cannot predict which country has the higher average product of labor.

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SPREADSHEET EXERCISES Solutions Available on MyLab Economics

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CHAPTER 6 COSTS SOLUTIONS TO END-OF-CHAPTER QUESTIONS

THE NATURE OF COSTS

1.1

The ships that return to Asia are half or completely empty; therefore, the cost of having more merchandise in them is almost zero. Hence, it is less expensive to ship wine to Asia.

1.2

Ming receives $225 of consumer surplus if he attends the Seahawks game and $175 of consumer surplus from going to the museum. His opportunity cost of going to the museum is the $225 he would give up by not attending the Seahawks game.

1.3

a. The incremental cost is the marginal cost to a corporation of an additional flight. Some of these marginal costs are the costs of fuel, flight attendants (if they are paid for each flight), landing and taking off fees, etc. b. The marginal opportunity cost of an executive’s flight is the price the company could have earned from leasing the jet to someone else.

1.4

The opportunity cost of a resource is the value of the next best alternative use of that resource. Thus, the opportunity cost of the pipe is $10 because that is the amount that it could otherwise be sold for. A sunk cost is a past expenditure that cannot be recovered. The pipe’s sunk cost is $9 because this the original cost of the pipe, but this amount cannot be recovered.

1.5

How you react to the snowstorm and your chance to attend the big hockey game depends, in part, on how you treat the underlying cost of attending. If you are a rational decision maker who more or less behaves as the standard economic model suggests, then the cost of the ticket (whether it was free or you paid your hard earn dollars for it) should not matter at all when it comes time to decide whether or not to brave the storm. The cost (or not) of the ticket is sunk at the time you need to decide. Many other costs, however, are not sunk at this point. Getting to the game will require both time and money and, given the weather, likely a bit of stress as well. The rational decision making process is to compare your projected benefit of attending the game against these non-sunk costs and to go for it if the expected benefits exceed the expected costs and to stay home if they do not. That said, there is plenty of evidence that people fall prey to what’s known as the sunk cost fallacy in which they do not appropriately ignore costs that cannot be changed. For someone susceptible to this line of thinking, a free ticket is a very different thing from one that was purchased. Many people will push on through the snowstorm to use the purchased ticket but stay home if it was free.

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SHORT-RUN COSTS 2.1

Nicolas’ average fixed cost is given by AFC = $8/q. The diagram will show a constantly and smoothly declining function (similar to the one in the solution to 2.3 below). His friend’s reasoning is incorrect in two ways. First, it fails to account for other costs associated with listening to music (like the opportunity cost which might be the value of getting homework done, going to the movies, or some other activity). His friend also fails to account for the benefit side of the decision. As Nicolas listens to more and more music, it is likely that the benefit he receives from listening to another song will decline.

2.2

If heavy equipment like a bulldozer becomes widely available in the rental market, then the companies like Platinum Pipeline will be swapping some of what used to be fixed cost for more variable cost. As noted in the mini-case this will allow long run planning much earlier than previously possible since some major expenses can be toggled on and off more frequently and easily.

2.3

C = VC + F; AC = AVC + AF = VC/q + F/q. By shopping online a consumer can lower the fixed cost F, thus also lowering the average cost, AC. This assumes, however, that there are no additional costs associated with searching online. A quick trip to the internet suggests that this is definitely not the case as finding accurate information on a variety of products can be difficult and time consuming. If a consumer knows exactly what they want then shopping online can be less costly because the search costs are lower. If, on the other hand, browsing is required (or even enjoyable), then the consumer may well find it less costly to visit a physical store where they can view a large variety of products.

2.4

a. AFC = 10/q.MC = 10. AVC = 10.AC = 10/q  10.

b. AFC = 10/q. MC = 2q. AVC = q. AC = 10/q  q. See the figure below.

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c. AFC = 10/q. MC = 10  8q  3q2q2. AVC = 10  4q  2q2. AC = 10/q  10  4q  2q2.

See the figure below.

2.5

TC = 900 + 5q, AFC = 900/q, AVC = 5, ATC = 900/q + 5, MC = 5. a. The graphs are produced in the audio-PowerPoint presentation. b. Note that ATC becomes smaller as the production increases, so there is an advantage to having only one big music publisher. This is because the fixed cost is spread over a larger production, although the MC is constant and equal to 5. c. Revenue – publishing cost = 300  15 – (900 + 5  300) = 4,500 – 2,400 = 2,100. The publisher is willing to pay up to 2,100 pfennigs to the composer.

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2.6 C  q, MC  AVC  AC  1 for q less than or equal to 80 per day. C  80  1.5 (q  80)  1.5q  40, MC  1.5, AVC  AC  1.5 40/q for all q greater than 80 per day. See figures below.

2.7 The total cost of building a 1-cubic-foot crate is $6. It costs four times as much to build an 8-cubicfoot crate, $24. In general, as the height of a cube increases, the total cost of building it rises with the square of the height, but the volume increases with the cube of the height. Thus the cost per unit of volume falls.

2.8

See figure below. Suppose L is measured in person-hours (number of workers times the hours they work), then the production function is Q = 4L. Then VC = 8L = 8(Q/4) = 2Q. Then AVC = MC = 2.

2.9

If the rental rate for capital is 𝑟 = $40 and capital is fixed at 100 units, then fixed costs are $4000 and average fixed costs are 𝐴𝐹𝐶 = $4000⁄𝑞 . In addition, since capital is fixed at 100 units the production function reduces to 𝑞 = 2𝐿0.5 × 10 = 20𝐿0.5. To find the firm’s variable cost we solve this expression for L. This gives us 𝑞 = 20√𝐿 or (squaring both 𝑞2 sides) 𝑞 2 = 400𝐿 which implies 𝐿 = ⁄400. Furthermore, we know that labor is priced at $20 per unit, so variable cost of producing q units is 𝑉𝐶(𝑞) = 20 ∗ 𝐿 or 𝑉𝐶(𝑞) = 𝑞2 𝑞2 20 ( ⁄400) which reduces to 𝑉𝐶(𝑞) = ⁄20. We can use this expression to calculate

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AVC and MC as follows. 𝐴𝑉𝐶(𝑞) =

𝑉𝐶(𝑞) 𝑞

𝑞

= 20 and 𝑀𝐶(𝑞) =

𝑑𝑉𝐶(𝑞) 𝑑𝑞

𝑞

= 10. We can

diagram these cost curves as follows:

2.10 Given these two cost functions, we know: a) The average cost of plant 1 is 𝐴𝐶1 = 10 − 4𝑞 + 𝑞 2 and at plant 2 𝐴𝐶2 = 10 − 2𝑞 + 𝑞 2 . We can find the point at which each AC is minimized by taking the derivative of the AC function, setting it equal to zero, and solving for q. In the first case this yields 𝑑𝐴𝐶 𝑑𝐴𝐶 = −4 + 2𝑞 = 0 which implies q=2. In the second case = −2 + 2𝑞 = 0 which 𝑑𝑞

𝑑𝑞

implies q=1. b) To minimize its cost, the firm should produce the four units such that the marginal cost in each plant is the same. If this were not true then the firm could shift some production at the margin from the high MC plant to the low MC plant. In this case the two marginal cost functions are 𝑀𝐶1 = 10 − 8𝑞1 + 3𝑞12 and 𝑀𝐶2 = 10 − 4𝑞2 + 3𝑞22 and we require two conditions to hold simultaneously. First 𝑀𝐶1 = 𝑀𝐶2 and 𝑞1 + 𝑞2 = 4.

If we rearrange the second expression we get 𝑞1 = 4 − 𝑞2 which we can substitute into the first equation to get 10 − 8(4 − 𝑞2 ) + 3(4 − 𝑞2 )2 = 10 − 4𝑞2 + 3𝑞22 . This expression can be simplified to 3(4 − 𝑞2 )2 − 8(4 − 𝑞2 ) = 3𝑞22 − 4𝑞2 which, with a bit of work, yields 𝑞𝑞2 = 1.33 and, therefore, 𝑞𝑞1 = 2.67. .

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LONG-RUN COSTS 3.1

a. See panel (a) of the following figure. b. See panel (a) of the figure. The firm chooses labor-machine technology. c. See panel (b) of the figure.

3.2

If the firm were minimizing its cost, the extra output it gets from the last dollar spent on labor, MPL / w  50/200  0.25, should equal the extra output it derives from the last dollar spent on capital, MPK /r  200/1,000  0.2. Thus, the firm is not minimizing its costs. It would do better if it used relatively less capital and more labor, from which it gets more extra output from the last dollar spent.

3.3

The price of labor (w) is now 25 percent cheaper. Assuming that the price of capital (r) does not change and remains the same, the isocost faced by producers becomes less steep (–w/r before the subsidy as compared to –0.75w/r after the subsidy). Assuming a strictly convex technology, at the optimum, the producer will use less of both workers and capital than before for the same output. However, since labor is now cheaper relative to capital (relatively cheaper), the firm will now employ relatively more labor than capital.

3.4

From the information given and assuming that there are no economies of scale in shipping baseballs, it appears that balls are produced using a constant return to scale, fixedproportion production function. The corresponding cost function is C(q) = (w + s + m)q, where w is the wage for the time period it takes to stitch one ball, s is the cost of shipping one ball, and m is the price of all material to produce a ball. Because the cost of all inputs other than labor and transportation are the same everywhere, the cost difference between Georgia and Costa Rica depends on w + s in both locations. As firms choose to produce in Costa Rica, the extra shipping cost must be less than the labor savings in Costa Rica.

3.5

Since the two flavorings are perfect substitutes, we can draw a linear isoquant. Assuming the alcohol-based flavoring produces more flavor per ounce than the nonalcoholic flavoring (we can use less of it), we draw our isoquant with a | MRTS| >1. If the cost of each flavoring is equal, the isocost curve has a slope of –1, and the producer will buy only the alcohol-based flavoring. After the tax, the alcohol-based flavoring will be so much more .

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expensive that the new isocost curve’s slope will likely have an absolute value greater than the | MRTS|, causing the producer to buy only nonalcoholic flavoring.

3.6

Firms will maximize profit by producing where the ratio of the marginal product of labor to the marginal product of capital is equal to the ratio of the input prices: MPL w  .

MPK r The ratio of marginal products equals MPL 0.5L0.5 K 0.5 K   .

MPK 0.5L0.5 K 0.5 L In the United States, the ratio of input prices equals 1, so when producing optimally K 1 L

K = L. To produce 100 units of output in the United States, 100 = L0.5L0.5 L = 100 and K = 100.

The cost of producing 100 units of output in the United States is C = 10(100) + 10(100) = 2,000.

In Mexico, the ratio of input prices equals 0.5, so when producing optimally

2K = L. To produce 100 units of output in Mexico, 100 = (2K)0.5(K)0.5 100 = 1.41K .

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K = 70.71 and L = 141.42.

The cost of producing 100 units of output in Mexico is C = 5(141.42) + 10(70.71) = $1,414.21.

3.7

The cost function for Google is C = F + cq. The marginal cost in this case is constant and equal to c (if you know calculus, this can be found by taking the derivative of the cost function). Average cost can be found by dividing the cost function by q, which gives AC = (F/q) + c. In addition, average variable cost and average fixed cost can be found as the two parts of the average cost equation (specifically AFC = F/q and AVC = c. Google enjoys economies of scale as long as the AC curve is falling. Since this AC function is always declining, Google will enjoy economies of scale anytime it increases output.

3.8

If it takes two units of labor (at a wage of w per unit) and one unit of labor (at a price of r per unit) in a fixed proportion to produce a unit of the good, then the cost associated with producing one unit will be 2w + r and the cost of producing q units will be (2w + r)q. In the case of two inputs that are prefect substitutes with identical marginal productivities (as implied by the q = L + K production function), then the firm will simply use which ever input is cheapest and its cost will be the price of that input multiplied by the number of units produced. For example, if labor is cheaper than capital, then the total cost of production will be C = wq.

3.9

The comment from Mr. Moody is based on economics of scale. He states that by making wine in large (700,000 gallon) vs. small (700 gallon) tanks that there is less cost on per unit basis (because it’s easier to control exposure to air). The comment form Mr. Wallace, on the other hand, focuses on choosing the right combination of inputs – using machines keeps labor costs low, but also introduces possible errors. Finding the right balance is key.

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THE LEARNING CURVE 4.1

Learning by doing is where the productive skills and knowledge that workers and managers gain from experience lowers the average cost of production. Workers who are given a new task perform it slowly the first few times they try, but their speed increases with practice.

Managers may learn how to organize production more efficiently, discover which workers to assign to which tasks, and determine where more inventories are needed and where they can be reduced. Engineers may optimize product designs by experimenting with various production methods. For these reasons, the average cost of production tends to fall over time, and the effect is particularly strong with new products.

4.2

A firm’s learning curve, which shows the relationship between average cost and cumulative output (the sum of its output since the firm started producing), is AC  a  bN r , where AC is its average cost; N is its cumulative output; and a, b, and r are constants.

If r = 0, then AC = a + b. If r = 0, then average cost does not fall with cumulative output (average cost remains constant with cumulative output), so there is no learning by doing.

If average cost decreases with output, then r < 0, which is a characteristic of learning by doing.If N = 0, then AC = a.

Therefore, a represents the average cost of production before any learning by doing.

4.3

a. The total cost is $20 per unit multiplied by 50 units in year 1 (total of $1000) and $40 per unit multiplied by 40 units in year two ($1600) for total over the two years of $2600. There are 60 units produced in total so AC = $2600 / 60 = $43.33. b. If the firm produces 60 units in year 1, then their average cost in year two will fall by $20 to $30 (10% or $5 decline for every 10 units over 20 produced in year 1). This means that total cost in the first year is 60 units times $50 (or $3000). In year 2 the additional 40 units are produced at only $30 each (so $1200). This is a total cost of $4200 and an average cost of $4200 / 100 = $42. c. The cost of the additional 40 units in year 1 is only $1680 on average because of the lower costs in year 2.

4.4

The question asks whether or not AC falls with additional experience (N). To determine if this is true, we can take the derivative of the AC function and determine it’s sign. If it is positive then the answer is ‘no’ to learning-by-doing, but if it is negative then learning-bydoing is present. In this case the average cost is 𝐴𝐶 = 𝑎 + 𝑏𝑁 −𝑟 and 𝑑𝐴𝐶⁄𝑑𝑁 = −𝑟𝑏𝑁 −𝑟−1 which does, in fact, have a negative sign for positive values of r and b. This shows that learning by doing is present in this example.

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THE COSTS OF PRODUCING MULTIPLE GOODS 5.1

Referring to Figure 6.7 in the chapter, a restriction on the size of a store might restrict output to the left of the minimum point in the long-run cost curve, q2. (This is likely because stores in other countries are larger than in the United Kingdom.) Thus, in the longrun the stores will not be able to take advantage of economies of scale and economies of scope to lower average fixed costs and total average costs of carrying a large amount of any single item, or a wider range of items.

5.2

Economies of scope is the situation in which it is less expensive to produce goods jointly than separately. Diseconomies of scope is the situation in which it is less expensive to produce goods separately than jointly. A measure of the degree to which there are economies of scope is C(q1 ,0)  C(0, q2 )  C(q1 , q2 ) SC = , C(q1 , q2 ) where C(q1,0) is the cost of producing q1 units of the first good by itself, C(0,q2) is the cost of producing q2 units of the second good by itself, and C(q1,q2) is the cost of producing both goods together. If the cost of producing the two goods separately is the same as producing them together, then SC is zero. If it is cheaper to produce the goods jointly, SC is positive. If SC is negative, there are diseconomies of scope, and the two goods should be produced separately. In this example, SC is positive, so Conner experiences economies of scope.

5.3

Economies of scope is the situation in which it is less expensive to produce goods jointly than separately. Diseconomies of scope is the situation in which it is less expensive to produce goods separately than jointly. A measure of the degree to which there are economies of scope is C(q1 ,0)  C(0, q2 )  C(q1 , q2 ) SC = , C(q1 , q2 ) where C(q1,0) is the cost of producing q1 units of the first good by itself, C(0,q2) is the cost of producing q2 units of the second good by itself, and C(q1,q2) is the cost of producing both goods together. If the cost of producing the two goods separately is the same as producing them together, then SC is 0. If it is cheaper to produce the goods jointly, SC is positive. If SC is negative, there are diseconomies of scope, and the two goods should be produced separately.

For example, if a firm produces fuel and heating oil in fixed proportions, then it does not produce heating fuel without producing gasoline (or, alternatively, it does not cost any extra to also produce gasoline when producing heating fuel). Similarly, the firm does not produce gasoline without producing heating fuel (or it does not cost any extra to also produce heating fuel when producing gasoline). Therefore, the firm’s measure of economies of scope is positive and equal to 1 because C(q1,0) = C(0,q2) = C(q1,q2).

5.4

The Freeman et al. (2018) paper cited in the mini-case is most relevant here. That paper shows significant diseconomies of scope between emergency and non-emergency services. .

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This implies that regularly scheduled surgeries (non-emergency) and emergency services will be more costly when provided together than when provided separately. This argues for separate facilities for these two types of medical services.

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MANAGERIAL PROBLEM 6.1

An isocost line shows all the combinations of inputs that require the same total expenditure. For the firm to be indifferent between using the wafer-handling stepper technology and the stepper technology, the isocost line must pass through the input combinations for both technologies, as shown by isocost line C4.

The slopes of the isocost lines equal the wage divided by the price of capital (multiplied by minus one). Since isocost line C4 is flatter than isocost line C2, the absolute value of the wage-cost of capital ratio on isocost line C4 is less than that ratio on isocost line C2. Since isocost line C4 is steeper than isocost line C3, the absolute value of the wage-cost of capital ratio on isocost line C4 is greater that ratio on isocost line C3.

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SPREADSHEET EXERCISES Solutions available on MyLab Economics

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CHAPTER 7 FIRM ORGANIZATION AND MARKET STRUCTURE SOLUTIONS TO END-OF-CHAPTER QUESTIONS

OWNERSHIP AND GOVERNANCE OF FIRMS

1.1

In the private sector, there are three main types of organizations: the sole proprietorship, the partnership, and the corporation (which is owned by shareholders). The private sector is sometimes referred to as the for-profit sector.

The nonprofit sector consists of organizations that are neither government-owned nor intended to earn a profit, but typically pursue social or public interest objectives.

1.2

A publicly traded corporation is a corporation whose shares can be readily bought and sold by the general public. The shares of most publicly traded corporations trade on major organized stock exchanges, such as the New York Stock Exchange (NYSE). In making the transition from privately held to publicly traded status, a closely held firm will make an initial public offering (or IPO) of its shares on an organized stock exchange.

The initial public offering (or IPO) is a way to raise money for the firm. This ability to raise money by issuing stock is one major advantage of going public. In addition, the owners of a corporation are not personally liable for the firm’s debts; they have limited liability. However, a major disadvantage from the point of view of the original owners is that ownership of the firm becomes broadly distributed, possibly causing the original owners to lose control of the firm.

1.3

Traditionally, the owners of sole proprietorships and partnerships were fully liable, individually and collectively, for any debts of the firm. In contrast, the owners of a corporation are not personally liable for the firm’s debts; they have limited liability: the personal assets of the corporate owners cannot be taken to pay a corporation’s debts even if it goes into bankruptcy.

1.4

Yes, today only 5% of firms are owned by the government in China. However, it should be noted that this relatively small number of state-owned firms still controls 40% of assets so the small number of firms still under state control does not tell the whole story.

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PROFIT MAXIMIZATION 2.1

Joshua is correct. A firm’s marginal costs are always avoidable: the firm only pays the variable costs such as marginal costs if it operates. In contrast, the firm’s short-run fixed cost is usually unavoidable: the firm incurs the fixed cost whether or not it shuts down.

Therefore, the firm should ignore the plant’s fixed cost. Instead, it should move production to the plant to avoid paying the higher marginal cost at the other plants.

2.2

A firm sets its output where its marginal profit is zero: Marginal profit(q) = MR(q) − MC(q) = 0, where MR is marginal revenue and MC is marginal cost. Marginal revenue is MR = 100 − 6q.

Marginal cost is MC = 10.

Therefore, the firm maximizes profit by producing MR(q) − MC(q) = 0 MR(q) = MC(q) 100 − 6q = 10 90 = 6q q = 15 units.

Profit equals revenue, R(q), minus the cost of production, C(q): Profit = R(q) − C(q) Profit = 100(15) − 3(15)2 − 100 − 10(15) Profit = $1,925.

2.3

Economic profit is business profits (revenue minus explicit costs) minus the excess profits that could be realized from alternative uses of the company’s resources (implicit cost).

Even if a company is making a negative economic profit, it may continue to produce as long as it is making positive business profits. However, it should move to the alternative use, which will mean making a positive economic profit and more business profit.

2.4

Only $200 of the fixed cost is sunk. The firm should shut down if its revenue is less than the avoidable cost. Avoidable cost in this case is $1,100 and revenue is $1,000. As revenue is less than the avoidable cost, the firm should shut down. Shutdown rule 1: The firm shuts down only if it can reduce its loss by doing so.

2.5

A firm sets its output where its marginal profit is zero. With a 25 percent tax on revenue, this is where Marginal profit(q) = (1 − 0.25)MR(q) − MC(q) = 0, where MR is marginal revenue and MC is marginal cost.

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2.6

No, not at all. Support of the Ronald McDonald House, in addition to providing many benefits to the families that use the facility, also serves to show community involvement on the part of McDonald’s. If customers (and potential customers) value this involvement, then it will help increase visits and sales to McDonald’s restaurants and thereby increase firm profit.

2.7

According to his stakeholder theory, managers have obligations to several groups in addition to shareholders, including workers, customers, and the communities in which firms reside and operate. For example, stakeholder theory suggests that corporations should not use child labor in poor countries; they should provide safe working conditions and safe products; and they should not contaminate communities where they operate with toxic waste, even if such corporate policies reduce profit.

2.8

Yes, it is possible that efforts by managers to address social responsibility (ESG activities) may increase profits. ESG activities intended to raise profit are referred to as strategic ESG. For example, it is possible that ending or reducing workplace harassment could increase productivity. It is also possible that ESG activities could enhance the brand image of a firm’s products, as with TOMS shoes or Ronald McDonald houses.

2.9

Managers can be disciplined through the market for corporate control, where outside investors use the stock market, buying enough shares to take over control of an underperforming publicly traded firm. There is a profit opportunity to seize control of a company where the current managers are doing a poor job, undertaking unprofitable projects and spending money on their own comfort and compensation, with little profit going to the shareholders in the form of dividends or capital gains. If the acquiring firm can convince enough shareholders that profit will rise after a takeover, the shareholders can vote out the existing board and management and vote in the one the acquiring firm recommends.

2.10 Many corporate managers, in the face of a hostile takeover, will construct a takeover defense. Common defenses include a shareholder rights plan, which is better known as a poison pill. A poison pill is a provision that a corporate board adds to its bylaws or charter that makes the firm a less attractive takeover target. That is, poison pills are designed to combat hostile takeovers with pyrrhic activity, where the firm damages itself, and stockholders, to make it a less attractive takeover target. For example, in the face of a hostile takeover, Yahoo’s management created a huge incentive for a massive employee walkout in the aftermath of a change in control by providing generous termination benefits.

2.11 For the poison pill to make firm T unattractive, it must make firm T’s value to firm A negative (or equal to zero). Thus, the poison pill must reduce the value of firm T by at least $100 million.

Absent the poison pill, the value of firm T is $20 million more if taken over by firm A (from a value of $100 million if taken over minus a value of $80 million if not taken over).

Thus, the cost of the poison pill to shareholders of firm A and firm T is $20 million.

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OWNERS’ VERSUS MANAGERS’ OBJECTIVES 3.1

Alexx will have his initial investment of $5,000 plus 5% interest (which amounts to $250) for a total of $5,250. Another way to calculate his holdings after one year is to multiply his investment by 1 + 𝑟 where 𝑟 is the interest rate. This calculation will look like $5,000(1 + 0.05) = $5,000 ∗ 1.05 = $5,250. For Spenser, the calculation is the same except he receives a lower return because of the administrative fee. His total holdings after one year are $5,000(1 + 0.0475) = $5,000 ∗ 1.0475 = $5,237.50.

3.2

If Alexx and Spenser make the initial $5,000 investment and then let the results of that investment compound at the same rate (5% for Alexx and 4.75% for Spenser), then at the end of 30 years, Alexx will have holdings of $21,609.71, while Spenser will have $20,118.28. These results can be calculated using a spreadsheet or an online compound interest calculator. The basic idea at work with compounding is that the investor earns interest in the second year on both the principal and the interest earned in the first year. If we use Alexx as an example, we recall that his $5,000 investment gave him $5,250 at the end of the first year. In year 2, he earns another 5%, but not just on the original $5,000 (or another $250 in interest) but also interest on the $250 of interest he earned in the first year (another $12.50). His final holdings after two years will be $5,000 + $250 (year 1 interest) + $262.50 (year 2 interest) = $5,512.50. Mathematically the calculation looks like [$5,000 ∗ 1.05] ∗ 1.05 = $5,000 ∗ (1.05)2 = $5,512.50. If the compounding continues for 30 years, the calculation is $5,000 ∗ (1.05)30 = $21,609.71 for Alexx and $5,000 ∗ (1.0475)30 = $20,118.28 for Spenser. Over the 30-year horizon, the 0.25% administrative fee costs Spenser a little less than $1,500 ($1,491.43 to be precise).

3.3

These three payments of $2,000 each happen at three points in time—today (t = 0), 1 year from today (t = 1), and 2 years from today (t = 2). The payment today have a present value of $2,000. The payment in one year must be discounted since it doesn’t occur for 1 year.

2000

The present value of $2,000 in one year is given by 𝑃𝑉1 = 1.05 = $1,904.76. The payment 2000

in two years has a present value of 𝑃𝑉2 = (1.05)2 = $1,814.06. The present value of the total payment amount is $2,000 + $1904.76 + $1,814.06 = $ 5,718.82.

3.4

The investment will increase the present value of the company if the present value of the revenue it generates is greater than its cost. The cost of the investment is the opportunity cost of $800,000. That is, the firm could invest $800,000 at an interest rate of r% and receive interest of r% multiplied by $800,000 per period. This will be less than the revenue generated by the investment if 50,000 ≥ (r%)800,000 r ≤ 6.25%.

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3.5

Unfortunately, owners and managers have conflicting objectives in some firms. A manager is especially likely to pursue an objective other than profit if the manager’s compensation system rewards the manager for something other than maximizing profit. For example, if the manager can allocate reported costs to a future year, then the manager can increase reported profit this year. If shareholders care only about the value of the company in the present period, then acsoi is not an appropriate measure because marketing and acquisition expenses are marginal costs and affect profits in the current period.

3.6

The answer to this question depends in large part on how sophisticated the shareholder and potential shareholders/investors in this company are when it comes to long-run versus short-run profitability and stock prices. The standard economic model suggests that shareholders and potential shareholders are quite sophisticated and can understand that sometimes investments in the near term are costly but may yield bigger benefits down the road. In this view, the stock price should perfectly reflect the present value of all future profit streams that the firm will earn, so a costly investment today may actually raise the price of the stock in the near term if this investment will generate big increases in profit down the road. In many cases, however, shareholders and potential shareholders do not take this long-term perspective or are unable to calculate and appreciate the long-term implications. In this case, it is quite possible that an expensive investment today could depress the stock price as the concerned CEO noted.

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THE MAKE OR BUY DECISION 4.1

The present value (PV) to Campbell’s from acquiring Bolthouse Farms is the $75 million annual value of the produce plus the $10 million annual savings in searching and negotiating costs received indefinitely minus one-time current-period costs of $1.55 billion for the acquisition and $50 million in transaction costs:

75  10  1,550  50 PV = 0.05 PV = $100.

4.2

For vertical integration to be profitable, the resulting average cost of quilts must be less than $100, which is the cost (on average) of purchasing quilts from the producer. The average cost (AC) of producing quilts if vertically integrated is C AC = q

10,000  50q q AC =

10,000 q AC = + 50.

This is less than $100 when 10,000 q 100 > + 50

10,000 q 50 >

50q > 10,000 q > 200 quilts.

4.3

A firm that participates in more than one successive stage of the production or distribution of goods or services is vertically integrated. The alternative to a firm producing an input or activity itself is to buy it. Probably, the most important reason to integrate is to reduce transaction costs. Firms may also vertically integrate to avoid government price controls, taxes, and regulations. Thus, if the government begins taxing ink, then the ballpoint pen company will be more likely to vertically integrate to avoid paying taxes on ink. This will decrease its cost of production.

4.4

NetFlix undertook backward integration by producing some of the shows it offered. These shows are an input used by NetFlix. Producing its own inputs is backward integration.

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NetFlix did not undertake forward integration in the form of internet service provision.

Consumers can connect to NetFlix using any service provider they like.

The advantage of backward integration is that NetFlix could obtain unique content, be flexible in choosing when to show particular shows, and could avoid opportunistic behavior by film studios—producing a reliable supply of content instead of having to bargain with traditional studio for each new show or new season. These three advantages allowed NetFlix to enhance consumer loyalty. NetFlix saw no advantage to forward integration as it preferred to allow as wide access to its service as possible by working with a wide range of internet service providers.

4.5

The gig economy has reduced the extent of vertical integration. Instead of hiring permanent employees, large firms such as FedEx and UPS contract out much their work to independent contractors. These independent contractors are separate firms, not regular employees. Therefore, instead of providing inputs such as driver services internally, firms purchase those inputs from independent contractors.

4.6

Adam Smith, writing in Scotland at the time of the American Revolution, gave an example of a pin factory to illustrate how the division of labor can have important advantages in manufacturing. In particular, he showed that workers commonly engage in highly specialized activities to more efficiently divide production processes into several small steps. However, the division of labor is limited by the extent of the market. That is, a firm can take advantage of specialization and economies of scale only if it produces a sufficiently large amount of output, which it produces only if there are enough consumers willing to buy it. When an industry is small, it does not pay for a firm to specialize. As the industry grows, firms vertically disintegrate (specialize). This has happened in the market for education over time. Teachers are becoming increasingly likely to teach only one subject to one grade to specialize as the market for education has become larger.

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MARKET STRUCTURE 5.1

A competitive market structure is one in which many firms produce identical products and firms can easily enter and exit the market. Because each firm produces a small share of the total market output and its product is identical to that of other firms, each firm is a price taker, meaning that the firm cannot raise its price above the market price. A monopoly is the only supplier of a good for which there is no close substitutes. An oligopoly is a market with only a few firms and with substantial barriers to entry. Because relatively few firms compete in such a market, each can influence the price, and hence, each affects rival firms.

Monopolistic competition is a market structure in which firms have market power (the ability to raise price profitably above marginal cost), but no additional firm can enter and earn positive profits. Monopolistically competitive firms sell products differentiated, often by brand.

Airline manufacturing is an oligopoly because there are only a few airline manufacturers, and airline manufacturing has entry barriers.

The market for electrical work in a small town is monopolistically competitive because electrical work may be differentiated and individual electricians have some ability to set price, particularly in a small town.

The market for cable television in a city is a monopoly because there is only one cable supplier. Further, barriers to entry prevent new suppliers from competing.

The market for tomatoes is perfectly competitive because there are many tomato farmers selling a homogeneous product. None of the tomato farmers has any market power, and tomato farmers may enter and exit the market easily.

5.2

It is safe to say that the growth of the Internet has substantially increased the degree of competitiveness in many markets and has made the study of perfect competition more relevant over time. The availability of product and price information has increased dramatically and, for the most part, search costs have declined. This is not to say that searches are always easy online or that there are no additional new costs associated with this way of doing business (shipping, not being able to see an item in person, etc.), but the overall effect has almost certainly been to increase competition.

5.3

Mini-mills had the effect of eliminating the scale economies previously associated with steel production. We should expect that this would allow smaller scale steel firms to exist alongside larger firms and would increase competition in the industry. This development might even provide opportunities for other innovations to impact the industry since they could be tried at a smaller scale (and lower cost) with no scale penalty relative to larger producers. This would further increase the competitive pressure in steel industry.

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MANAGERIAL PROBLEM 6.1

Amazon’s new venture requires a large, up-front investment that may even be large enough to cause total profits to be negative in the year the investment is made. The payoff comes in year 2 when profits are higher than they would have been without the initiative. The text gives the following generic description of this tradeoff. Let 𝜋1 be profit in year 1 and 𝜋2 be profit in year 2. It is likely that 𝜋1 < 0 and 𝜋2 > 0. The present value of the loss in year 1 is just 𝜋1 , but in year 2, the profit value must be discounted to allow us to make an applesto-apples comparison today of the costs and benefits of the plan. The present value of 𝜋2 is 𝜋 𝜋 𝑃𝑉 = 2 . The total return is 𝜋1 + 2 . As interest rates rise, the discounted profit in year 2 1+𝑟

1+𝑟

decreases which means that the cost (negative profit) in year 1 is harder to overcome. This makes the investment less attractive as it effectively amplifies the negative effects of the loss in year 1 and dampens the benefits of the gain in year 2.

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SPREADSHEET EXERCISES Solutions available on MyLab Economics

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CHAPTER 8 COMPETITIVE FIRMS AND MARKETS SOLUTIONS TO END-OF-CHAPTER QUESTIONS

PERFECT COMPETITION 1.1

A market is considered to be perfectly competitive if consumers believe that all firms in the market sell identical products, if firms freely enter and exit the market, if buyers and sellers know the prices charged by firms, and if transaction costs are low. The characteristics of this market that are consistent with perfect competition are that there are lots of coffee shops and that new shops have historically entered the industry freely. The characteristics of the market that are not consistent with perfect competition are the cap on the number of licenses which acts as an entry barrier and the fact that all coffee is not identical.

Economists say that a market is competitive if each firm in the market is a price taker: a firm that cannot significantly affect the market price for its output or the prices at which it buys its inputs. Such a firm has a horizontal demand curve. The coffee shop market is unlikely to be nearly perfectly competitive because the cap on licenses will limit the number of shops in the future which will provide existing shops with more price-setting power. In addition, each shop likely sells differentiated coffee, so it may have the ability to affect the prices it charges due to brand loyalty as well.

1.2

If buyers know the prices that other firms charges—the market price—a firm cannot raise its price without losing its customers. In contrast, if consumers do not know the prices that other firms charge, a firm can charge more than other firms without losing all its customers, so its demand curve is downward sloping. Similarly, if transaction costs are low, it is easy for a customer to buy from a rival firm if the customer’s usual supplier raises its price. With high transaction costs, a firm can charge more than other firms without losing all its customers.

1.3

The characteristics of perfect competition include many small buyers and sellers, identical products, full information about price and product characteristics, negligible transaction costs and, in the long run, free entry and exit. These conditions lead to price taking behavior by buyers and sellers. Agriculture comes closest to having these characteristics.

For most agricultural products, there are many producers of nearly identical products, information about prices and products is readily available, transaction costs are low, and entry and exit are easy. Individual buyers and sellers are normally price takers. Aircraft manufacturing and social media are both dominated by a small number of firms each of which can raise its prices without losing all its customers.

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COMPETITION IN THE SHORT RUN 2.1

The logic behind the first claim is that the firm chooses not to charge the full price of one of the inputs, the rent on its land. Just because the firm owns the land outright does not mean that it should ignore the opportunity cost of using the land to run its business. A full accounting of the firm’s economic profit would count the market value of the rent on the land as a cost. Ignoring this cost provides the logic for the second claim: that since it is charging itself a lower price for one of the inputs (rent/land), then it can offer output price at a lower price. This may be true, but it is likely also true that such behavior is not optimal.

2.2

Suppose that a U-shaped marginal cost curve cuts a competitive firm’s demand curve (price line) from above at q1 and from below at q2. By increasing output to q1 + 1, the firm earns extra profit because the last unit sells for price p, which is greater than the marginal cost of that last unit. Indeed, the price exceeds the marginal cost of all units between q1 and q2, so it is more profitable to produce q2 than q1. Thus, the firm should either produce q2 or shut down (if it is making a loss at q2). We can also derive this result using calculus. The second-order condition, Equation 8.3, for a competitive firm requires that marginal cost cut the demand line from below at q*, the profit-maximizing quantity: dMC(q*)/dq > 0.

2.3

A firm should shut down only if it can reduce its loss by doing so. A firm cannot reduce its loss by shutting down if revenue is greater than the avoidable cost of production (or, in a competitive market, if price is greater than the average variable cost of production).

Initially, the firm should not shut down because marginal revenue or price, which is $50, is greater than average variable cost, which is $42.

If average variable cost increases by $9 at every unit, then average cost increases by $9 at every unit as well. Now the firm should shut down because the price of $50 is less than the average variable cost of $51.

2.4

A firm shuts down only if it can reduce its loss by doing so. That is, the firm shuts down only if its revenue is less than its avoidable variable cost. This is because if the firm shuts down, it does not incur the variable cost, so its only loss is its unavoidable fixed cost.

In the first case, revenue is greater than variable cost, so the firm should not shut down to minimize losses.

In the second case, revenue is less than variable cost, so the firm should shut down to minimize losses.

In the third case, avoidable costs are $1,900 (VC + avoidable FC), which are greater than revenue, so the firm should shut down.

2.5

The firm’s profit is π = pq − (10 + 10q + q2).

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2.9

The lower of average minimum variable cost will extend the firm’s supply curve downward. As a result, the market supply curve shifts rightward.

2.10 a. See the figure below. The firm’s supply curve shifts leftward due to the storm as average costs increase. As a result, the market supply curve shifts leftward as well.

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b. We can assume TomatoFest chose to operate optimally by growing tomatoes garnering economic profit before the storm. If TomatoFest had been able to make a higher profit from an alternative use of its land in the case of there being a storm, it would be making negative economic profit. However, it is likely that the storm affected all uses of land, and TomatoFest’s land use is still the most economically profitable.

2.11 a. Assuming that the average cost and marginal cost all have a U-shape, a firm’s marginal and average costs are likely to rise with extra business, at least in the short term. b. As shown in the figure below, because the increased demand is only seasonal, it will not affect firms’ long-run supply curve and the number of firms in the market if there is considerable entry cost. During peak demand period, firms will operate to the right of the minimum of the short-run average cost curve.

2.12 As shown in the figure below, due to the lower marginal cost, the long-run average cost curve shifts downward and firms’ supply curves shift rightward. As a result, the horizontal market supply curve shifts downward. The entire incidence (benefit) of the subsidy accrues to consumers.

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COMPETITION IN THE LONG RUN 3.1

Such a tax will not affect the marginal cost of the product because it is the “price” of a bag and the consumer can choose not to purchase one (they may bring their own bag).

However, the tax incidence will be shared by the grocers and the consumers. The amount of tax passed on to consumers will be determined by the demand elasticity of grocery bags.

3.2

The shutdown notice reduces the firm’s flexibility, which matters in an uncertain market. If conditions suddenly change, the firm may have to operate at a loss for six months before it can shut down. This potential extra expense of shutting down may discourage some firms from entering the market initially.

3.3

If the world demand curve crosses the supply curve in the flat section of the Brazil supply, there will be a unique equilibrium price and quantity, and Pakistan, Argentina, Australia, and some Brazilian firms will provide cotton. If the world demand curve crosses the supply curve in the following vertical section, all of the Brazilian firms will supply, but the price will still not be high enough for Turkey or Nicaragua to produce. In either case, farmers in the United States will not supply cotton.

3.4

The demand for generic art is represented by D. Suppose that without Chinese art, the supply of generic art is represented by S1, where Western artists must receive $W per painting to be willing to supply art. The market equilibrium is represented by point e1, where the market price is $W per painting and the equilibrium quantity is Q1.

Assume Chinese artists are willing to supply up to QC generic paintings for a price of $C per painting.

The entry of Chinese artists shifts the market supply curve out horizontally to QC at $C. The intersection of the long-run market supply and demand curves determines the long-run competitive equilibrium.

At the new market equilibrium (with Chinese artists), the market price is above the minimum amount Chinese artists must receive to be willing to supply their art but is below the minimum amount Western artists must receive to be willing to supply their art.

Therefore, in this instance, only Chinese artists supply art.

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3.5

Assume each firm uses the same size plant in the short and long run. Before the change in demand, the market will have reached a long-run equilibrium, where each firm produces Q1 at the minimum average cost, the market produces where the long-run supply curve intercepts the demand curve, and there will be N1 firms producing. When demand shifts to D2, in the short run, each firm will increase production to Q2. If the shift is expected to be permanent, in the long run, more firms will enter increasing their number to N2, each producing once again Q1. If the shift is temporary, demand will eventually shift back down, and the number of firms and quantity will revert to the original levels.

3.6

One reason that firms increase the price of coffee only 14 percent may be that the demand of coffee is elastic. On the other hand, since the roast coffee producers do not have good substitute for raw coffee beans, they have to bear the burden of a large portion of the increase in raw coffee beans.

3.7

In the long run, farms will stay in business if their average cost is at or below the market price. With a large annual fee (fixed cost), average costs per acre will be lower for the .

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larger farms than for smaller farms if smaller farms are be unable to produce at the most efficient (lowest average cost) quantity. If there are two types of farms, small and large, as shown in panel (a), the large farms will have a lower average cost than the small farms if the least-cost quantity per farm is higher than the farm’s capacity. Whether all of the smaller farms go out of business depends on the number of larger farms and the shape of the demand curve, as shown in panel (b).

3.8

The long-run equilibrium price will be at the minimum of the AC curve (found either by using calculus or by setting MC equal to AC). In this case, MC = 4q and AC = 800/q + 2q.

Setting these two equations equal to one another and solving gives q = 20. This value implies that the long-run equilibrium price will be equal to $80.

3.9

Since the long-run equilibrium price calculated in 3.8 is $80, the quantity demanded by the market overall will be 2,400 − 5 ∗ 80 = 2000 units. As we learned in 3.8, each firm will produce 20 units in the long-run equilibrium so there will be industry in the long run.

.

2000 20

= 100 firms in the

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COMPETITION MAXIMIZES ECONOMIC WELL-BEING 4.1

David’s quantity demanded will increase to 4 units, and his consumer surplus will grow from $3 to $10.

4.2

The consumer surplus at a price of 30 is 450 = 1/2 (30 × 30).

4.3

As of the second quarter of 2018, Twitter had 335 million users. If we assume that the most anyone would be willing to pay for Twitter access is $150, then the demand curve for Twitter access runs from $150 on the (vertical) price axis to 335 million on the (horizontal) quantity axis. The consumer surplus generated by a free good is the area under the demand curve all the way down to the horizontal axis. This is shown in the diagram below.

4.4

Profit is the difference between total revenue and total cost, but producer surplus is the difference between total revenue and variable cost. In the long run, fixed costs are zero, so producer surplus and profit are the same in the long run.

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4.5

The intersection of the market supply and demand curves determines the competitive equilibrium (Q* at point e). A supplier’s gain from participating in the market is measured by producer surplus, which is the difference between the amount a good sells for and the minimum necessary for the producers to be willing to produce the good. The minimum amount a firm must receive to be willing to produce is the firm’s avoidable production cost.

The monetary difference between what a consumer is willing to pay for the quantity of the good purchased and what the consumer actually pays is called consumer surplus.

Consumer surplus is a dollar-value measure of the extra economic benefit the consumer receives from a transaction over and above the good’s price. Total surplus equals producer surplus plus consumer surplus. Suppose the quantity produced is Q. When output is greater than the competitive level (Q*), total surplus decreases because the cost of producing units between the competitive level and Q exceeds the value consumers place on it. The reduction in surplus is equal to the area between the supply curve and demand curve for units between the competitive equilibrium quantity (Q*) and Q. This is indicated by “DWL.”

4.6

PS = 10  10 + 20  10/2 = 200. Draw a graph of the supply function to verify.

4.7

See the figure below. Nicholas is willing to pay up to WTPNicholas for a sweater, but the price of the sweater is Psweater. The difference between the price and Nicholas’ willingness to pay is the deadweight loss of this gift.

4.8

A binding minimum wage is one that affects the competitive market equilibrium wage.

That is, a binding minimum wage raises the market wage. At a higher wage, employers demand less labor, so the market equilibrium employment level decreases.

The minimum wage reduces employment below the competitive equilibrium level. When employment is less than the competitive level, total surplus decreases because the minimum amount workers require to be willing to supply their labor between the competitive level and the employment level with the minimum wage is less the value .

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employers place on it. The reduction in surplus is equal to the area between the supply curve and demand curve for units between the competitive equilibrium quantity and the employment level with the minimum wage. Consumer surplus decreases because the market wage is higher and employment is lower. Producer surplus likely increases, however, because those who keep their jobs receive higher wages, although there is a partially offsetting decrease in producer surplus from reduced employment.

Consumers are the ones who demand labor, and producers are the ones who supply labor.

Thus, consumers are the employers, and producers are the workers.

4.9

a. With the price ceiling, the equilibrium will be p = 3 and Q = 30. b. The consumer surplus increases by 2  30 − 2  (50 − 30)/2 = 40, producer surplus decreases by 2  (50 + 30)/2 = 80. So, the social deadweight loss is 40.

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MANAGERIAL PROBLEM 5.1

We assume that Mexican costs are lower than U.S. costs, but that the number of Mexican truckers is limited. If the demand curve looks like D1, all U.S. truckers would be replaced

by Mexican truckers as the new supply curve becomes stepped, as in panel (b). If there is higher demand, the United States may still retain some trucking, but it will be greatly reduced to QT – QM2 . If the number of Mexican firms is unlimited, U.S. trucking firms will be forced out of the market.

5.2

A fixed cost is a cost that does not vary with output. Lump-sum fees collected annually and only once are both fixed costs. Therefore, the effect of a fee collected only once would not be different than the effect of a fee collected annually. A fee collected annually and a fee collected only once will both increase the long-run average cost of production by an amount equal to the fee divided by the output level. The long-run market supply curve, which is horizontal at the minimum point of the long-run average cost curve, shifts up by the same amount as the minimum average cost increase.

5.3

The registration fees raise the fixed cost of production. This increases the individual truckers’ average cost of production. If the trucking industry was initially in long-run equilibrium, with truckers earning zero economic profits, then the higher average cost results in the truckers incurring losses in the short run. However, none of the truckers will shut down in the short run because the market price remains above the average variable cost of production. (This is because the market price has not changed and the lump-sum fixed costs do not affect the average variable cost of production.) Since no truckers shut down in the short run, the market price and quantity remain unchanged. Furthermore, truckers continue to produce the same amount of output in the short run, where the unchanged market price equals the marginal cost of production, although they lose money doing so.

5.4

In perfectly competitive markets in the long run, individual firms will produce the level of output that occurs at the lowest point on their long-run average cost curve. Market supply is the sum of the supply of individual firms. The competitive market equilibrium is where market demand equals market supply. At the long-run equilibrium, the market price will equal the minimum long-run average cost of production. Otherwise, if firms were earning .

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economic profits, then new firms would enter, and if firms were incurring losses, existing firms would exit.

A specific, per-unit tax will shift each firm’s long-run average cost curve up by an amount equal to the size of the tax. The quantity produced by an individual firm will not change because the minimum point on the long-run average cost curve will occur at the same quantity. Absent any other changes, the market price would be below the long-run average cost of production, so firms would incur losses. This will prompt firms to exit the industry, reducing market supply, until the market price again equals the minimum long-run average cost of production. Thus, at the new market equilibrium, the market price will have increased by an amount equal to the size of the tax and the market equilibrium quantity will have decreased, although the amount produced by an individual firm will remain unchanged.

Competitive firms operating where price equals marginal cost maximizes total surplus at the competitive equilibrium. Total surplus is maximized at the competitive equilibrium because the marginal cost of production equals the marginal value to consumers.

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SPREADSHEET EXERCISES Solutions can be found in MyLab Economics

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CHAPTER 9 MONOPOLY SOLUTIONS TO END-OF-CHAPTER QUESTIONS

MONOPOLY PROFIT MAXIMIZATION

1.1

The marginal revenue function has the same intercept as the demand function ($800) but is twice as steep, so 𝑀𝑅 = 800 − 8𝑄 [Note: you can also find MR by first writing the revenue function and then taking the first derivative]. The diagram below shows demand (D) and marginal revenue (MR). The demand curve hits the quantity axis at 200 units and marginal revenue at 100 units.

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1.2

Marginal revenue (MR) is the change in revenue (R) with respect to quantity so start by finding 𝑅(𝑄) = 𝑝 ∗ 𝑄 = 50𝑄 −0.5 ∗ 𝑄 = 50𝑄 0.5. Then, we can find the change in revenue (or marginal revenue) by taking the first derivative of the revenue function with respect to quantity. This expression is 𝑀𝑅 =

1.3

𝑑𝑅(𝑄) 𝑑𝑄

= (0.5)(50)𝑄 −0.5 = 25𝑄 −0.5.

The elasticity of demand is the percentage change in quantity divided by the percentage change in price: ε=

Q p  Q p

ε=

Q  p   . p  Q 

When Q = 10, p = 500 − 10(10) = $400. The demand function is Q = 50 − 0.10p. The slope of the demand function is Q  0.10 . p

Therefore, the elasticity of demand is

 400 ε =  0.1   4 .  10  Revenue is price multiplied by quantity, which is $400 × 10 = $4,000.

1.4

Price and quantity are related through the demand function. Therefore, when one is determined, the other one is simultaneously fixed. Therefore, the monopoly cannot determine both. As long as the monopoly chooses the level that maximizes its profit, it does not matter whether it chooses the price level or the quantity.

1.5

Revenue is maximized when the change in revenue is zero. This occurs at the quantity where marginal revenue is zero, which is at Q = 12 units.

A monopoly maximizes profit by producing the quantity where marginal revenue equals marginal cost. Revenue is maximized at the quantity where marginal revenue equals zero.

Because marginal revenue is decreasing with output and marginal costs are positive,

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marginal revenue equals marginal cost at a smaller quantity than when marginal revenue equals zero.

Revenue equals price multiplied by quantity. Revenue is zero when price is zero and when the quantity demanded is zero and is maximized when quantity equals 12 units.

1.6

This test is relevant because if the club were maximizing revenue, it would be operating at the level MR = 0, where the elasticity is −1.

1.7

A monopoly maximizes profit by producing the quantity where marginal cost (MC) equals marginal revenue (MR). Price is then set according to the demand curve (D). The profitmaximizing price and quantity for a monopoly are indicated by point “e” below. The longrun average cost of production at that quantity is indicated by the long-run average cost curve.

A monopoly will shut down in the long run if it would incur losses when producing optimally. A firm will incur losses if its price is less than the long-run average cost of production. Since a monopoly maximizes profit by charging the price indicated by its demand curve at the quantity where marginal revenue equals marginal cost, a monopoly would incur losses when producing optimally if the long-run average cost curve is above (greater than) the demand curve at the profit-maximizing quantity.

For example, at the long-run average cost indicated by LRAC in the graph below, the monopoly breaks even in the long run when producing optimally (at Q*). If long-run average costs were higher, then the monopoly would shut down; if lower, it would earn profit.

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1.8

A competitive firm operates at the lowest point of its long-run average cost curve due to competition: if it raises its price above the lowest possible long-run average cost, then it will sell no output (because other firms would be able to sell output for less). The firm would not lower its price below the lowest possible long-run average cost because it would incur losses. A monopoly faces no competition, so it is able to maximize profit by producing where marginal revenue equals marginal cost without other firms charging lower prices until price equals the lowest possible long-run average cost. That is, even if a monopoly is not operating where long-run average costs are minimized, no other firms are present in the market to profitably charge lower prices.

1.9

When demand is D1, the price the monopoly sets (vertically above the point of intersection of MR1 and MC on D1) is above the AC, and thus, the monopoly makes a positive profit.

However, when the demand curve shifts to the left, to D2, the demand is below the AC curve, and there is no price where the monopoly can make a positive profit.

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1.10 Set MC = MR and solve: MR  100  2Q MC  5 5  100  2Q Q*  47.5 p*  52.5

If C(Q)  100  5Q, the answer does not change because marginal cost is still MC  5, and therefore, the profit-maximizing condition is still the same.

1.11 The optimal output is found by setting MR=MC. We derived MR for this demand function back in question 1.2. The result was 𝑀𝑅(𝑄) = 25𝑄 −0.5. We can find MC by taking the first derivative of the cost function, so 𝑀𝐶(𝑄) = equal to one another gives us 25𝑄 −0.5 = 5 or

25 √𝑄

𝑑𝐶(𝑄) 𝑑𝑄

= 5. Setting these two expressions

= 5 which can be rearranged to get √𝑄 =

5 which implies 𝑄 ∗ = 25.

1.12 See the figure below. If the demand curve shifts from D0 to D1, output increases from Q0 to Q1, but price remains unchanged. The monopoly does not have a supply curve because there is not a unique correspondence between price and quantity supplied.

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MARKET POWER 2.1

The Lerner Index or price markup is the ratio of the difference between price and marginal cost to the price: L=

p  MC , p

which is equal the negative of the reciprocal of the elasticity of demand: L= 

1



.

Thus,

 p = .

MC 1   That is, as the elasticity of demand, which is negative and greater than 1 in absolute value p when the monopoly produces optimally, gets smaller in absolute value, the ratio gets MC larger. Monopolies that face demand curves that are only slightly elastic set prices that are multiples of their marginal cost and have Lerner Indexes close to 1.

A monopoly maximizes profit by producing the quantity where marginal cost equals marginal revenue. Because marginal costs are assumed to be positive, this occurs where marginal revenue is positive. Marginal revenue equals the change in revenue with respect to output, which is only positive when the elasticity of demand is elastic. If demand were inelastic, then marginal revenue would be negative.

2.2

A monopolist may set price equal to marginal cost if other firms can enter costlessly. If there is free entry, any price above marginal cost will attract other firms. Thus, even though the firm has no current competitors, it sets price equal to marginal cost to deter entry of potential competitors. Also, if not all customers are charged the same price (price discrimination), the firm may want to sell the last unit where price equals marginal cost.

2.3

The Lerner Index is (84.95 − 37)/84.95 = 0.56. Hence, Stamps.com believes that it faces a demand elasticity of −1.79.

2.4

The Lerner index is (1840.8 − 100)/1840.8 = 0.95. Hence, Tenet believes that the elasticity it faces is −1.06.

2.5

Apple’s price/marginal cost ratio was $349/84 = 4.155.

The Lerner Index or price markup is the ratio of the difference between price and marginal cost to the price: L= Therefore,

.

p  MC . p

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L=

= 0.76.

Finally, a monopoly operates optimally where MR = MC  1 p1   = MC.  

With a marginal cost of $84 and a profit-maximizing price of $349, the elasticity of demand is ε = −1.317.

2.6

Amazon’s Lerner Index was (p − MC)/p = (359 − 159)/359  0.557. Using Equation 11.11, we know that (p − MC)/p  0.557 = −1/, so   −1.795.

2.7

Given that Apple’s marginal cost was constant, its average variable cost equaled its marginal cost, $200. Its average fixed cost was its fixed cost divided by the quantity produced, 736/Q. Thus, its average cost was AC = 200 + 736/Q. Because the inverse demand function was p = 600 − 25Q, Apple’s revenue function was R = 600Q − 25Q2, so MR = dR/dQ = 600 − 50Q. Apple maximized its profit where MR = 600 − 50Q = 200 = MC. Solving this equation for the profit-maximizing output, we find that Q = 8 million units. By substituting this quantity into the inverse demand equation, we determine that the profit-maximizing price was p = $400 per unit, as the figure shows. The firm’s profit was  = (p − AC)Q = [400 − (200 + 736/8)]8 = $864 million. Apple’s Lerner Index was (p − MC)/p = [400 − 200]/400 = ½. According to Equation 9.10, a profit-maximizing monopoly operates where (p − MC)/p = −1/. Combining that equation with the Lerner Index from the previous step, we learn that ½ = −1/, or  = −2.

2.8

The market power of these firms (and many others) has been eroded by changes in consumer tastes and preferences, changes in technology, and increased competition from competitors.

2.9

There is no change needed in the diagram since fixed costs are not included in this picture.

An increase in fixed cost will certainly affect Ms. Swift’s profit, but the fact that for any given level of fixed cost, her profit is maximized by not selling out (i.e., selling 𝑄1 < 𝑄2 = 𝑠𝑒𝑙𝑙𝑜𝑢𝑡 tickets remains the same. Her final profit will be given by the area A minus the fixed cost. The only possible change from this outcome would be if the fixed cost was so large that it used up all of the operating profit (A) and caused total profit to become negative. In this case, Ms. Swift would be better skipping this venue and moving to a location with lower fixed cost.

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MARKET FAILURE DUE TO MONOPOLY PRICING 3.1

See the figure below. The values of price and quantity depend on the demand curve drawn by the student. Profits are area abcd and the deadweight loss is area bef.

3.2

The monopoly’s profit-maximizing quantity can be found by setting MR=MC or 480 − 8𝑄 = 40 which implies 𝑄 ∗ = 55 units. The monopoly price is 𝑝 = 480 − 4 ∗ 55 = $260.

The competitive price is found where the (inverse) demand curve equals MC (or 480 − 4𝑄 = 40 which implies 𝑄 = 110. The competitive price is equal to MC (or $40). The deadweight loss is a triangle with a base equal to the difference in the monopoly quantity and the competitive quantity (110 − 55 = 55) and a height equal to the difference in the 1

monopoly price and the competitive price (260 − 40 = 220), so 𝐷𝑊𝐿 = $220 ∗ 55 ∗ 2 = $6050.

3.3

The monopolist originally produces where MR = MC or 160 − 4𝑄 = 12 which implies 𝑄 ∗ = 37 and a price of $86. At this price/quantity combination, consumer surplus is $74 ∗ 1

37 ∗ 2 = $1369 and producer surplus is $74 ∗ 37 = $2738. After the innovation (and the subsequent cost reduction), the firm maximizes profit by producing where 160 − 4𝑄 = 4 which implies 𝑄 ∗ = 39 and a price of $82. This increase in output (and decrease in cost and price) increases both consumer and producer surplus—consumer surplus rises to $78 ∗ 1

39 ∗ = $1521 and producer surplus increases to $78 ∗ 39 = $3042. Total surplus 2

increases by $456, and of this increase, $152 (or 1/3) goes to consumers.

3.4

3.5

The effect of a franchise tax or lump-sum tax on a monopoly is to reduce profits by the amount of the tax. Because there is no change in marginal cost, the profit-maximizing/lossminimizing output and price remain unchanged, with one exception. If the tax is large enough, losses may exceed fixed costs. If that is the case, the firm will shut down (produce no output) in order to minimize losses.

Prior to the imposition of the tax, the monopolist will produce where MR = MC which implies 200 − 4𝑄 = 20 or 𝑄 = 45 and will sell at a price of 𝑝 = $110. In this case,

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1

consumer surplus is $2025 (calculated as $90 ∗ 45 ∗ ) and producer surplus is $4050 2

(calculated as $90 ∗ 45). Total welfare is $6075. After the tax is imposed marginal cost rises to $40 and the monopolist now produces 𝑄 = 40 units at a price of $120. Since the price rises from $110 to $120 (a $10 increase from a $20 tax), the tax incidence falls equally on consumers and producers. After the tax, consumer surplus falls to $1600 1

(because $80 ∗ 40 ∗ 2 = $1600), producer surplus falls to $3200, and tax revenue (society’s welfare) of $800 is generated. Overall welfare is $5600—a decrease of $475 from the pre-tax scenario.

3.6

Suppose that the monopoly faces a constant-elasticity demand curve, with elasticity , and has a constant marginal cost, m, and that the government imposes a specific tax of . The monopoly sets its price such that p = (m  )/(1  1/). Thus, dp/d = 1/(1  1/) > 1.

3.7

A tax on profit will not change firm behavior unless it causes profit to fall below zero (in which case the firm/market may cease to exist). Equilibrium price and quantity remain the same as does consumer surplus. Producer surplus is reduced by the amount of the tax, but as that tax revenue remains part of the broader market outcome, overall surplus remains unchanged as well.

CAUSES OF MONOPOLY 4.1

Yes. The demand curve could cut the average cost curve only in its downward-sloping section. Consequently, the average cost is strictly downward sloping in the relevant region.

4.2

No. In order for a firm to be a natural monopoly, its production must exhibit economies of scale; that is, firm’s average cost curve must be downward sloping. If the firm operates in the upward-sloping region of its average cost curve, it is possible that two or more firms could produce in the same industry more efficiently than one firm.

4.3

Yes. Because the AC curve is always downward sloping, it will always be less expensive for a single firm to produce 2x than for 2 different firms to each produce x units.

4.4

Once a book is online, it is available to consumers for free. As a result, the publisher may lose some consumers after the copyright expires. Limiting the length of a copyright (in the United States or elsewhere) would encourage the publisher to charge a higher price for the novel, as the publisher attempts to recoup the cost of publishing the novel and earn profit in a shorter period before the copyright expires. After the copyright runs out, the publisher may lower the price of the novel to stay competitive with the online version.

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4.5

When the demand curve is linear, the marginal revenue curve will always be linear with twice the slope of the demand curve. This is true because when multiplying the demand curve by Q to obtain total revenue, we always obtain a squared term in the revenue function, which then doubles the slope when we take the derivative to obtain marginal revenue. For example, if the demand curve is P = a − bQ TR = aQ − bQ2 MR 

dTR  a  2bQ. dQ

Because the slope of MR is double of the slope of the linear demand curve, the MR curve always crosses the MC segment in the middle between the y-axis and point ec . Hence, triangles A and C have one equal side and three equal angles, which implies that these triangles are equal.

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ADVERTISING 5.1

In the figure, let D1 and MR1 be demand and marginal revenue before advertising. Assume the monopoly has a constant marginal cost with no fixed cost such that MC1 = AC1. Then, suppose the monopoly advertises and that the advertising shifts demand and marginal revenue to D2 and MR2.

Assume advertising is a marginal cost, such that marginal cost continues to equal average cost after advertising, and that marginal costs remain constant.

A monopoly maximizes profit by producing the quantity where marginal revenue equals marginal cost. For the monopoly to break even from advertising, the marginal cost curve with advertising must shift up by enough that the increase in cost cancels the increase in revenue.

A marginal cost curve (MC2 = AC2), reflecting the cost of the advertising, is illustrated such that the monopoly breaks even from advertising.

5.2

To maximize profit, the monopoly must set marginal revenue MR ( = R/Q) equal to marginal cost, MC, and must set the marginal revenue of advertising, MRA ( = Q/A) equal to the marginal cost of advertising, which is 1. R = pQ = 100Q − Q2 + 5A − A2.

Setting MR = MC yields 100 − 2Q = 10 or Q = 45. Setting MRA = 1 yields 5 − 2A = 1 or A = 2.

5.3

The marginal revenue function (MR) is MR = 0.75Q–0.25A0.5.

Set marginal revenue from output equal to its marginal cost and solve for Q to find the profit-maximizing output level: Q = A2/4096.

(1)

The change in profit given a small change in advertising is 0.5Q0.75A–0.5 − 0.25. .

Solutions Manual—Chapter 9/Monopoly 229

Set marginal revenue from advertising equal to its marginal cost and solve for A to find the profit-maximizing level of advertising: A = Q1.5/0.25.

(2)

Substituting this expression for A into equation (1) above and solving for Q, Q = 16 units.

Substituting this value for Q into equation (2) above and solving for A, A = 256.

Substitute the profit-maximizing values for Q and A into the demand equation and solve for p to find the profit-maximizing price (p = $8.00).

5.4

A fixed subsidy has no effect on the price or number of subscriptions sold. However, it might keep a magazine from shutting down.

5.5

Assume the following figure illustrates the effect of Super Bowl advertising but not the effect of social media for a monopoly. Before the advertising, demand is D1, marginal revenue is MR1, and marginal cost is MC1. The monopoly initially maximizes profit at a price of p1 and a quantity of q1 at point e1. Then, the monopoly advertises with a commercial during the Super Bowl. Assume the advertising increases the marginal cost of production to MC2 and increases demand and marginal revenue to D2 and MR2. The new profit-maximizing price and quantity are p2 and q2 at e2.

Super Bowl commercials receive extra exposure because these ads often go viral on the Internet. Consequently, once the effects of social media are added, the demand curve (and, correspondingly, the marginal revenue curve) shifts further to the right at no additional advertising cost. This increases the demand for Super Bowl commercials (to D3), increasing the price and quantity that maximizes profits.

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NETWORKS, DYNAMICS, AND BEHAVIORAL ECONOMICS 6.1

When the hoi polloi buy the chocolate, the snobs won’t buy. So, the monopoly is facing a relatively flat demand curve, which suggests a low-price, high-quantity outcome. On the contrary, if the hoi polloi do not buy the chocolate, the snobs will buy. In this situation, the monopoly will face a steep demand curve, resulting in a high-price, low-quantity outcome.

If the demand curve for the snobs is substantially steeper than that for the hoi polloi such that the profit from the former is larger than that from the latter, the monopoly will choose to cater to the snobs.

6.2

Given that the demand curve is p = 10 − Q, its marginal revenue curve is MR = 10 − 2Q. Thus, the output that maximizes the monopoly’s profit is determined by MR = 10 − 2Q = 2 = MC, or Q* = 4. At that output level, its price is p* = 6, and its profit is π* = 16. If the monopoly chooses to sell 8 units in the first period (it has no incentive to sell more), its price is 2, and it makes no profit. Given that the firm sells 8 units in the first period, its demand curve in the second period is p = 10 − Q/β, so its marginal revenue function is MR = 10 − 2Q/ β. The output that leads to its maximum profit is determined by MR = 10 − 2Q/ β = 2 = MC, or its output is 4 β. Thus, its price is 6, and its profit is 16 β. It pays for the firm to set a low price in the first period if the lost profit, 16, is less than the extra profit in the second period, which is 16 (β − 1). Thus, it pays to set a low price in the first period if 16 < 16(β − 1), or 2 < β.

6.3

The main factor is the large base of buyers and sellers, that is the network that eBay created by reaching a critical mass of users. By providing a single online location where buyers and sellers can meet, eBay is able to create these positive externalities in the form of lower search costs and easier and safer transactions via their feedback rating system.

6.4

The original solution for Games Unlimited (GU) can be found by setting MR = MC or 60 − 2𝑄 = 20 which implies 𝑄 ∗ = 20 and a price of $40. Consumer surplus is $20 ∗ 20 ∗ 1 2

= $200, and profit for the firm is $40 ∗ 20 − (100 + 20 ∗ 20) = $300. After the switch

to selling games online, the new solution is found where MR = MC or 60 − 2𝑄 = 0 which 1

implies 𝑄 ∗ = 30 and a price of $30. Consumer surplus increases to $30 ∗ 30 ∗ = $450 2

and firm profit rises to $30 ∗ 30 − (500) = $400.

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MANAGERIAL PROBLEM 7.1

A monopoly maximizes profit by producing the quantity where marginal revenue equals marginal cost. It then charges the price indicated by the demand curve. When generic drugs enter the market after the patent on a brand-name drug expires, the demand curve facing the brand-name firm shifts toward the origin (to the left). It also becomes less elastic at the original price (and becomes steeper). The firm now maximizes its profit at a point where the quantity is smaller. However, the new profit-maximizing price may be higher than the initial price because the demand curve is less elastic at the new optimum. This is possible if the brand-name firm has two types of consumers with different elasticities of demand who differ in their willingness to switch to a generic. Loyal consumers may prefer the brandname drug because they are more comfortable with a familiar product, worry that new products may be substandard, or fear that differences in the ingredients might affect them.

7.2

A monopoly maximizes profit by producing the quantity where marginal revenue equals marginal cost. It then charges the price indicated by the demand curve. When generic drugs enter the market after the patent on a brand-name drug expires, the demand curve facing the brand-name firm shifts toward the origin (to the left). The firm now maximizes its profit at a point where the quantity is smaller. The new profit-maximizing price may be higher than the initial price if the demand curve is less elastic (steeper) at the new optimum. However, if the leftward shift is parallel, then the new demand curve’s slope does not change. That is, the demand curve becomes no steeper. At the smaller quantity, the elasticity of demand becomes more elastic. Therefore, the brand-name firm will not charge a higher price.

7.3

A patent is an exclusive right granted to the inventor of a new and useful product, process, substance, or design for a specified length of time. The length of a patent varies across countries, although it is now 20 years in the United States and in most other countries. This right allows the patent holder to be the exclusive seller or user of the new invention.

A monopoly maximizes profit by producing the quantity where marginal revenue equals marginal cost. It then charges the price indicated by the demand curve. When generic drugs enter the market after the patent on a brand-name drug expires, the demand curve facing the brand-name firm shifts toward the origin (to the left).

If patent lengths were reduced, then a monopoly drug manufacturer while under the patent would not charge higher prices because demand would be unchanged. Furthermore, reducing patent lengths would not change the marginal cost of production, although the monopoly would have fewer periods with the patent to recoup the fixed cost of developing the drug.

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SPREADSHEET EXERCISES Solutions found in MyLab Economics

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CHAPTER 10 PRICING WITH MARKET POWER SOLUTIONS TO END-OF-CHAPTER QUESTIONS CONDITIONS FOR PRICE DISCRIMINATION

1.1

Suppose the theater charges an intermediate price. In that case, no seniors will buy a ticket, and all college students will buy tickets. By lowering the price to the highest price that the seniors will pay, all seniors will buy tickets and so will the college students. On the other hand, the theater can raise the price to the highest amount that the students are willing to pay and still keep all college student customers, but no seniors will buy a ticket. Therefore, it will only lose revenue at the intermediate price.

1.2

The pharmaceutical firms offer the discount to low-income seniors because the seniors would probably not purchase the medicines if they were not discounted. By segregating this portion of the market, they are able to price discriminate profitably because the marginal cost of producing the extra medications is very low. Thus, if they can still charge higher prices to the rest of the market, they will profit from the discounted prescriptions as well. (In addition to the short-run profits, the pharmaceutical firms get good publicity, which could forestall more costly regulation in the future.)

1.3

In order to price discriminate, the firm must have market power—the ability to set prices.

Consumers must have varying price sensitivities, and the firm must be able to identify individual consumers or groups of individuals based on willingness to pay. The firm must also be able to prevent reselling after the initial sale.

1.4

The colleges may be providing scholarships as a form of charity, or they may be price discriminating by lowering the final price for less wealthy families (who presumably have higher elasticities of demand).

1.5

Since adults cannot use children’s tickets to enter Disneyland, there won’t be a resale problem. On the other hand, for nonlocal visitors, a small difference in ticket price does not mean much compared to their travel cost. In other words, their willingness to pay the price is higher than it is for locals.

1.6

Price discrimination is charging consumers different prices for the same good based on individual characteristics of consumers, membership in an identifiable subgroup of consumers, or on the quantity purchased by the consumers. To practice price discrimination, a firm must be able to prevent or limit resale. In some industries, preventing resale is easier than others. In industries where resale is initially easy, managers can act to make resale more costly. Some firms act to raise transaction costs or otherwise make resale difficult. For example, firms could require customers to sign a contract that forbids resale.

Government tariffs (taxes on imports) limit resale by making it expensive to buy a branded good in a low-price country and resell it in a high-price country. In another example, firms 233

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could provide a warranty that is only good in the country in which the good is supposed to be sold. Limiting the quantity purchased is also designed to prevent resale.

It is hard to say without knowing the underlying costs of providing each car in the rental fleet. It is very likely that much or even all of the difference in rental rates can be attributed to the fact that Ferraris are significantly more expensive for the rental company to purchase than Toyotas. That said, if the difference in rental rate is not entirely explained by cost, then price discrimination is a likely explanation.

These restrictions help prevent access to their films—effectively segregating the different markets and paving the way for the possibility of price discrimination.

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PERFECT PRICE DISCRIMINATION 2.1

The difference in profit between a single price monopoly and perfect price discrimination is the areas A and C in the application, which is $375 million.

2.2

With perfect price discrimination, the firm sells each unit at the maximum amount any customer is willing to pay for it, so prices differ across customers, and a given customer may pay more for some units than for others. By selling each unit of its output to the customer who values it the most at the maximum price that person is willing to pay, the perfectly price-discriminating monopoly captures all possible consumer surplus. Maximum potential consumer surplus (CS) is equal to the area under the linear demand curve and above the marginal cost. This is the area of a triangle with a base equal to the quantity demanded, which is 60 units (from 30 = 90 − Q), and a height equal to the difference in where the demand curve hits the vertical, price axis (90) and the $30 marginal cost, which is 60: CS = 0.5(60)(60); CS = $1,800.

This becomes the monopoly’s profit.

With perfect price discrimination, the firm sells each unit at the maximum amount any customer is willing to pay for it, so prices differ across customers, and a given customer may pay more for some units than for others. By selling each unit of its output to the customer who values it the most at the maximum price that person is willing to pay, the perfectly price-discriminating monopoly captures all possible consumer surplus. Perfect price discrimination is efficient because the price of the last unit sold equals marginal cost.

Thus, the monopoly’s profit is $1,800, consumer surplus is $0, welfare is $1,800, and deadweight loss is $0.

If the firm charges a single price, then the firm maximizes profit by setting marginal cost ($30) equal to marginal revenue. The marginal revenue curve is the same as the demand curve but with twice the slope: MR = 90 − 2q.

Setting marginal cost equal to marginal revenue, the profit-maximizing quantity is q = 30 units.

The profit-maximizing price is that where consumers demand this quantity: p = $60.

Profit equals the difference in price ($60) and marginal cost ($30) multiplied by the units produced (30): π = (60 − 30)(30) = $900.

Consumer surplus is equal to the area under the linear demand curve and above the price.

This is the area of a triangle with a base equal to the quantity demanded, which is 30 units, and a height equal to the difference in where the demand curve hits the vertical, price axis (90) and the $60 price: .

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CS = $450.

Welfare equals the monopoly’s producer surplus (which equals profit since there are no fixed costs) plus consumer surplus: Welfare = 900 + 450 = 1,350.

Deadweight loss equals the area under the demand curve and above the marginal cost curve for units not produced. This is equal to the area of a triangle with a base equal to the difference in the profit-maximizing quantity (30) and the efficient quantity where demand equals marginal cost (60, from 30 = 90 − Q) multiplied by a height equal to the difference in the profit-maximizing price ($60) and marginal cost ($30): DWL = 0.5(30)(30) = $450.

2.3

If the reservation price for senior citizens is $5, then the profit-maximizing single price is $20. Surplus for college students is $0, and surplus for senior citizens is $0. Producer surplus equals profit (assuming no fixed costs), which is $200. Total surplus is $200.

Price discrimination is charging consumers different prices for the same good based on individual characteristics of consumers, membership in an identifiable subgroup of consumers, or on the quantity purchased by the consumers. Perfect price discrimination is when the firm sells each unit at the maximum amount any customer is willing to pay. With perfect price discrimination, consumer surplus is zero, and producer surplus equals profit (assuming no fixed costs), which is $400.

Thus, the change in surplus from perfectly price discriminating is $200, from surplus of $400 with perfect price discrimination minus surplus of $200 when charging a single price.

2.4

If Google can effectively monitor an individual customer’s shopping pattern and history and offer advertisers specific targets, it allows them to charge personalized prices for each type. This is essentially first-degree price discrimination.

2.5

a. The marginal cost is zero, so the MC curve is the X axis. The amount of tickets sold will be T*, where the MR curve intersects X axis. b. The concerts’ failure may indicate monopoly price, but not that the monopoly set too high a price. c. If the monopoly can perfectly price discriminate, it can obtain all the producer surplus below the demand curve.

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2.6

The monopoly, when maximizing profit at a single price, produces Q* units (where marginal cost equals marginal revenue) and charges the price indicated by the demand curve at the profit-maximizing quantity (p*).

The monopoly could not profitably produce where price equals marginal cost because at that quantity (indicated below by QMC), the price is below the average cost of production, so the monopoly would incur losses.

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GROUP PRICE DISCRIMINATION 3.1

When the firm is operating in two markets, its profit is P1Q1  P2Q2 − C(Q1  Q2).

Therefore, if it sells in two markets and price discriminates it is because this maximizes its overall profit. So, its profit in a low price market cannot be negative.

3.2

By differentiating, we find that the American marginal revenue function is MRA = 100 − 2QA, and the Japanese one is MRJ = 80 − 4QJ. To determine how many units to sell in the United States, the monopoly sets its American marginal revenue equal to its marginal cost, MRA = 100 − 2QA = 20, and solves for the optimal quantity, QA = 40 units. Similarly, because MRJ = 80 − 4QJ = 20, the optimal quantity is QJ = 15 units in Japan. Substituting QA = 40 into the American demand function, we find that pA = 100 − 40 = $60. Similarly, substituting QJ = 15 units into the Japanese demand function, we learn that pJ = 80 − (2  15) = $50. Thus, the price-discriminating monopoly charges 20 percent more in the United States than in Japan. We can also show this result using elasticities. We know that the elasticity of demand is A = −pA/QA in the United States and  J  1/2 pJ /QJ in Japan.

In the equilibrium, A = −60/40 = −3/2 and J = −50/(2  15) = −5/3. The ratio of the prices depends on the relative elasticities of demand: pA/pJ = 60/50 = (1 + 1/J)/(1 + 1/A) = (1 − 3/5)/(1 − 2/3) = 6/5.

3.3

The two marginal revenue curves are MRJ = 3,500 − QJ and MRA = 4,500 − 2QA. Equating the marginal revenues with the marginal cost of $500, we find that QJ = 3,000 and QA = 2,000. Substituting these quantities into the inverse demand curves, we learn that pJ = $2,000 and pA = $2,500. We know that the elasticities of demand are J = p/(MC − p) = 2,000/(500 − 2,000) =  43 and A = 2,500/(500 − 2,500) =  54 . Thus, we find that 1  1/( 45 ) 1  1/ A pJ 2,000   0.8   . pA 2,500 1  1/( 43 ) 1  1/ J

The profit in Japan is (pJ − m)QJ = ($2,000 − $500)  3,000 = $4.5 million, and the U.S. profit is $4 million. The deadweight loss is greater in Japan, $2.25 million (= 12  $1,500  3,000), than in the United States, $2 million (= 12  $2,000  2,000).

3.4

pUS (1 − 1/2) = 10 = pJ (1 − 1/5) pUS = $20,

pJ = $12.50.

3.5 Electronic textbooks are more difficult to resell and can be programmed to “expire” (disappear) after a set period of time agreed to at the time of purchase. They also are more likely to appeal to younger students who are more comfortable with reading material on electronic devices. Finally, they have substantially lower production costs—differences that are not likely fully reflected in lower prices.

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3.6

With the ban, the profit-maximizing price and quantity for Country 1 is $3.50 and 5 units and the profit-maximizing price and quantity for Country 2 is $5.00 and 4 units. Thus, profit is Π = (p1 − M) × Q1 + (p2 − M) × Q2 Π = (3.5 − 1) × 5 + (5 − 1) × 4 Π = $28.50.

Without the ban, the profit-maximizing price and quantity are $4.00 and 9 units. Thus, profit is Π = (p − M) × Q Π = (4 − 1) × 9 Π = $27.00.

3.7

If MC = 7, then marginal cost is sufficiently high that the monopoly will only be able to profitably sell to one of the two groups (Country 2), and price discrimination will not be possible. That is, if marginal cost is so high that a monopoly is uninterested in selling to one of two groups, then the monopoly is not able to practice second degree price discrimination (and the monopoly will maximize profits as it would if it could only charge a single price).

In this case, the ban is irrelevant. Selling only to Country 2, the monopoly maximizes profit by producing where marginal revenue (marginal revenue for Country 2 is MR = 9 − 2Q2) equals marginal cost: MR = MC 9 − 2Q2 = 7 2Q2 = 2 Q2 = 1.

From the demand curve, the profit-maximizing price is P = 9 − Q2 P = $8.

3.8

Yes. The monopoly’s ability to price discriminate depends on the marginal cost. Suppose there are two groups of potential consumers, if the marginal cost is so high that one group will not buy the good at a price acceptable to the monopoly, then the monopoly is not able to price discriminate in this case.

3.9 Output expands, as do profit and consumer surplus. When the markets are combined, the monopolist sells Q2* for $5, all to customers in Market 2. When the markets can be separated, price and quantity remain unchanged in Market 2, but the monopolist also sells Q1* for p1.

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3.10 There are a number of possibilities including coupons (both paper and electronic), various purchase restrictions (such as a Saturday night stay requirement for airline tickets), reverse auctions such as Priceline.com where the buyer places a bid and sellers decide whether to accept that bid or not, and rebates (which require extra time to redeem).

3.11 This policy allows the firm to maximize its profit by price discriminating if people who put a lower value on their time (so are willing to drive to the store and move their purchases themselves) have a higher elasticity of demand than people who want to order over the phone and have the goods delivered.

3.12 No, it is not reasonable to conclude that U.S. drivers subsidize European gasoline prices. If oil companies have market power in the United States and Europe and can price discriminate, they will treat each market as a separate market setting prices and quantities at profit-maximizing levels independent of the other market.

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NONLINEAR PRICE DISCRIMINATION 4.1

Yes. Even if a consumer purchased 40 units per day, the average price would just equal the monopoly price, but the consumer surplus would fall from $450 to $400. In addition, the consumer in panel (b) pays $60 for 30 units, but the consumer in panel (a) must purchase 40 units to achieve the same average price. If they only bought 30 units, their average price would be $63.33.

4.2

Setting marginal revenue equal to marginal cost yields Q* = 30, p* = 60. Profit is $900, consumer surplus is $450, welfare is $1,350 (PS + CS), and deadweight loss is $450.

4.3

For simplicity, assume the demand function is linear and its equation is Q = a − bP, where a and b are positive numbers and a  m. The nonlinear price discriminating utility’s profit is:  = P1Q1  P2(Q2 − Q1)  P3(Q3 − Q2) − mQ3  = P1(a − bP1)  P2[(a − bP2) − (a − bP1)]  P3[(a − bP3) − (a − bP2)] − m(a − bP3)  = P1(a − bP1)  bP2[(P1 − P2)]  bP3[P2 − P3)]  m(a − bP3).

F.O.C:  p/ P1 = a − 2bP1  bP2 = 0,  p/ P2 = bP1 − 2bP2  bP3 = 0,  p/ P3 = bP2 − 2bP3  mb = 0.

Solving these three equations, we get: P1 = (3a/4b)  m/4, P2 = (a/2b)  m/2, P3 = (a/4b) 3m/4.

4.4

a. The monopoly can set the price to be 60 and the minimum amount to be 60 to achieve the same outcome as in the perfect price discrimination case. b. For an initial price of 90, the total demand will be zero.

4.5

a. The supermarket cannot approach perfect price discrimination. Therefore, it is multimarket price discrimination. b. The price markup (P – MC) is inversely related to elasticity. Consumers who demonstrate high elasticity for certain products should be offered discounts in those products, resulting in greater purchases.

4.6

The mini-case provides a very nice example where a firm (Whistler) uses both group price discrimination with different prices for different age groups (kids, seniors, adults, students, etc.) along with discounts for buying multiday tickets (nonlinear price discrimination). .

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Similar schemes can be used in other industries that have a ticket-based pricing system (amusement parks, movie theaters, etc.). Also, in cases where nonlinear price discrimination is popular (e.g., supermarkets with different unit costs for larger quantity packages), the same outcome can be achieved by adding discount cards for some groups (e.g., students or seniors) on top of the nonlinear price discrimination that already occurs.

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p = 120 – 2(25) p = 120 – 50 p = $70.

Profit equals the difference in price ($70) and marginal cost ($20) multiplied by the units produced (25): Π = $1,250.

Thus, the difference in profit from using the two-part tariff is $1,250 (from profit of $2,500 with the two-part tariff minus profit of $1,250 from charging a single price).

5.4

A two-part price is where a firm charges a consumer a lump-sum fee for the right to buy as many units of the good as the consumer wants at a specified price. The optimal two-part price for the Club is to charge Joe and Susan a per-unit price equal to marginal cost ($20) and then set the lump-sum fee equal to Susan’s consumer surplus (since her consumer surplus is smaller than Joe’s). Susan’s consumer surplus (CS) is equal to the area under her linear demand curve and above the per-round price. This is the area of a triangle with a base equal to the quantity demanded, which is 40 units, and a height equal to the difference in where the demand curve hits the vertical, price axis and the $20 price, which is 80: CS = 0.5(40)(80) CS = $1,600.

If the firm charges the same two-part tariff to Joe and Susan, then profit will equal the lump-sum fee for both consumers (since the per-round price equals the marginal cost of the round): π = $3,200.

Shown for Question 5.3 above, the optimal lump-sum fee for Joe is $2,500.

With different two-part tariffs, Joe pays a lump-sum fee of $2,500 and Susan pays a lumpsum fee of $1,600, so profit is π = $4,100.

Thus, the difference in profit from using different two-part tariffs is $900 (from profit of $4,100 with different two-part tariffs minus profit of $3,200 from charging the same twopart tariff).

5.5

A two-part price is where a firm charges a consumer a lump-sum fee for the right to buy as many units of the good as the consumer wants at a specified price. The optimal two-part price is a per-unit price equal to marginal cost, which is zero, and then set the lump-sum

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fee equal to consumer surplus (the area under the demand curve and above the per-unit price).

The actual price per download is positive because consumers are not identical (with different demands). By raising price, the monopoly earns more per unit from customers but lowers its customers’ potential consumer surplus. If the monopoly can capture each customer’s potential surplus by charging different lump-sum fees, it sets it price equal to marginal cost. However, if the monopoly cannot capture all the potential consumer surplus because it must charge everyone the same lump-sum fee, the increase in profit from the higher per-unit price more than offsets the reduction in the lump-sum fee (and per-unit prices will not equal the marginal cost of zero).

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BUNDLING 6.1

No. If no consumers want the second product, profits are reduced by bundling it with the first product. The reason is that, because there is no demand for the second product, consumer demand for the bundled products will be equal to the demand for the first (desired) product alone. If there is no secondary market for the undesired product and the consumer must pay to dispose of it, then profits will be reduced rather than increased, as consumer demand falls to reflect the disposal cost.

6.2

a. If the firm charges $1,000 for laptops, then demand will be one, and profit will be $1,000. If the firm charges $800 for laptops, then demand will be two, and profit will be $1,600. If the firm charges $600 for laptops, then demand will be three, and profit will be $1,800. If the firm charges $150 for printers, then demand will be one, and profit will be $150. If the firm charges $100, then demand will be two, and profit will be $200. If the firm charges $50, then demand will be three, and profit will be $150.

Thus, the firm will charge a price of $600 for laptops and $100 for printers for profit of $2,000. b. If the firm charges a bundled price of $1,050, then demand will be one, and profit will be $1,050. If the firm charges a bundled price of $900, then demand will be two, and profit will be $1,800. If the firm charges a bundled price of $750, then demand will be three, and profit will be $2,250. Thus, the firm should charge a bundled price of $750 to earn profit of $2,250. c. In this example, bundling pays because customer reservation values are negatively correlated. In general, bundling only pays when customer reservation values are negatively correlated.

6.3

It is likely that in the past the reservation prices across individuals were positively correlated. In this scenario it is often the case the price the goods separately will maximize the firm’s profit (see Table 10.3). Over time reservation prices for the two products may have shifted and become negatively correlated (as in Table 10.2) leading to the decision to bundle the goods together in order to maximize profit.

6.4

This emphasis on “genuine Honda parts” is undoubtedly an attempt to bundle the maintenance of the vehicle with the original purchase. If customers take this suggestion seriously then it allows Honda to be more competitive on the original sale of the vehicle knowing that they will be locking the customer in to a series of required tie-in maintenance purchases down the road. In many cases the warranty provisions of the vehicle require following the recommended maintenance schedule and using approved (if not “genuine” parts).

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PEAK-LOAD PRICING 7.1

The resort practices peak-load pricing by selling a quantity in each period where marginal revenue equals marginal cost. For the low season, marginal revenue (MR1) is MR1 = 100 – 2Q1.

Setting this equal to marginal cost, MR1 = MC 100 – 2Q1 = 50 Q1 = 25 units.

Substituting this back into the inverse demand equation, the profit-maximizing price for the low season is p1 = $75. Similarly, for the high season, marginal revenue (MR2) is MR2 = 300 – 2Q2.

Setting this equal to marginal cost, MR2 = MC 300 – 2Q2 = 50 Q2 = 125 units.

This is above the room capacity of 100. Substituting the maximum capacity of 100 into the inverse demand equation, the profit-maximizing price for the high season is p2 = $200.

This is illustrated below.

7.2

Assume the marginal cost of production is zero. The yacht firm practices peak-load pricing by selling a quantity in each period where marginal revenue equals marginal cost. For summer, marginal revenue (MRS) is MRS = 200 – 4QS. .

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Setting this equal to marginal cost, MRS = MC 200 – 4QS = 0 QS = 50 units.

Substituting this back into the inverse demand equation, the profit-maximizing price for summer is pS = $100. Similarly, for winter, marginal revenue (MRW) is MRW = 200 – 2QW. Setting this equal to marginal cost, MRW = MC 200 – 2QW = 0 Q2 = 100 units.

This is above the yacht capacity of 50. Substituting the maximum capacity of 50 into the inverse demand equation, the profit-maximizing price for winter is pW = $150.

7.3

For simplicity, assume Paradise has no limit on the number of yachts available for rental on a monthly basis and that the marginal cost of production is zero.

The yacht firm practices peak-load pricing by selling a quantity in each period where marginal revenue equals marginal cost. For summer, marginal revenue (MRS) is MRS = 200 – 4QS. Setting this equal to marginal cost, MRS = MC 200 – 4QS = 0 QS = 50 units.

Substituting this back into the inverse demand equation, the profit-maximizing price for summer is pS = $100. Similarly, for winter, marginal revenue (MRW) is MRW = 200 – 2QW. Setting this equal to marginal cost, MRW = MC 200 – 2QW = 0 Q2 = 100 units.

Substituting this back into the inverse demand equation, the profit-maximizing price for winter is pW = $100.

Profit equals the difference in price and marginal cost multiplied by the quantity produced: Π = (pS – M) × QS + (pW – M) × QW Π = (100 – 0) × 50 + (100 – 0) × 100 Π = $15,000.

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Consumer surplus equals the area under the demand curve and above the price. In the summer, this is equal to the area of a triangle with a base equal to the quantity demanded (50 units) and a height equal to the difference in where the demand curve intersects the price axis (200) and the summer price (100): CS = 2,500.

In the winter, this is equal to the area of a triangle with a base equal to the quantity demanded (100 units) and a height equal to the difference in where the demand curve intersects the price axis (200) and the winter price (100): CS = $5,000.

Combined consumer surplus is $7,500.

In this example, without a capacity constraint, the single price that maximizes profit is $100 (because the optimal price in the summer is $100 and the optimal price in the winter is $100). This occurs because both the summer and winter demand curves intersect the vertical price axis at the same place and marginal cost is constant. Thus, when charging a single price, profit and consumer surplus are unchanged.

7.4

Under the non-dynamic (static) pricing approach the firm will solve its profit maximization problem assuming (inverse) demand is 𝑝 = 100 − 𝑄. Given this, marginal revenue will be 𝑀𝑅 = 100 − 2𝑄 and the firm will optimize where MR=MC or 100 − 2𝑄 = 0 which implies 𝑄 = 50 and 𝑝 = 50. However, actual quantity from day to day will not necessarily be 50 units. The firm will sell 30 units when 𝑎 = 80, 50 units when 𝑎 = 100, and 70 units when 𝑎 = 120. Profit will be ($50 ∗ 30 + $50 ∗ 50 + $50 ∗ 70) − $2500 = $5000.

1

1

Consumer surplus will be $30 ∗ 30 ∗ 2 on the day when 𝑎 = 80, $50 ∗ 50 ∗ 2 when 𝑎 = 1

100, and $70 ∗ 70 ∗ 2 when 𝑎 = 120 for a total of $4150.

Using dynamic pricing the firm simply solves the problem three times for each of the three values of 𝑎. When 𝑎 = 100 the solution is 𝑄 = 50 and 𝑝 = $50 and operating profit that day is $2500. When 𝑎 = 80 then 𝑀𝑅 = 80 − 2𝑄 which, after setting MR=MC=0, implies 𝑄 = 40 and 𝑝 = $40. In this case operating profit is $1600. Finally, when 𝑎 = 120 we have 𝑀𝑅 = 120 − 2𝑄 = 0 which implies 𝑄 = 60 units and 𝑝 = $60. Profit for this day is $3600. Overall profit is $1600 + $2500 + $3600 − $2500 = $5200. Consumer surplus 1

is $40 ∗ 40 ∗ 2 = $800 when 𝑎 = 80 and $1250 and $1800 for the days when 𝑎 = 100 and 𝑎𝑎 = 120 respectively. Total consumer surplus is $3850.

7.5

If Uber has a capacity constraint, then the increase in fares will not help draw in additional supply (drivers) and surge pricing will only serve to increase Uber’s profits. Rides will be allocated to those who value them the most (as evidenced by a higher willingness to pay).

The diagram below shows this scenario. Suppose that Uber drivers are willing and able to provide a ride at price 𝑃𝑃1 up to 1000 rides. After that point, no additional rides will be .

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available. If demand is low or moderate (like 𝐿𝑜𝑤 or 𝑀𝑜𝑑) then competition will drive the price down to cost. Once demand reaches a high level (𝐻𝑖𝑔ℎ) then surge pricing kicks in and price rises to 𝑃2.

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MANAGERIAL PROBLEM 8.1

Before the item is discounted, the department store attempts to sell the item to customers with relatively high reservation prices. If after a while the item is not sold out, the department store may try to sell the item to customers with lower reservation prices by putting the item on sale.

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SPREADSHEET EXERCISES Solutions available in MyLab Economics

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CHAPTER 11 OLIGOPOLY AND MONOPOLISTIC COMPETITION SOLUTIONS TO END-OF-CHAPTER QUESTIONS

CARTELS

1.1

Assume the marginal cost and average cost of production for one of the n members of OPEC are illustrated in the figure. The cartel price is pm, at which each member is allowed to produce qm units of output to maximize cartel profits. For simplicity, assume a single OPEC member can increase production without substantially changing the cartel price.

At the cartel price, pm, each cartel member has an incentive to increase output from qm to that level where price (pm) equals the marginal cost of production. This will increase profit by an amount equal to the area under the price (pm) and above the marginal cost curve for additional units purchased (for units between qm and the profit-maximizing quantity, qpm).

1.2

Cartel members agree to restrict output to raise price to maximize joint profits. However, cartel members have an incentive to cheat by producing more than the agreed-upon amount (or by lowering their price) and increasing their own profits at the expense of other cartel members. Matching lower prices reported by customers is a way to detect cheating by cartel members. It might also be a way of punishing cartel members who cheat.

1.3

Oligopolistic firms have an incentive to form cartels in which they collude in setting prices or quantities so as to increase their profits. Typically, each member of a cartel agrees to 253

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reduce its output from the level it would produce if it acted independently. As a result, the market rises, and the firms earn higher profits. If the firms reduce market output to the monopoly level, they achieve the highest possible collective profit. However, cartels often fail because of government policies that forbid cartels or because members of the cartel “cheat” on the cartel agreement. Cartels are more likely to be successful when they are able to detect cheating from the cartel agreement and punish violators.

1.4

The cartel will maximize joint profit. The cartel’s profit function (π) can be written as Π = (100 − 2Q)Q − 20Q where Q is total output. Maximizing with respect to Q,

 = 100 − 2Q − 2Q − 20. Q Setting this equal to zero and solving for Q, 100 − 2Q − 2Q − 20 = 0 80 = 4Q Q = 20 units.

In turn, each of the four firms will produce five units.

1.5

Both Apple and the publishers would like to charge the monopoly price. They split the proceeds 70/30, but both sides benefit if the cartel can maintain the collusive price.

1.6

It is definitely possible for buyers to gain an advantage by acting collectively. The “nopoaching” clauses discussed in the mini-case are one example. In this situation, the employers, acting as buyers in the labor market, conspired to intentionally not compete for workers. This meant that a software engineer at Google would not be actively recruited by Apple which suppress the wage that this worker can earn. Another example involves bidding in auctions. There are many ways collusion can happen among buyers in an auction setting. The most common involve bid rotation (taking turns winning) and bid suppression (aggressive moves meant to scare off outside bidders). In all cases, the goal is to secure the item up for sale at a lower-than-expected price.

1.7

The Maple Syrup Cartel uses a variety of monitoring tactics (including posting guards on the property of suspected cheaters) in an attempt to maintain the production quotas that support the artificially high price of syrup. Figure 11.1 shows that firms have an incentive to cheat on the cartel by selling additional units—but this drives down price for everyone and will eventually destabilize the cartel itself.

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rearrange the terms, the first firm’s best-response function is q1  360  12 q2. Similarly, the second firm’s best-response function is q2  360  12 q1. By substituting one of these bestresponse functions into the other, we learn that the Nash-Cournot equilibrium occurs at q1 = q2 = 240, so the equilibrium price is 52¢.

2.3

The Cournot equilibrium quantity for each of the duopoly firms is q = (a − m)/(3b) = (150 − 60)/3 = 30. As a result, the Cournot price is p = (a + 2m)/3 = (150 + 120)/3 = 90.

2.4

The monopoly will make more profit than the duopoly will, so the monopoly is willing to pay the college more rent. Although granting monopoly rights may be attractive to the college in terms of higher rent, students will suffer (lose consumer surplus) because of the higher textbook prices.

2.5

Assume that markets with multiple bail-bond firms (n firms) are oligopolistic, produce a homogenous good, face a linear inverse market demand of p = a – bQ, and have constant marginal costs of m per unit. Also assume that the market outcome is a Cournot-Nash equilibrium.

Firm 1’s profit function is 1  q1(a  b(q1  q2  ...  qn ))  mq1.

Firm 1 maximizes profit by first taking the derivative of their profit function with respect to their output (q1): d1  a  b(2q1  q2  ...  qn )  m. dq1

If all n firms are identical, then in equilibrium q1 = q2 = … = qn = q. Therefore, setting the first-order condition equal to zero and solving for q, q

am . ( n  1)b

Q

n(a  m) . (n  1)b

Total market supply is

Substituting this back into the inverse demand function and solving for p, you find the market price the price consumers pay before the tax is  a  mn  p .  n 1 

If markets with one or two firms charge prices (fees) that are essentially equal to the

 3 

maximum, then the state maximum must be no more than a  2m , which is the optimal price with n equal to 2, but if markets with more than two firms charge prices (fees) that

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 4 

are less than the maximum, then the state maximum must be greater than a  3m , which is the optimal price with n equal to 3.

2.6

The effect of a reduction in the number of producers in the Cournot model is to increase the price of the product being sold. Furthermore, assuming equal cost conditions in small and large cities and the reasonable assumption that large cities are likely to have more cement producers than small ones, the effect of a reduction in the number of producers will larger in small cities which will move closer to monopoly than in large cities.

2.7

The graph below shows response curves for the two airlines. The airline with the lower marginal cost produces more: Southwest transports Q1 passengers, and United Airlines transports Q2 passengers.

2.8

The profit for each of the two firms in this model is given by 𝜋𝑖 = (𝑝 − 𝑚) ∗ 𝑞. Since 𝑝 = (𝑎+2𝑚) 3

and 𝑞 =

(𝑎−𝑚) 3𝑏

, profit can be written as 𝜋𝑖 = [

this expression gives us [

(𝑎+2𝑚)

simplification gives 𝜋𝑖 = 2.9

(𝑎−𝑚)

− 3 ] ∗ [ 3𝑏 ] or [

3 (𝑎−𝑚)2 9𝑏

3𝑚

(𝑎+2𝑚)

3 𝑎+2𝑚−3𝑚 3

(𝑎−𝑚)

− 𝑚] ∗ [ 3𝑏 ]. Simplifying (𝑎−𝑚)

] ∗ [ 3𝑏 ]. Finishing off the

.

Beginning with Equation 11.3 in the text and substituting the new marginal cost levels, the best-response functions and output levels become qU = 119.5 − 1/2 qA qA = 69.5 − 1/2 qU qU = 113 qA = 13. .

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2.10 a. First, consider the Nash-Cournot equilibrium. Profit for Firm 1 is π = pQ1 − 20Q1 π = (120 − Q1 − Q2)Q1 − 20Q1.

Firm 1 maximizes profit by producing where marginal revenue equals marginal cost: 120 − 2Q1 − Q2 = 20.

Firm 1’s best-response function is Q1 = 50 − 0.5Q2.

Similarly, Firm 2’s best-response function is Q2 = 45 − 0.5Q1.

Substituting Firm 2’s best-response function into the best-response function for Firm 1 and solving for Q1, Q1 = 50 − 22.5 + 0.25Q1 0.75Q1 = 27.5 Q1 = 36.667 units.

Substituting this into the best-response function for Firm 2, Q2 = 26.667.

The market price is p = 120 − 36.667 − 26.667 = $56.667. Total market output is 63.333 units. b. When considering the collusive monopoly equilibrium, only Firm 1 will produce because its marginal cost is lower ($20 versus $30 per unit). The monopoly’s profit function will be π = (120 − Q)Q − 20Q. Setting marginal revenue equal to marginal cost, 120 − 2Q = 20 100 = 2Q Q = 50 units, all of which are to be produced by Firm 1. Price is p = 120 − 50 = $70.

2.11 When a firm or group of firms experiences an increase in cost, there will typically be upward pressure on prices. In the case of Delta and its fellow airlines, these cost increases resulted in an increase of 4%. The puzzle is that the jump in fuel prices was much bigger (33%), so why didn’t fares rise even more. The likely explanation has to do with the fact that Delta and its competitors need to compete not only amongst themselves for airline customers, but the airlines as a group are (even if not formally colluding) competing against other forms of transportation—driving, train, or even staying home. In other words, .

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the demand for air travel is far from perfectly inelastic so while an increase in cost may be passed on in some part to customers, much of the burden is on the firm in the form of tighter margins.

2.12 By differentiating its product, a firm makes the residual demand curve it faces less elastic everywhere. For example, no consumer will buy from a firm if its rival charges less and the goods are homogeneous. In contrast, some consumers who prefer this firm’s product to that of its rival will still buy from this firm even if its rival charges less. As the chapter shows, a firm sets a higher price the lower the elasticity of demand at the equilibrium.

2.13 Firm 1’s best-response function is q1 = 60 − 0.25q2.

Symmetrically, Firm 2’s best-response function is q2 = 60 − 0.25q1.

Substituting the best-response function for Firm 2 into the best-response function for Firm 1 and solving for q1, the equilibrium quantity for Firm 1 is 48 units. Symmetrically, the equilibrium quantity for Firm 2 is 48 units.

2.14 You can solve this problem using calculus or the formulas for the linear demand and constant marginal cost Cournot model from the chapter. a. For the duopoly, q1 = (15 − 2  2)/3 = 5, q2 = (15 − 4  1)/3 = 4, pd = 6, 1 = (6 − 1)5 = 25, 2 = (6 − 2)4 = 16. Total output is Qd = 5  4 = 9. Total profit is d = 25  16 = 41.

Consumer surplus is CSd  1/2(15  6)9  81/2  40.5. At the efficient price (equal to marginal cost of 1), the output is 14. The deadweight loss is DWLd  1/2(6 1)(14  9)  25/2 12.5.

b. A monopoly equates its marginal revenue and marginal cost: MR = 15 − 2Qm = 1 = MC. Thus, Qm = 7, pm = 8, m = (8 − 1)7 = 49. Consumer surplus is CSm  1/2 15  8 7  49/2 = 24.5. The deadweight loss is DWLm  1/2(8 1)(14  7)  49/2  24.5.

c. The average cost of production for the duopoly is [(5  1)  (4  2)]/(5  4) = 1.44, whereas the average cost of production for the monopoly is 1. The increase in market power effect swamps the efficiency gain, so consumer surplus falls while deadweight loss nearly doubles.

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BERTRAND OLIGOPOLY 3.1

A Nash-Bertrand equilibrium is a set of prices such that no firm can obtain a higher profit by choosing a different price if the other firms continue to charge these prices. If the products are identical, in any Nash-Bertrand equilibrium, the firms must charge the same price, or no one will buy from the high-price firm. This holds regardless of the number of firms because consumers will always purchase from the firm with the lowest price and the other firms will receive no sales. The result of this is that the Nash-Bertrand equilibrium price equals the marginal cost, as in the price-taking equilibrium. Knowing that rivals will set price equal to marginal cost, a firm would receive no sales if it charged a price above marginal cost. Firms have no incentive to charge less than marginal cost because they would incur losses.

3.2

Given that the duopolies produce identical goods, the equilibrium price is lower if the duopolies set price rather than quantity. If the goods are heterogeneous, we cannot answer this question definitively.

3.3

Assume the figure illustrates the best-response curves for two firms with differentiated products. These best-response curves initially intersect at e1. Then, suppose the demand curve for Firm 1 shifts to the right.

The best-response curves show the price each firm picks to maximize its profit, given its belief about its rival’s price. As demand for Firm 1’s product increases, Firm 1’s bestresponse curve shifts to the right. The Nash-Bertrand equilibrium occurs at the intersection of the best-response curves (at e2). At this point, the new equilibrium price for Firm 1 is higher, and the new equilibrium price for Firm 2 is higher.

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3.4

Firm 1 wants to maximize its profit: π1 = (p1 − 10)q1 = (p1 − 10)(100 − 2p1 + p2).

Its first-order condition is dπ1/dp1 = 100 − 4p1 + p2 + 20 = 0, so its best-response function is p1  30  14 p2 . Similarly, Firm 2’s best-response function is p2  30  14 p1. Solving, the Nash-Bertrand equilibrium prices are p1 = p2 = 40. Each firm produces 60 units.

3.5

This problem is solved using the same methodology as in the previous two questions, except that now the response functions are asymmetric due to the difference in marginal cost. The best-response functions are p1 = 40  0.25p2 p2 = 30  0.25p1, and the new equilibrium prices are p1 = 50.67, p2 = 42.67.

3.6

The degree of profitability in a Bertrand market is directly related to the degree of product differentiation (more differentiation = more profit). This differentiation can be real or imaginary. In this instance if both Coke and Pepsi are bottling tap water, the differentiation would fall into the imaginary category created by advertising. Nonetheless, the effect on profits is the same (and may make the advertising expenditures pay off).

3.7

a. Assuming that the newly merged firm will exercise its new monopoly power, surplus will definitely fall. .

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b. If MC falls for the newly merged firm, then even though there is a deadweight loss relative to a competitive industry with the new (lower) marginal cost, the monopoly solution may be generate more surplus than the original industry did with the higher MC. See the figure below for an extreme example.

3.8 It’s possible that the lower costs cited in the problem are the answer, though we cannot say for sure without knowing about possible efficiencies in the proposed Staples/Office Depot merger. If costs are lower, then we might see higher surplus even though the market becomes less competitive (see problem 2.14).

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MONOPOLISTIC COMPETITION 4.1

Because firms must bear part of the burden of the tax, profits are reduced. With each firm earning smaller profits, beginning from a point where all firm profits are zero, some firms must exit the industry to restore equilibrium.

4.2

In monopolistic competition, free entry drives profits to zero for the marginal firm in the long run. If firms have identical costs and produce a homogeneous good, all firms earn zero profits. However, even with free entry, firms face downward-sloping demand curves and are therefore able to charge prices that exceed marginal costs. One important reason why demand curves slope downward is that firms may sell differentiated products. As a result, in the long-run equilibrium, a monopolistically competitive firm operates where its downward-sloping demand curve is tangent to its average cost curve. The government subsidy reduces the fixed cost of production, pivoting each firm’s average cost curve down.

The market returns to a long-run equilibrium when firms again earn zero profit. This occurs after new firms enter the industry, shifting individual firm demand curves to the left until they are tangent to the new average cost curve with the subsidy. At the new long-run equilibrium, individual firm prices are lower (because the tangency point between the new demand and new average cost curves is lower).

4.3

With competition, if firms produce identical products, then they’ll have horizontal demand curves, and it will be possible to produce at full capacity. However, if the firm produces a differentiated product, then it will have a downward-sloping demand curve (representing the demand for its brand of the product), and the firm will not produce at full capacity.

4.4

Monopolistic competition is a market structure that has the price setting characteristics of monopoly or oligopoly and the free entry characteristic of perfect competition. In monopolistic competition, free entry drives profits to zero for the marginal firm in the long run. If firms have identical costs and produce a homogeneous good, all firms earn zero profits. However, even with free entry, firms face downward-sloping demand curves and are therefore able to charge prices that exceed marginal costs. One important reason why demand curves slope downward is that firms may sell differentiated products. However, it is possible that, even with homogeneous products, the number of firms is small enough that firms face downward-sloping firm-specific demand curves. As a result, in the long-run equilibrium, a monopolistically competitive firm operates where its downward-sloping demand curve is tangent to its average cost curve. Because its demand curve is downward sloping, its average cost curve must also be downward sloping in the equilibrium.

4.5

The restriction on the number of scooter companies will reduce the quantity of scooter rentals, raise the price, increase the profits of the scooter companies that already exist, and lower both consumer and overall surplus compared to a situation with no restriction on the number of firms.

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MANAGERIAL PROBLEM 5.1

a. The Cournot equilibrium in the absence of a government intervention is q1 = 30, q2 = 40, p = 50, π1 = 900, and π2 = 1,600. b. The Cournot equilibrium is now q1 = 33.3, q2 = 33.3, p = 53.3, π1 = 1,108.9, and π2 = 1,108.9.

5.2

As Firm 2’s profit was 1,600 in Question 5.1, a fixed cost slightly greater than 1,600 will prevent entry.

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SPREADSHEET EXERCISES Solutions provided in MyLab Economics

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CHAPTER 12 GAME THEORY AND BUSINESS STRATEGY SOLUTIONS TO END-OF-CHAPTER QUESTIONS

OLIGOPOLY GAMES

1.1

The payoff matrix in this prisoners’ dilemma game is Duncan Squeal Stay Silent −2 −5 Squeal 0 −2 Larry 0 −1 Stay Silent −5 −1 If Duncan stays silent, Larry gets 0 if he squeals and −1 (a year in jail) if he stays silent. If Duncan confesses, Larry gets −2 if he squeals and −5 if he does not. Thus, Larry is better off squealing in either case, so squealing is his dominant strategy. By the same reasoning, squealing is also Duncan’s dominant strategy. As a result, the Nash equilibrium is for both to confess.

1.2

A best response is the strategy that maximizes a player’s payoff given its beliefs about its rivals’ strategies. A dominant strategy is a strategy that produces a higher payoff than any other strategy the player can use no matter what its rivals do. If Firm 2 does not advertise, then Firm 1 should not advertise, and if Firm 2 advertises, then Firm 1 should not advertise.

Thus, Firm 1’s dominant strategy is to not advertise. If Firm 1 does not advertise, then Firm 2 should advertise, and if Firm 1 advertises, then Firm 2 should advertise. Thus, Firm 2’s dominant strategy is to advertise.

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibrium is for Firm 1 to not advertise and for Firm 2 to advertise. If either firm changes their behavior, their payoff will decrease. At the Nash equilibrium, both firms are following their dominant strategy.

1.3

If the payoff to Firm 1 in the Advertise/Advertise cell changes from 1 to 3, then both firms will want to advertise and this will be the new, unique Nash equilibrium.

1.4

Firm 2 wants to match Firm 1’s price, but Firm 1 does not want to match Firm 2’s price.

Instead, Firm 1’s dominant strategy is to always pick the high price. (Firm 2 does not have a dominant strategy because their best response is to pick the low price when Firm 1 picks the low price and to pick the high price when Firm 1 picks the high price.) In turn, the Nash equilibrium is for Firm 1 to pick the high price (which is its dominant strategy) and for Firm 2 to match by picking the high price. If either firm changes its behavior, then its payoff decreases. For example, if Firm 1 instead picks the low price, then its payoff 266

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decreases by 1 from 7 to 6. If Firm 2 instead picks the low price, then its payoff decreases by 5, from 6 to 1.

1.5

There is no change in the Nash equilibrium.

1.6

We start by checking for dominant strategies. Given the payoff matrix, Toyota always does at least as well by entering the market. If GM enters, Toyota earns 10 by entering and 0 by staying out of the market. If GM does not enter, Toyota earns 250 if it enters and 0 otherwise. Thus, entering is Toyota’s dominant strategy. GM does not have a dominant strategy. It wants to enter if Toyota does not enter (earning 200 rather than 0), and it wants to stay out if Toyota enters (earning 0 rather than −40). Because GM knows that Toyota will enter (entering is Toyota’s dominant strategy), GM stays out of the market. Toyota’s entering and GM’s not entering is a Nash equilibrium. Given the other firm’s strategy, neither firm wants to change its strategy. Next, we examine how the subsidy affects the payoff matrix and dominant strategies. The subsidy does not affect Toyota’s payoff, so Toyota still has a dominant strategy: It enters the market. With the subsidy, GM’s payoff if it enters increases by 50: GM earns 10 if both enter and 250 if it enters and Toyota does not. With the subsidy, entering is a dominant strategy for GM. Thus, both firms’ entering is a Nash equilibrium.

1.7

According to the mini-case, advertising in the cola market has almost no effect on the size of the market (does not bring in new customers). The ads run by Coke and Pepsi only serve to steal customers from one another. This is similar to a prisoner’s dilemma game.

1.8

(Suppose the payoff for Firm 1 when picking low and Firm 2 picks high is 7, so there won’t be any ties.) A best response is the strategy that maximizes a player’s payoff given its beliefs about its rivals’ strategies. If Firm 2 picks low, then Firm 1 should pick high; if Firm 2 picks medium, then Firm 1 should pick high; and if Firm 2 picks high, then Firm 1 should pick low.

If Firm 1 picks low, then Firm 2 should pick medium; if Firm 1 picks medium, then Firm 2 should pick high; and if Firm 1 picks high, then Firm 2 should pick low.

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibrium is for Firm 1 to pick high and for Firm 2 to pick low. If either firm changes their behavior, their payoff will decrease. The other outcomes are not Nash equilibria because at least one of the two firms could pick another level and increase their payoff.

1.9

(Suppose the payoff for Firm 1 when picking medium and Firm 2 picks high is 7, so there won’t be any ties and so that there will be a Nash equilibrium). A best response is the strategy that maximizes a player’s payoff given its beliefs about its rivals’ strategies. If Firm 2 picks low, then Firm 1 should pick medium; if Firm 2 picks medium, then Firm 1 should pick high; and if Firm 2 picks high, then Firm 1 should pick medium.

If Firm 1 picks low, then Firm 2 should pick medium; if Firm 1 picks medium, then Firm 2 should pick high; and if Firm 1 picks high, then Firm 2 should pick low.

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A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibrium is for Firm 1 to pick medium and for Firm 2 to pick high. If either firm changes their behavior, their payoff will decrease. The other outcomes are not Nash equilibria because at least one of the two firms could pick another level of quality and increase their payoff.

1.10 The chapter gives two examples of two-sided or matching markets, credit cards and online dating sites, but there are many more examples in the economy. Some of the more famous examples discussed by Alvin Roth, one of the leading economists studying matching markets (and recipient of the 2012 Nobel Memorial Prize in Economic Sciences) are organ donation/exchanges, school choice, and marriage “markets.” All of these examples are cases where there are individuals on both sides of the market with preferences about their match. This is in contrast to single-side markets where, for example, a seller is happy to sell their goods to whoever enters their shop.

The organ donation problem is a natural example of a matching market because there a biological and physiological reasons why organ recipients need to be matched with specific donors and vice versa (blood type, etc.). In school choice markets (whether in public school programs, placing medical students into residency programs, business majors into internships, or even new graduates with potential employers), the problem is one to find the best fit where both sides have preferences over the outcome. Finally, in an extension of the online dating example mentioned in the book, the search for a marriage partner is one in which both sides are looking for “the one.” In some cultures, this problem is solved by an actual market exchange, but in the west, searchers typically look for a match via trial and error.

1.11 These two examples (credit cards in Table <CORE>12.</CORE>4 and online dating in Table <CORE>12.</CORE>5) are quite different.

In the credit card example, the Nash equilibrium is for both Visa and Mastercard to select Unbalanced because they each have a dominant strategy to pick Unbalanced over Balanced. There is, however, a Pareto improving outcome if both firms were to pick Balanced so given the opportunity to collude I would expect these firms to at least attempt to reach the higher payoffs in the Balanced/Balanced outcome. How successful they will be depends on whether they can make an enforceable agreement, something that is made much easier via a merger.

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In the online dating example, things are different. Both eHarmony and Match.com have a dominant strategy to play Balanced and so the Nash equilibrium is Balanced/Balanced which results in payoffs of 7 each. Neither firm can improve their payoff by making a unilateral changed (which is essentially the definition of a Nash equilibrium) but, in addition, there is no Pareto improving outcome that they might want to try to coordinate on, so allowing collusion/merger will not change the outcome in this game.

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TYPES OF NASH EQUILIBRIA 2.1

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibria are for Network 1 to schedule on Wednesday and Network 2 to schedule on Thursday and for Network 1 to schedule on Thursday and for Network 2 to schedule on Wednesday. If either firm changes their behavior, their payoff will decrease. In particular, if either network instead schedules on the same day as the other network, then their payoff will become negative.

2.2

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibria are for Network 1 to schedule on Wednesday and Network 2 to schedule on Thursday and for Network 1 to schedule on Thursday and for Network 2 to schedule on Wednesday. If either network changes their behavior, their payoff will decrease. In particular, if either network instead schedules on the same day as the other network, then their payoff will become negative.

Cheap talk is communication before the game starts, but the communication does not directly affect the payoffs of the game. Cheap talk does not mean that firms can agree in advance on their strategies. In a real-world, noncooperative game, firms may not make binding agreements. A firm might make a cheap-talk claim but then do something different. In this game, however, the networks have an incentive to be truthful, so the cheap talk is credible. Each network wants the other to know its actual choice and therefore has an incentive to truthfully reveal its intentions and follow through accordingly. For example, if Network 1 announces in advance that it will broadcast on Wednesday, Network 2 will choose Thursday, and both networks will benefit from communicating.

2.3

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibria are for Network 1 to schedule on Wednesday and Network 2 to schedule on Thursday and for Network 1 to schedule on Thursday and for Network 2 to schedule on Wednesday. If either network changes their behavior, their payoff will decrease. In particular, if either network instead schedules on the same day as the other network, then their payoff will become negative.

When a game has multiple Nash equilibria, it is possible that one of the Nash equilibria provides a higher payoff to all players than the other Nash equilibria. If so, we expect firms acting independently to choose strategies that lead to that outcome even without communicating. Selecting an outcome that is better for all parties is called the Pareto Criterion. In this game, however, the Nash equilibrium where Network 1 schedules on Wednesday and Network 2 schedules on Thursday is better for Network 2 relative to when Network 1 schedules on Thursday and Network 2 schedules on Wednesday. Similarly, the Nash equilibrium where Network 1 schedules on Thursday and Network 2 schedules on Wednesday is better for Network 1 relative to when Network 1 schedules on Wednesday and Network 2 schedules on Thursday.

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2.4

Yes, two stations are both better off if they time their ads to play at the same time than if they play at different times.

2.5

The firms do not have dominant strategies, and the game does not have a pure-strategy Nash equilibrium.

A mixed strategy is one in which each player chooses among possible actions according to probabilities it assigns. Equate expected payoffs to determine the mixed-strategy equilibrium. In particular, if Firm 2 picks the low price with probability θ2, Firm 1’s expected payoff (EP) from picking the low price is EP(Low) = 7 − 7θ2 and Firm 1’s expected payoff from picking the high price is EP(High) = 2θ2 + 6(1 − θ2) EP(High) = 6 − 4θ2.

Firm 1’s expected payoffs are equal when 7 − 7θ2 = 6 − 4θ2 1 = 3θ2 θ2 = 0.333.

Similarly, if Firm 1 picks the low price with probability θ1, then Firm 2’s expected payoff from picking the low price is EP(Low) = 2θ1 + (1 − θ1) EP(Low) = 1 + θ1, and Firm 2’s expected payoff from picking the high price is EP(High) = 6 − 6θ1.

Firm 2’s expected payoffs are equal when 1 + θ1 = 6 − 6θ1 7θ1 = 5 θ1 = 0.714.

Thus, the mixed-strategy Nash equilibrium is for Firm 1 to pick the low price with probability 0.714 and for Firm 2 to pick the low price with probability 0.333.

2.6

In this modified game, Firm 1 has a dominant strategy to pick High Price. Firm 2 can recognize this dominance and will, in turn, play High Price as well. There is a single Nash equilibrium where both firms play High Price. There are no (non-degenerate) mixed strategy Nash equilibira.

2.7

The payoff matrix is shown below. Given these payoffs, mixed strategies are required.

There is no Nash equilibrium because in any given cell, the outcome (winner) changes if one player changes strategies. Thus, in any given cell, the loser would always prefer to switch given the opponent’s strategy. .

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Suppose the payoff is 1 if you win, 0 if you tie, and −1 if you lose. The payoff matrix will be the following: Sotheby’s Rock Paper Scissors Rock 0, 0 −1, 1 1, −1 Paper 1, −1 0, 0 −1, 1 Christie’s Scissors −1, 1 1, −1 0, 0 Assuming the 11-year-old girls provide the correct insight and the rival would be very likely to take their advice (of selecting scissors), then a pure strategy of rock should be recommended (assuming the rival didn’t know that we knew their consultation with the girls).

2.9

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. A pure strategy is one where each player chooses a single action. This game does not have a pure-strategy Nash equilibrium. For example, it is not a Nash equilibrium for Mimi to support and Jeff to look for work because Jeff can increase his payoff by instead loafing. It is not a Nash equilibrium for Mimi to support and Jeff to loaf because Mimi can increase her payoff by not supporting instead. It is not a Nash equilibrium for Mimi to not support and Jeff to look for work because Mimi can increase her payoff by instead supporting. Finally, it is not a Nash equilibrium for Mimi to not support and Jeff to loaf because Jeff can increase his payoff by instead looking for work.

A mixed strategy is one in which each player chooses among possible actions according to probabilities it assigns. Equate expected payoffs to determine the mixed-strategy equilibrium. In particular, if Mimi provides support with probability θM, Jeff’s expected payoff (EP) from looking for work is EP(Looking) = 1 + θM and his expected payoff from loafing is EP(Loafing) = 4θM. His expected payoffs are equal when θM = 0.333.

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Similarly, if Jeff looks for work with probability θJ, then Mimi’s expected payoff from supporting him is EP(Supporting) = 5θJ – 1 and her expected payoff from not supporting is EP(Not Supporting) = -θJ. Her expected payoffs are equal when θJ = 0.167.

2.10 Lori will offer no bonus, and Max will loaf, which are the players’ dominant strategies.

This game does not have a mixed-strategy Nash equilibrium because the players have dominant strategies. (In Question 2.7, the players did not have dominant strategies.)

2.11 A Nash equilibrium is a set of strategies such that, holding the strategies of all other firms constant, no firm can obtain a higher profit by choosing a different strategy. A mixed strategy is one in which each player chooses among possible actions according to probabilities it assigns. Equate expected payoffs to determine the mixed-strategy equilibrium. In particular, if Firm 2 does not enter with probability θ2, Firm 1’s expected payoff (EP) from not entering is EP(Don’t enter) = 0θ2 + 0(1 − θ2) EP(Don’t enter) = 0 and Firm 1’s expected payoff from entering is EP(Enter) = θ2 + (−2)(1− θ2) EP(Enter) = 3θ2 − 2.

Firm 1’s expected payoffs are equal when EP(Don’t enter) = EP(Enter) 0 = 3θ2 − 2 3θ2 = 2 θ2 = 0.667.

Similarly, if Firm 1 does not enter with probability θ1, then Firm 2’s expected payoff from not entering is EP(Don’t enter) = 0θ1 + 0(1 − θ1) EP(Don’t enter) = 0 and Firm 2’s expected payoff from entering is EP(Enter) = θ1 + (−2)(1− θ1) EP(Enter) = 3θ1 − 2.

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Firm 2’s expected payoffs are equal when EP(Don’t enter) = EP(Enter) 0 = 3θ1 − 2 3θ1 = 2 θ1 = 0.667.

Thus, the mixed-strategy Nash equilibrium is when both firms enter with probability 0.333.

2.12 A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. A pure strategy is one where each player chooses a single action. This game has two Nash equilibria: for Amazon and the other group to select the AZW format, and for Amazon and the other group to select the EPUB format. If Amazon and the other group both select the AZW standard, then if either player selects the other format, their payoff will become negative. Similarly, if Amazon and the other group both select the EPUB standard, then if either player selects the other format, their payoff will become negative. The other outcomes are not Nash equilibria. If Amazon and the other group select different formats, then either player can instead select the same format as the other player to make their payoff positive.

A mixed strategy is one in which each player chooses among possible actions according to probabilities it assigns. Equate expected payoffs to determine the mixed-strategy equilibrium. In particular, if Amazon selects the AZW format with probability θA, the other group’s expected payoff (EP) from selecting the AZW format is EP(AZW) = 3θA + (−1)(1 − θA) EP(AZW) = 4θA − 1 and the other group’s expected payoff from selecting the EPUB format is EP(EPUB) = −1θA + 2(1 − θA) EP(EPUB) = −3θA + 2.

The other group’s expected payoffs are equal when EP(AZW) = EP(EPUB) 4θA − 1 = −3θA + 2 7θA = 3 θA = 0.429.

Similarly, if the other group selects the AZW format with probability θO, then Amazon’s expected payoff from selecting the AZW format is EP(AZW) = 3θO + (−1)(1 − θO) EP(AZW) = 4θO − 1

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and Amazon’s expected payoff from selecting the EPUB format is EP(EPUB) = −1θO + 2(1 − θO) EP(EPUB) = −3θO + 2.

Amazon’s expected payoffs are equal when EP(AZW) = EP(EPUB) 4θO − 1 = −3θO + 2 7θO = 3 θO = 0.429.

Therefore, the mixed-strategy Nash equilibrium is for Amazon to select the AZW format with probability 0.429 and the other group to select the AZW format with probability 0.429.

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INFORMATION AND RATIONALITY 3.1

a. A dominant strategy is a strategy that produces a higher payoff than any other strategy the player can use no matter what its rivals do. If Guys does not invest, then Blues Bros. should invest, and if Guys invests, then Blues Bros. should invest. Thus, Blues Bros.’s dominant strategy is to invest. If Blues Bros. does not invest, then Guys should not invest, and if Blues Bros. invests, then Guys should invest. Thus, Guys does not have a dominant strategy. b. A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibrium is for Blues Bros. and Guys to invest. If either firm changes their behavior, their payoff will decrease. For example, if Blues Bros. instead does not invest, then their payoff will change by –$10. If Guys instead does not invest, then their payoff will change by –$20. c.A maximin strategy maximizes the minimum payoff. This approach ensures the best payoff if your rival takes the action that is worst for you. Blues Bros. avoids a payoff of $0 by investing. Guys avoids a payoff of –$100 by not investing. So, Blues Bros. investing and Guys not investing is the maximin outcome.

3.2

A dominant strategy is a strategy that produces a higher payoff than any other strategy the player can use no matter what its rivals do. If Guys does not invest, then Blues Bros. should not invest, and if Guys invests, then Blues Bros. should invest. Thus, Blues Bros. does not have a dominant strategy. If Blues Bros. does not invest, then Guys should not invest, and if Blues Bros. invests, then Guys should invest. Thus, Guys does not have a dominant strategy either.

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibria are for Blues Bros. and Guys to invest and for Blues Bros. and Guys to not invest. If either firm changes their behavior, their payoff will decrease. For example, if Blues Bros. and Guys both do not invest, then if either instead invests, their payoff will become negative. If Blues Bros. and Guys both invest, then if either instead does not invest, their payoff will become zero.

A maximin strategy maximizes the minimum payoff. This approach ensures the best payoff if your rival takes the action that is worst for you. Blues Bros. avoids a payoff of –$5 by not investing. Guys avoids a payoff of –$100 by not investing. So, Blues Bros. not investing and Guys not investing is the maximin outcome.

3.3

In the second case (Problem 3.2), both firms face a coordination problem and a merger would help them solve this problem and coordinate on the “better” Nash equilibrium (where they both invest).

3.4

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibrium is for Harrison and Julie to invest. If either firm changes their behavior, their payoff will decrease. For example, if Harrison instead does not invest, then his payoff will change from $6 to $0. If Julie instead does not invest, then her payoff will change from $10 to $0. .

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Managers can use several methods to solve coordination problems. One approach is through merger or acquisition. Julie and the manager could form a joint venture such that they jointly invest in the marketing. In this case, however, Harrison already has sufficient incentive to invest, so adding penalties for not investing or using the Pareto Criterion would not seem to be necessary. Pregame communication with cheap talk could also help.

3.5

SSOs are particularly helpful in games with incomplete information/uncertainty. Since the choice of a standard can be very costly, firms would like to avoid picking a technology that will not be supported by the rest of the industry leading to costly changes down the road.

This is particularly true when some part of the game is unknown to a firm. An SSO allows managers and firms to engage in pre-play communication that can help resolve the uncertainty and reassure managers that others in their industry see the same incentives.

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BARGAINING 4.1

Initially, the Nash product (NP) is NP = (12 − p)(p − 10).

The p that maximizes the Nash product is

NP = 12 − p − (p − 10) p 12 − p − (p − 10) = 0 2p = 22 p = $11 thousand.

If instead Bo can only get $9 (thousand) elsewhere, the Nash product is NP = (12 − p)(p − 9), and the p that maximizes the Nash product is

NP = 12 − p − (p − 9) p 12 − p − (p − 9) = 0 2p = 21 p = $11.5 thousand.

Thus, the price that maximizes the Nash product changes by –$.5 thousand, which is in Jane’s favor because she pays less for the car.

4.2

The Nash product is NP = (50 – p)(p – 10), and the p that maximizes the Nash product is

NP = 50 – p – (p – 10) p 50 – p – (p – 10) = 0 2p = 60 p = $30 million.

4.3

In Nash bargaining, the price that maximizes the Nash product is designed to maximize the net surplus for the parties without either party having a negative payoff. However, negotiations may fail to quickly reach an agreement due to bounded rationality, irrational behavior, or incomplete information about the other side’s payoffs. The parties may be doing the best they can but are unable to determine the best possible strategies, and therefore, they make mistakes.

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4.4

The generalize Nash product is

We maximize this Nash product by taking the derivative with respect to p and setting it equal to zero. This gives us

This last expression implies that p = 50 is the price that maximizes the generalized NP. If, on the other hand, a = 0 then the manufacturer holds all of the bargaining power and therefore will extract all of the profit.

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AUCTIONS 5.1

An auction is a sale in which a good or service is sold to the highest bidder. Auction goods are normally described as having private value or common value. If each potential bidder places a different personal value on the good, we say the good has a private value. Many auctions involve a good that has the same fundamental value to everyone, but no buyer knows exactly what that common value is. Celebrity dates have private values. When the auction item is private value, the best strategy with open bids is to raise the current bid as long as your bid is less than the value you place on the good, and the best strategy with sealed bids is to shave your bid to less than the value you place on the good to an amount equal to or slightly greater than what you expect will be the second-highest bid, given that your value is the highest. Thus, secret and open bids are expected to raise the same amount of money when the bidders have private values for the auction item. Formally, for private value auction items, the winner is the person with the highest value, and the winner pays roughly the second-highest value.

5.2

This is a private-value auction because each potential bidder places a different personal value on the good. The expected price in a private-value auction is the value of the good to the person who values it second highest. The price differs each night, probably because the audience and their valuations are different each night. The fact that the proceeds go to charity increases the auction price.

5.3

In a sealed-bid second-price auction bidding your value weakly dominates all other bidding strategies, that bidding your value leaves you as well off as, or better off than, bidding any other value. Therefore, Alpha should bid its value for the land, which is $1.3 million, Richardson should bid its value of $1.05 million, and K-Tek should bid its value which is $950,000. With these bids, Alpha will win the auction with a bid of $1.3 million. Since the auction is second-price, they will not pay $1.3 but rather the amount of the next highest bid which, in this case, is $1.05 million (from Richardson). Alpha will earn a surplus of $250,000 and the other two firms will get zero.

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MANAGERIAL PROBLEM 6.1

A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. The Nash equilibrium is for Firm 1 not to invest and for Firm 2 not to invest. If either firm instead invests, then their payoff will decrease from $200 to $100.

Cheap talk is communication before the game starts, but the communication does not directly affect the payoffs of the game. Cheap talk does not mean that firms can agree in advance on their strategies. In a real-world, noncooperative game, firms may not make binding agreements. A firm might make a cheap-talk claim but then do something different. In this game, the firms do not have an incentive to be truthful, so the cheap talk is not credible. This is because each firm has a dominant strategy, which is to not invest, regardless of whether the other firm invests. For example, if both firms invest, then either firm could instead not invest and increase their payoff from $225 to $250.

It will be a Nash equilibrium for both firms to invest if, at that outcome, neither firm has an incentive not to invest. In particular, if the government sets the fine at $25, then neither firm can increase their payoff by instead not investing because the payoff of $250 minus the $25 fine will not be more than the payoff of $225 from investing.

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SPREADSHEET EXERCISES Solutions available in MyLab Economics

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CHAPTER 13 STRATEGIES OVER TIME SOLUTIONS TO END-OF-CHAPTER QUESTIONS REPEATED GAMES 1.1

a. There are two Nash equilibria (the off diagonals). If either firm produces 20 while the other produces 10, neither player has an incentive to change strategies given the strategy of the other player. b. If Firm 1 moves first and picks Q = 10, then Firm 2 will pick Q = 20, and Firm 1’s profit will be $50. If Firm 1 moves first and picks Q = 20, then Firm 2 will pick Q = 10, and Firm 1’s profit will be $40. Profit of $50 is greater than $40, so Firm 1 will pick Q = 10, and Firm 2 will pick Q = 20.

c. If Firm 2 moves first and picks Q = 10, then Firm 1 will pick Q = 20, and Firm 2’s profit will be $60. If Firm 2 moves first and picks Q = 20, then Firm 1 will pick Q = 10,

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and Firm 2’s profit will be $35. Profit of $60 is greater than $35, so Firm 2 will pick Q = 10, and Firm 1 will pick Q = 20.

1.2

If the discount rate of firms is sufficiently high, which implies that the firms only care about their current profit and do not care about the future possible punishment, they will not collude, and we will still get the inefficient prisoner’s dilemma outcome.

1.3

a. If the game is repeated indefinitely, then collusion is more likely than in a single-period game. This is because in an infinitely repeated game, a firm can influence its rival’s behavior by signaling and threatening to punish the other firm for cheating on a cartel agreement. b. If the game is repeated a finite number of periods, then the Nash equilibrium is likely to result as in a single-period game. This is because punishment for cheating on the cartel agreement cannot be imposed after the last period. Consequently, the last period will not have cooperation and will result in the competitive Nash equilibrium. By the same reasoning, punishment for cheating on the cartel agreement cannot be imposed in the second-to-last period (because the last period will have the competitive outcome).

Continuing with this type of argument, maintaining an agreement will be difficult if the game has a stopping point. c. If the game is repeated a finite number of times, but the firms are unsure as to which period will be the last, then the game will be treated as if it were played infinitely (because the players will not know when the last period is). As with games repeated indefinitely, collusion is more likely than in a single-period game. This is because firms can signal and threaten to punish for cheating on a cartel agreement.

1.4

a. A Nash equilibrium is a set of strategies such that, holding the strategies of all other firms constant, no firm can obtain a higher profit by choosing a different strategy. The Nash equilibrium is for both restaurants to advertise. If either restaurant instead does not advertise, then their payoff decreases by $1, from a payoff of $1 when advertising, to a payoff of $0 from not advertising.

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b. When repeated indefinitely, a Nash equilibrium is any set of strategies where each restaurant won’t advertise unless the other restaurant advertises, in which case the restaurant will then advertise for at least one month. c. A firm does not have to punish its rival forever to induce it to cooperate. All it has to do is punish it for enough periods that it does not pay to cheat in any one period. The benefit from advertising when the other restaurant does not advertise is $4, from a payoff of $3 when neither restaurant advertises to a payoff of $1 from both restaurants advertising. The cost of the punishment for the firm who first cheats is $2 per month, from a payoff of $3 from colluding to a payoff of $1 when both restaurants advertise.

For the cost of cheating ($2) to be greater than (or equal to) the benefit from cheating ($1), such that it does not pay to cheat, the punishment must be imposed for at least one month. d. If the game is not repeated, then pre-play communication (to achieve the outcome where both firms do not advertise) is not credible because both players have a dominant strategy, which is to advertise. Advertising is best for both firms regardless of what the other firm does. This also limits the effectiveness of using the Pareto criterion.

However, if the game is played an infinite number of times, then pre-play communication or the Pareto criterion could be used to get both firms to not advertise.

In an infinitely-repeated game, this outcome would be optimal.

1.5

a. In this new version of the game there are 2 pure-strategy Nash equilibria – one where both Romano’s and Giardino’s do not advertise and one where they do. b. Since the new game is not a prisoner’s dilemma the problem is not how to sustain the cooperative outcome as an equilibrium, but how to coordinate on the ‘best’ equilibrium. c. The game will have multiple equilibria if played indefinitely – one in which each of the static equilibria will be played forever, one in which the firms bounce back in forth, and likely others as well. Again, however, this isn’t the real problem in the modified game.

The difficulty is coordination as discussed in part (d). d. The Pareto criterion will point to the equilibrium in which both firms do not advertise as the likely outcome. Pre-play communication could help each firm reassure the other that they know which equilibria is best for both.

1.6

By not shooting at the enemy a soldier creates the potential for tacit collusion in which neither side shoots at the other. This will likely lead to an outcome in which soldiers on both sides survive as opposed to the case where both sides shoot to kill, with many casualties as the result.

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1.7

Tacit collusion is when two or more firms agree to play a certain strategy (like keeping prices high / avoid undercutting one another) without explicitly making an agreement. One example of this kind of behavior is price leadership in which one firm acts as the ‘traffic cop’ in the market and the other firms fall in line behind them. Typically this occurs with the largest / strongest firm in the market taking charge. The weaker firms know they are better off tagging along with the strong firm than trying to go head-to-head and likely losing. There are cases, airline ticket pricing being one, in which price leadership seems to rotate with no real permanent leader. Airline ticket pricing is often characterized by one firm (not always the same one) very publicly announcing a change in prices and giving their competitors a reason to do the same.

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SEQUENTIAL GAMES 2.1

A set of strategies forms a subgame perfect Nash equilibrium if the players’ strategies are a Nash equilibrium in every subgame. If Firm 1 produces 180 units, then Firm 2 should produce 64 units for profit of $72, which gives Firm 1 profit of $54. If Firm 1 produces 240 units, then Firm 2 should produce 64 units for profit of $58, which gives Firm 1 profit of $58. If Firm 1 produces 360 units, then Firm 2 should produce 48 units for profit of $32, which gives Firm 1 profit of $64. Since profit of $64 is greater than profit of $54 and profit of $58, Firm 1 should produce 360 units. Joint profit maximization occurs when Firm 1 produces 180 units and Firm 2 produces 48 units. Joint profit, when maximized, is $130. At any other outcome, joint profits are lower. For example, when Firm 1 produces 180 units and Firm 2 produces 64 units, joint profit is $126. When Firm 1 produces 240 units and Firm 2 produces 64 units, joint profit is $116. Given that Firm 1 is producing 180 units, Firm 2 has an incentive to produce 64 units instead for profit of $72 instead of a profit of $65 from producing 48 units.

2.2

First we determine the Nash-Cournot equilibrium. The inverse demand curve is p = 1 – 0.001Q. The first firm’s profit is π1 = [1 – 0.001(q1 + q2)]q1 – 0.28q1. Its first-order condition is dπ1/dq1 = 1 – 0.001(2q1 + q2) – 0.28 = 0. If we rearrange the terms, the first firm’s best-response function is q1  360  12 q2 . Similarly, the second firm’s best-response function is q2  360  12 q1. By substituting one of these best-response functions into the other, we learn that the Cournot-Nash equilibrium occurs at q1 = q2 = 240, so the total output is 480, and the equilibrium price is 52¢. Next we determine the Stackelberg equilibrium. In this case Firm 1 substitutes the best response function of Firm 2 into Firm 1’s profit function: π1 = [1 – 0.001(q1 + (360 – ½ q1)]q1 – 0.28q1. Taking the derivative of this profit function and setting it to zero yields dπ1/dq1 = 0.36 – 0.001q1 = 0 or q1 = 360.

Therefore q2 = 360 – ½ (360) = 180. The total Stackelberg output is 360 + 180 = 540, which exceeds the Cournot output of 480. The Stackelberg price is 1 – 0.001(540) = $0.46 or 46¢, which is lower than the Cournot price. Relative to the Cournot case, profit is higher for the leader and lower for the follower and aggregate profits are lower in the Stackelberg case.

2.3

Inverse demand in this case is given by 𝑝 = 40 − 0.1(𝑞𝐴 + 𝑞𝐵 ) where 𝑞𝐴 and 𝑞𝐵 denote the output for firm A and B respectively. Firm B’s profit is: 𝜋𝐵 = (40 − 0.1𝑞𝐴 − 0.1𝑞𝐵 )𝑞𝐵 − 20𝑞𝐵 which can be simplified to 𝜋𝐵 = 20𝑞𝐵 − 0.1𝑞𝐴 𝑞𝐵 − 0.1𝑞𝐵2 . The first 𝜕𝜋

order condition for Firm B’s optimization is 𝜕𝑞 = 20 − 0.1𝑞𝐴 − 0.2𝑞𝐵 = 0 which can be 𝐵

solved for Firm B’s best-response function 𝑞𝐵 = 100 − 0.5𝑞𝐴 . Firm A has a symmetric best-response function of 𝑞𝐴 = 100 − 0.5𝑞𝐵 .

Solving these two best-response functions simultaneously gives us the Nash-Cournot solution of 66.7 units for each firm. To solve for the Stackelberg outcome substitute Firm B’s best-response function into Firm A’s profit function and maximize. This gives Firm A’s optimal output as 100 and Firm B’s response as 50. Finally, if the two firms collude

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they each produce half of the monopoly outcome (which is 100), so they each produce 50 units.

Here is a diagram for Firm B’s best-response function showing these outcomes.

2.4

Here is a screen shot of the relevant spreadsheet. Note that when Firm A sets output equal to 100 their profit is maximized (at $500).

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2.5

a.A dominant strategy is a strategy that produces a higher payoff than any other strategy the player can use for every possible combination of its rivals’ strategies. If Wrangler picks white, then Levi Strauss will pick violet because a payoff of $40 is greater than a payoff of $10 from picking white or a payoff of $30 from picking black. If Wrangler picks black, then Levi Strauss will pick violet because a payoff of $35 is greater than a payoff of $20 from picking white or a payoff of $0 from picking black. If Wrangler picks violet, then Levi Strauss will pick black because a payoff of $20 is greater than a payoff of $15 from .

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picking white or a payoff of $0 from picking violet. So, Levi Strauss does not have a dominant strategy. Much the same, if Levi Strauss picks white, then Wrangler will pick violet because a payoff of $40 is greater than a payoff of $10 from picking white or a payoff of $30 from picking black. If Levi Strauss picks black, then Wrangler will pick violet because a payoff of $35 is greater than a payoff of $20 from picking white or a payoff of $0 from picking black. If Levi Strauss picks violet, then Wrangler will pick white because a payoff of $30 is greater than a payoff of $15 from picking black or a payoff of $0 from picking violet. So, Wrangler does not have a dominant strategy.

The Nash equilibria are for Levi Strauss to pick violet and Wrangler to pick white and for Levi Strauss to pick black and Wrangler to pick violet. For example, if Levi Strauss picks violet and Wrangler instead picks black, then Wrangler’s profit decreases to $15 from $30, and if Wrangler instead picks violet, then Wrangler’s profit decreases to $0.

If Wrangler picks white and Levi Strauss instead picks white, then Levi Strauss’s profit decreases to $10 from $40, and if Levi Strauss instead picks black, then Levi Strauss’s profit decreases to $30. For the next equilibrium, if Levi Strauss picks black and Wrangler instead picks white, then Wrangler’s profit decreases to $20 from $35, and if Wrangler instead picks black, then Wrangler’s profit decreases to $0. If Wrangler picks violet and Levi Strauss instead picks white, then Levi Strauss’s profit decreases to $15 from $20, and if Levi Strauss instead picks violet, then Levi Strauss’s profit decreases to $0. b. If Wrangler picks white, then Levi Strauss will pick violet because a payoff of $40 is greater than a payoff of $10 from picking white or a payoff of $30 from picking black, so Wrangler’s payoff will be $30. If Wrangler picks black, then Levi Strauss will pick violet because a payoff of $35 is greater than a payoff of $20 from picking white or a payoff of $0 from picking black, so Wrangler’s payoff will be $15. If Wrangler picks violet, then Levi Strauss will pick black because a payoff of $20 is greater than a payoff of $15 from picking white or a payoff of $0 from picking violet, so Wrangler’s payoff will be $35. Since a payoff of $35 from picking violet is greater than a payoff of $30 from picking white or a payoff of $15 from picking black, Wrangler will pick violet.

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2.6

Levi Strauss would want Wrangler to believe this claim because, if it did, Wrangler would choose white and Levi Strauss would choose violet and earn a profit of $40, the highest possible profit. However, Wrangler should not believe this claim. If, for example, Wrangler chooses violet, then Levi would be better off choosing black rather than also choosing violet. Levi’s claim that it would choose violet in this case is not credible.

2.7

With the bottom row removed, the choice of Violet is now dominant for Levi Strauss.

Wrangler will notice this and will pick White leading to a Nash equilibrium in the upper right hand corner. In the sequential game Levi Strauss will pick Violet at each decision node (i.e. they will pick Violet if Wrangler first picks White and they will pick Violet if Wrangler first picks Black). Wrangler will use this information to predict a move of Violet.

Furthermore, Wrangler knows that if they pick White followed by Levi Strauss’ choice of Violet that they (Wrangler) will earn $30. If they pick Black followed by Levi Strauss’ choice of Violet then Wrangler’s payoff will be $15. Wrangler picks White to get the higher payoff of $30.

2.8

a. The safe owner (S) moves first and decides whether to “open” the safe or “don’t open” the safe. Then the thug decides to “kill” or “don’t kill.”

b. The subgame perfect Nash equilibrium is “don’t open” for the safe owner and “don’t kill” for the thug irrespective of whether the owner opens the safe or not. So the safer owner will not open the safe, and the thug will not kill. c. The thug’s threat is not credible. Therefore the safe owner should not believe it. d. He will not open the safe.

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DETERRING ENTRY 3.1

The short answer is that Ricardo will improve his profits by paying for exclusivity. He will earn $140,000 after he pays the $100,000 fee compared to the $120,000 he would earn if he did not sign the exclusivity agreement. Entry will not occur and Ricardo’s Gift Emporium will remain the only gift shop on the pier.

Here is a game-tree that shows this result:

3.2

There are significant profits for incumbent producers if they can maintain their monopoly position for a while longer via one of these pay-for-delay agreements. Since the generic producers that are likely to enter without such an agreement are likely to earn relatively small profits, the incumbent firm can share its wealth with the potential entrant and still be better off than if they allow entry (though not as well off if no entry occurs at all). If the FTC begins to investigate and even prosecute these types of cases, then the expected fine needs to be figured in as a cost and would make it less likely that a pay-for-delay agreement would make economic sense to the incumbent firm.

3.3

A set of strategies forms a subgame perfect Nash equilibrium if the players’ strategies are a Nash equilibrium in every subgame. In the example below, if the incumbent produces the small quantity, then the rival should enter because profit of $50 from entering is better than profit of $0 from not entering, and the incumbent’s profit will be $50. If the incumbent produces the large quantity, then the incumbent’s profit will be $60. Since profit for the incumbent of $60 is greater than profit of $50, the incumbent should produce the large quantity. Thus, the subgame perfect Nash equilibrium is for the incumbent to produce the large quantity and for the rival to enter if the incumbent produces the small quantity. If the incumbent’s profit from producing the large quantity is less than $50, then the incumbent will have no incentive to produce the large quantity.

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3.4

Draw the game tree and analyze the game using backward induction (moving from right to left in the diagram). If the incumbent commits to the small quantity, its rival enters and the incumbent earns $450. If the incumbent commits to the larger quantity, its rival does not enter and the incumbent earns $800. Clearly, the incumbent should commit to the larger quantity because it earns a larger profit and the potential entrant chooses to stay out of the market. In the subgame perfect Nash equilibrium, the incumbent produces the large quantity and the potential rival stays out.

3.5

Xavier makes the first move, and Ying, observing Xavier’s decision, makes his choice. The setup is like the Stackelberg model of noncooperative behavior. Xavier knows that Ying maximizes his utility and considers his optimal choice when making his own decision.

Ying chooses how much he needs to work to maximize his utility: dUY /dhY = 0  9(hX

hY)0.5

 hX

hY = 81

 hY =

hX.

=0

Knowing Ying’s choice, Xavier maximizes his utility: UX =

hY)0.5

hX

hX  UX = 18(hX  UX =

hX)0.5

hX

hX.

The optimum for Xavier is to not work at all; that is, hX*  0, and thus the optimum for Ying will be to work hY*  81. Therefore, Ying’s threat that he will not work is not credible.

3.6 An entry game can be repeated over time or over space. A successful, profitable firm is likely to face repeated threats of entry by potential rivals over time. For example, suppose the incumbent firm faces a potential rival in one town and knows that other potential rivals may later enter in other towns. Because what it does in the current game may affect future entry, the manager of the chain may conclude that engaging in an unprofitable price war when the first entry occurs is a good idea if it doing so is likely to deter many future rivals.

Fighting may be a good strategy for a firm if the firm’s profits are not common knowledge so that potential rivals have incomplete information. If the firm fights with the first entrant, potential rivals may falsely conclude that the firm’s profits are such that fighting is its best strategy even if the game is played only once. If potential rivals conclude that the .

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incumbent will always fight, they won’t enter because they know they lose money in a price war. Based on this, Walmart may fight unionization at one store even if the fight at that store is unprofitable because that may deter unionization at other stores.

3.7

In the two-fold replication (assuming both the incumbent and the entrant know the game will only be played twice), the only strategy that would be supported as part of an equilibrium would be for the incumbent to accommodate both times. This can be shown via backward induction in which we consider the 2nd round first. In the second (and last) round play will proceed exactly as if the game is being played a single time – the incumbent might make some vague threats, but the entrant knows the threats aren’t credible so they enter. The incumbent, faced with the option of accommodating entry and earning an additional 3 or fighting and only earning 1 will accommodate. The entrant can anticipate that reaction and rightly will enter to get a payoff (after accommodation) of 3 themselves versus the 0 they earn if they do not enter. Now, backing up a period, consider the play in the first round. You might think that the incumbent would fight in period 1 to establish a reputation for being mean (so as to stop entry in round 2). The problem with that line of reasoning is that we’ve already established that the incumbent will accommodate in round 2, so any sabre rattling in round 1 will be dismissed by the entrant as another empty threat and they will enter. The incumbent will make the same calculation and opt to accommodate in period 1 as well.

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COST AND INNOVATION STRATEGIES 4.1

If we apply backward induction to this picture we see that the rival will choose to enter if the incumbent does not invest, and not enter if the incumbent does invest. The incumbent will anticipate these reactions and will decide between not investing (followed by the rival entering) resulting in a payoff of $12,500 or investing (which will be followed by a do not enter choice by the rival) and earning $16,000. The incumbent will invest and the rival will not enter. The payoffs will be $16,000 for the incumbent and $0 for the rival.

4.2

Draw the game tree. It is worth more to the monopoly to keep the potential entrant out than it is worth to the potential entrant to enter, as the figure shows. Before the pollution-control device requirement, the entrant would pay up to $3 to enter, whereas the incumbent would pay up to  m   d  $7 to exclude the potential entrant. With the device, the incumbent’s profit is $6 if entry does not occur, and it loses $1 if entry occurs. Because the new firm would lose $1 if it enters, it does not enter. Thus, the incumbent has an incentive to raise costs by $4 to both firms. The incumbent’s profit is $6 if it raises costs and only $3 if it does not.

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4.3

Assume pricing below marginal cost reduces profits but gives the incumbent a cost advantage over potential rivals. A set of strategies forms a subgame perfect Nash equilibrium if the players’ strategies are a Nash equilibrium in every subgame. If the incumbent prices below marginal cost, then the rival should not enter because profit of $0 from not entering is better than profit of $–25 from entering, and the incumbent’s profit will be $150. If the incumbent prices above marginal cost, then the rival should enter because profit of $100 from entering is better than profit of $0 from not entering, and the incumbent’s profit will be $100. Since profit for the incumbent of $150 from pricing below marginal cost is greater than profit of $100 from pricing above marginal cost, the incumbent should price below marginal cost. Thus, the subgame perfect Nash equilibrium is for the incumbent to price below marginal cost and for the rival to only enter if the incumbent prices above marginal cost.

4.4

If Firm 1 chooses the high wage, then Firm 2 should produce low output because profit of $5 from low output is better than profit of $4 from high output, and Firm 1’s profit will be $12. If Firm 1 chooses the current wage, then Firm 2 should produce high output because profit of $11 from high output is better than profit of $7 from low output, and Firm 1’s

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profit will be $14. Since profit for Firm 1 of $12 from picking the high wage is less than profit of $14 from picking the current wage, Firm 1 should pick the current wage.

4.5

Bargaining with multiple firms will allow the labor union to play one off versus the other via the threat of a crippling strike. If they can get one firm to agree to higher wage demands then the other firms are likely to follow suit which raises the cost of operation to all firms.

This is likely to be an advantage compared to bargaining with a single firm because while the union can still strike against a monopolist, the damage is not as great if there are no competitors to sweep in and steal customers away. In addition, if labor provided is specialized (as it likely is in the auto industry) it is better for the union to bargain in a situation where firms need to compete for the services of their members than to be selling to a single buyer (a monopsonist) in the labor market.

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DISADVANTAGES OF MOVING FIRST 5.1

If ExxonMobil realizes that Venezuela will nationalize, then it does not invest in Venezuela because, after nationalization, its Venezuelan profit is less ($8) than what it can earn elsewhere ($10). However, if the value of x is at least $2 (from a payoff of $10 from investing elsewhere minus a payoff of $8 from investing in Venezuela), then ExxonMobil will be compensated for Venezuela nationalizing and would be willing to invest in Venezuela.

5.2

While Venezuela will have succeeded in capturing Exxon’s assets from there prior investments, it seems likely that the amount captured will be dwarfed the potential investments that have been redirected to Guyana and other countries by Exxon as well as many other oil companies. These forgone investments are harder to see because they never happened, but all estimates suggest that the plan was definitely a failure from Venezuela’s perspective.

5.3

A set of strategies forms a subgame perfect Nash equilibrium if the players’ strategies are a Nash equilibrium in every subgame. If Clarion opens, then Ford will pick a price of p2 because profit of $140 is greater than profit of $0 from picking p1 and profit of $25 from picking p3, and Clarion’s profit will be $–90. If Clarion does not open, then its profit will be $0. Since profit of $0 from not opening is better than profit of $–90 from opening, Clarion will not open. Thus, the subgame perfect Nash equilibrium is for Clarion to not open and Ford to pick p2 if Clarion opens.

Clarion will open if Ford provides compensation at least equal to $90 for Clarion to open, from the difference in Clarion’s profit of $–90 from opening and $0 from not opening.

Suppose Ford provides Clarion $95 to open through a binding contract.

If Clarion opens, then Ford will pick a price of p2 because profit of $45 is greater than profit of $–95 from picking p1 and profit of $–70 from picking p3, and Clarion’s profit will be $5. If Clarion does not open, then its profit will be $0. Since profit of $5 from opening is better than profit of $0 from not opening, Clarion will open. Thus, the subgame perfect Nash equilibrium is for Clarion to open and Ford to pick p2 if Clarion opens.

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5.4

Suppose an investment by the incumbent benefits both the incumbent and its rival (if its rival enters), as illustrated below. Because the investment is costly for the incumbent (but not the rival), profits at the subgame-perfect Nash equilibrium in this game are higher for the rival.

In particular, if the incumbent does not invest, then the rival should enter because profit of $100 from entering is better than profit of $0 from not entering, and the incumbent’s profit will be $100. If the incumbent invests, then the rival should enter because profit of $400 from entering is better than profit of $0 from not entering, and the incumbent’s profit will be $200. Since profit for the incumbent of $200 is greater than profit of $100, the incumbent should invest. Thus, the subgame perfect Nash equilibrium is for the incumbent to invest and for the rival to enter regardless of whether the incumbent invests.

5.5

There are three advantages cited in the mini-case. The first-mover firm may gain an advantage by preventing entry via new production processes that lower its marginal cost, if may be able to raise the cost to its potential rivals, and it could get an early start on learning by doing compared to its rival. Moving first is not always advantageous however. The mini-case cites the experience of Toshiba in the HD-DVD market and Sony in the smartwatch market as cases where second movers won out.

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BEHAVIORAL GAME THEORY 6.1

The subgame-perfect Nash equilibrium is for the Proposer make the lowest possible offer and for the Responder to accept that offer. This can be derived via backward induction.

Consider the Responder’s reaction to any offer first. They clearly prefer a high offer, but even the lowest offer will result in them (the Responder) getting $5, which is better than the $0 that they get if they reject the offer. They will accept an offer of $5 and, for that matter, any of the other offers. Now back up to the Proposer’s initial move. Since they know that the Responder will accept any of the offers they can simply choose the one that gives them (the Proposer) the highest payoff. This is the $5 offer which leaves the Proposer $95.

So the subgame-perfect equilibrium is an all-or-nothing offer in which the Proposer captures all (or nearly all) of the money. In practice this does not seem to happen. The Ultimatum Game has been played literally thousands of times for real money in laboratory and field experiments. A general description of the results is that Responders typically reject low offers – so if the Proposer says “$95 for me and $5 for you, what do you think?” the Responder usually shows them exactly what they think by hitting the ‘reject’ button.

Because of the likelihood that lowball offers will be rejected, Proposers typically offer significant amounts (but still typically less than half) to the Responders, and when faced with more reasonable offers Responders typically accept.

6.2

Students may cooperate in experiments such as a multi-period prisoner’s dilemma because some students feel they should oppose unfair behavior, and confessing to obtain a lower prison sentence at the expense of the other player could be considered unfair. Another concern with experiments such as these is that the payoffs are small enough that not all participants take the game seriously.

Otherwise, if the game is repeated indefinitely, then collusion is more likely than in a single-period game or in a game with a known number of finite periods. This is because in an infinitely repeated game, a player can influence its rival’s behavior by signaling and threatening to punish the other player for cheating on an agreement.

6.3

If Chloe expects other players to choose randomly, then she would expect the average among those players to be about 50. Her own bid will lower the average slightly, but we will assume that there are enough players so that her effect on the average is too small to affect her optimal bid. She should therefore pick the integer closest to 2/3 of 50, which would be 33. If you are playing and you think everyone else is like Chloe, then you should bid 2/3 of 33, which is 22.

6.4

Definitely – in the section on levels of reasoning using the Beauty Contest game (from Keynes) the winning player is the one who best estimates their rival – neither overestimating nor underestimating their rivals’ talents.

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6.5

Yes. The Managerial Implication cites the case of cold openings for bad movies. If movie goers were fully rational and put forth the effort to evaluate all information about a movie, then a cold opening would not make sense from the perspective of the studio. However, it appears that it is a successful strategy in some cases, likely due to the less-than-optimal behavior of movie goers.

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MANAGERIAL PROBLEM

7.1

If Intel has low advertising, then AMD should have high advertising because profit of $8 from high advertising is better than profit of $2 from low advertising, and Intel’s profit will be $4. If Intel has high advertising, then AMD should have high advertising because profit of $9 from high advertising is better than profit of $4 from low advertising, and Intel’s profit will be $8. Since profit for Intel of $9 is greater than profit of $4, Intel should have high advertising. Thus, the subgame perfect Nash equilibrium is for Intel to have high advertising and AMD to have high advertising regardless of Intel’s advertising level.

7.2

Let the probability that a firm chooses low be α for Intel and β for AMD. If the firms choose their advertising independently, then αβ is the probability that both choose low advertising, (1 – α(1 – β) is the probability that both choose high advertising, α(1 – β) is the probability that Intel chooses low and AMD chooses high, and (1 –α)β is the probability that Intel chooses high and AMD chooses low.

A mixed-strategy is one where the players choose between possible actions with probabilities. Intel’s expected profit is E(π) = 2αβ + 4α(1 – β) + 3(1 – α)(1 – β) + 8(1 – α)β E(π) = (–7β + 1)α + 3 + 5β.

Similarly, AMD’s expected payoff is E(π) = 2αβ + 8α(1 – β) + 3(1 –α)(1 – β) + 4(1 – α)β E(π) = (–7α + 1)β + 3 + 5α.

To find α, set AMD’s payoff when choosing low equal to its payoff when choosing high.

To find β, set Intel’s payoff when choosing low equal to its payoff when choosing high.

Thus, α = 0.142 and β = 0.142.

If Intel chooses low advertising with a probability greater than 0.142, then AMD can maximize expected profits by always choosing high advertising. However, then Intel would not pursue a mixed strategy. Similarly, if AMD chooses low advertising with a probability greater than 0.142, then Intel can maximize expected profits by always choosing high advertising. However, then AMD would not pursue a mixed strategy. Intel and AMD will only use mixed strategies if they are indifferent between low and high advertising. Intel will only be indifferent if it believes AMD will choose low with probability 0.142, and AMD will only be indifferent if it believes Intel will choose low with probability 0.142.

Thus, the only possible mixed-strategy Nash equilibrium is α = 0.142 and β = 0.142.

Substituting these values into the expected profit functions and simplifying, expected profits for both firms equal 3.71.

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SPREADSHEET EXERCISES Solutions can be found in MyLab Economics

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CHAPTER 14 MANAGERIAL DECISION MAKING UNDER UNCERTAINTY SOLUTIONS TO END-OF-CHAPTER QUESTIONS

ASSESSING RISK

1.1

The expected value, EV, is the value of each possible outcome times the probability of that outcome. The expected value of the frocks is a 20 percent chance of them being stylish and worth $10,000 and an 80 percent chance of them being passé and being worth $2,000: EV = 0.2($10,000) + (1–0.2)($2,000) = 2,000 + 1,600 = $3,600.

1.2

Assuming that the painting is not insured against fire, its expected value is $550  (0.2  $1,000)  (0.1  $0)  (0.7  $500).

1.3 The expected value is the value of each possible outcome times the probability of that outcome.

So, the expected value of the contract is 𝐸𝑉 = Pr(𝑁𝑜𝑃𝑖𝑒𝑟𝑠) ∗ ($9000) + Pr(𝑃𝑖𝑒𝑟𝑠𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑) ∗ (−$2000) which substituting in for the appropriate probabilities is 𝐸𝑉 = 0.8(9000) + 0.2(−2000) = $6800.

If EZ pays for the study then they would only sign the contract if no piers are required and will not sign if piers are necessary. This changes the expected value calculation to 𝐸𝑉 = 0.80(9000) + 0.20(0)=$7200.

Since the difference between the amount they can earn (in expectation) with the study ($7200) and without the study ($6800) is $400, that is the maximum that EZ would be willing to pay for the seismic study.

1.4

The expected value of the stock is (0.25  0.25(40

 200) = 250. The variance is

2

2 2

= 0.25(150)2

=

= 7,500.

1.5

There are three possible outcomes: 1. Both the patent application and the FDA application are successful. In this case the drug is worth $10 (million). This outcome happens with probability 0.3 which comes from a 60% chance of patent approval combined with a 50% chance of FDA approval (so the joint probability is 60% ∗ 50% = 30% = 0.30.

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2. FDA approval is secured but the patent application is unsuccessful. This occurs 20% of the time (or probability 0.20) which is the joint probability of no patent success (40%) and FDA approval (50%). In this case the drug is worth $4 (million).

3. The application to the FDA is denied (this happens 50% of the time or probability 0.50) in which case the drug is worthless ($0) with or without patent approval.

Given these three outcomes the expected value of the drug is 0.3(10) + 0.2(4) + 0.5(0) = $3.8 𝑚𝑖𝑙𝑙𝑖𝑜𝑛.

The variance of the value of the drug is the sum of squared differences of the different outcomes compared to the expected value, each weighted by the appropriate probabilities.

So 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 0.3(10 − 3.8)2 + 0.2(4 − 3.8)2 + 0.5(0 − 3.8)2 = 0.3(38.44) + 0.2(0.04) + 0.5(14.44) = 11.532 + 0.008 + 7.220 = 18.760.

1.6

For individuals, gambling at a casino and buying a stock might not be too different. Both serve to redistribute wealth within a society. For the society as whole, a stock market places an important role in the financial market, which influences the general economy directly. On the other hand, gambling is generally considered an undesirable good, or a “bad,” as it does not contribute to the productivity of the society.

1.7

The expected punishment for violating traffic laws is θ V, where θ is the probability of being caught and fined and V is the fine. If people care only about the expected punishment (that is, there’s no additional psychological pain from the experience), increasing the expected punishment by increasing θ or V works equally well in discouraging bad behavior. The government prefers to increase the fine, V, which is costless, rather than to raise θ, which is costly due to the extra police, district attorneys, and courts required.

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ATTITUDES TOWARD RISK 2.1

A fair bet has an expected value of zero. From Kristin’s perspective the expected value of this bet can be calculated by multiplying each possible outcome by the probability of that outcome occurring. There are two possible outcomes – Ryan pays Kristin $5 (so +$5 for her) and Kristin pays Ryan $3 (so -$3 for her). The first outcome occurs with probability 1/3 (since a roll of 1 or 2 is 1/3 of the possible outcomes from rolling the die) and the second outcome occurs with probability 2/3. The formal calculation of Kristin’s expected value is:

2 5 6 5 6 1 1 𝐸𝑉𝐾𝑟𝑖𝑠𝑡𝑖𝑛 = ( ) (5) + ( ) (−3) = ( ) + (− ) = − = − 3 3 3 3 3 3 3

So the bet is not a fair one for Kristin (or Ryan for that matter). Kristin would lose money on average from taking this bet and Ryan would earn a small amount. Since Ryan’s expected payoff is positive (it is just the opposite of Kristin’s) it, in fact, does make sense for Ryan to offer this bet.

2.2

No. Risk-neutral individuals are indifferent between certainty and a fair bet. Thus they may or may not purchase fair insurance but would not be willing to purchase unfair insurance.

Because the risk premium for a risk-neutral person is zero, he or she is unwilling to pay anything to avoid taking a risk.

2.3

The function is concave; therefore, Maoyong is risk averse. Marginal utility, MUW = 1/W, is declining. (See the figure below.) Maoyong prefers to have a certain outcome = U(4.195) = 1.434) than to have an uncertain outcome (0.5U (U(0.5(1) 0.5U(7.39) = 1), even though the expected value of the certain and uncertain outcomes are the same (EV = 0.5(8.39) = 4.195).

2.4

To answer this question we need to know if the second derivative of the utility function is positive, equal to zero, or negative. A second derivative less than zero implies risk

.

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aversion, a second derivative equal to zero implies risk neutrality, and a second derivative greater than zero implies risk preference. Here are the calculations for each case. a.

and

. Since the second derivative is less than zero we can

conclude that this utility function exhibits risk aversion. b.

and

. Again, this second derivative is less than

zero so the utility function shows risk aversion. c.

d.

2.5

2.6

and

. This utility function exhibits risk preference.

and

. This utility function exhibits risk neutrality.

Originally Abu has wealth of $900 and that wealth generates utility of 𝑈(900) = √900 = 30. The gamble (a 50/50 shot at adding or subtracting $80 in wealth) has an expected value of $900 and, therefore, is a fair gamble. The expected utility of the gamble is the weighted average of the utility values associated with each possible outcome, or 0.5𝑈(980) + 0.5𝑈(820) which we know is 0.5 ∗ √980 + 0.5 ∗ √820 = 0.5(31.305) + 0.5(28.636) = 15.6525 + 14.318 = 29.9705. This is utility generated by wealth of $898.23 (since 𝑈(898.23) = √898.23 = 29.9705) and so the risk premium is $900 − $898.23 = $1.77.

Hugo’s expected wealth is EW   23  144    13  225   96  75  171.

His expected utility is EU   23  U (144)    13  U (225)   23  144    13  225      2 1   3  12    3  15  13.

He would pay up to an amount P to avoid bearing the risk, where U(EW – P) equals his expected utility from the risky stock, EU. That is, U(EW – P) = U(171 – P) = 171  P = 13 = EU. Squaring both sides, we find that that 171 – P = 169, or P = 2. That is, Hugo would accept an offer for his stock today of $169 (or more), which reflects a risk premium of $2.

2.7

Irma’s expected utility of 133 at point f (where her expected wealth is $64) is the same as her utility from a certain wealth of Y.

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2.8

When x increases from x0 to x1, the chord showing expected utility shifts downward.

Initially the risk premium is $10. After the increase in x, the risk premium increases to $40.

2.9

Yes. Investors require a higher return on stocks because stocks are riskier (more variable) in their valuation. This is consistent with risk aversion. If investors exhibited risk preference instead of risk aversion, they would be willing to accept a lower return on stocks than on bonds because they were seeking out the riskier asset.

2.10 Job 1’s expected value is 30, its variance is 100, and its standard deviation is 10. Job 2’s expected value is 36, its variance is 189, and its standard deviation is 13.74. Job 3’s expected value is 30, its variance is 0, and its standard deviation is 0. We cannot conclude anything about the job Joanna will select if she’s risk averse because Job 2 has the highest expected value but also the highest variance. If she’s risk-neutral, then she’ll select the job with the highest expected value, which is Job 2.

2.11 a) The expected value is 𝐸𝑉 = 0.6(150000) + 0.4(−30000) = $78,000 and the variance is 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 0.6(150000 − 78000)2 + 0.4(−30000 − 78000)2 = 3,110,400,000 + 4,665,600,000 = $7.776 𝑏𝑖𝑙𝑙𝑖𝑜𝑛. b) Yes, she would accept the offer because the expected value of the harvest ($78,000) is less than the sure-thing payment being offered by Ethan ($92,000). c) There are a number of possible explanations for Ethan’s offer. One – he may not understand the laws of probability and how to calculate the expected return of the vineyard.

Two – he many not be as informed as Catalina about the probabilities of good and bad weather. Three – he may be risk loving or risk preferring and actually enjoy / gain utility from taking the gamble. A risk loving individual is willing to take a less-than-fair bet (as is the case here).

2.12There are a number of reasons that a risk averse person might gamble in a casino. The minicase provides three possible explanations. First, gambling is a form of entertainment – some people simply like playing games of chance. Second, some individuals may gamble because they don’t understand the probabilities and do not realize that they are participating in an .

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unfair bet. Finally, some people may know the bet is unfair (in the house’s favor), but may simply overestimate their own chances of winning.

2.13 Here is a replication of the spreadsheet from Q&A 14.3. I’ve added columns for Joachim’s utility and Cindy’s utility. In each case, the calculation uses the utility functions from the question. Here is the spreadsheet:

Based on this information Joachim would select Project A and Cindy would pick Project C as these are the projects that will maximize each of their expected utility.

2.14 Even though they each are risk averse as shown by the shape of their utility functions (both are convex), they have differing degrees of risk aversion as shown below:

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REDUCING RISK

3.1

If she sends them together, the expected utility is qU(0) + (1 – q)U($2000). If they are sent separately and losses are independent events, she might lose both, one, or neither. The expected utility is (1 – q2)U($2000) + 2q(1 – q)U(1000) + (q2)U($0).

3.2

This is a simple diversification strategy. If you invest all of your savings in the company that you work for and things go poorly you stand to lose both your job and your savings. If instead, you invest in a different, unrelated company the a negative event for either the company you work for or the company you’ve invested in will be more insulated from one another.

3.3

Fair insurance is a bet between an insurer and a policyholder in which the value of the bet to the policyholder is zero. In this example, the cost of a $1.00 insurance payment if successfully sued is $0.05263 if not sued (from a 5 percent probability of being successfully sued divided by a 95 percent probability of not being successfully sued).

Because Lucy is risk averse, she fully insures by buying enough insurance to eliminate risk altogether. With this amount of insurance, she has the same amount of wealth whether sued successfully or not. The expected value of Lucy’s profits (EV) is EV = 0.95(100) + 0.05(10) EV = $95.5.

Thus, at a cost of $0.05263 if not sued per $1.00 insurance paid if successfully sued, Lucy will purchase insurance such that she receives an insurance payment of $85.5 if successfully sued (from an expected value of $95.5 minus profit if successfully sued of $10). That is, Lucy will spend $4.50 on insurance (from a price of $0.05263 multiplied by insurance coverage of $75.5).

3.4

a. The household’s expected utility (EU) without insurance is EU = 0.98*4(160,000)0.5 + 0.02*4(70,000)0.5 EU = 1,592.

Its utility with income of $145,000 (from $160,000 –$15,000) with certainty is EU = 4(145,000)0.5 EU = 1,523.25.

So the household should not buy the insurance. b. Fair insurance is a bet between an insurer and a policyholder in which the value of the bet to the policyholder is zero. In this example, the insurance company will make a $70,000 payment with probability 0.02, so the cost should be $1,400. c. This level of utility (1,592) can be obtained with income of $158,404 with certainty, from 1,592 = 4(X)0.5 398 = X0.5 X = $158,404.

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Thus, the most the household would be willing to pay for the insurance policy is $1,596, from $160,000 minus income of $158,404 with certainty.

3.5

a. Risk neutral: Y is the wealth UINS = Y  150.

The expected utility of no insurance = (1/36)(Y  400)  (35/36)Y = Y  11.11. A riskneutral person doesn’t buy insurance.

Risk averse and poor: Y is the wealth and is equal to 4,000.

UINS = (4,000  150)0.5 = 62.04 The expected utility of no insurance = (1/36)(0)0.5  (35/36)(4,000)0.5 = 61.49. A riskaverse and poor person purchases insurance.

Risk averse and wealthy: Y is the wealth and equal to 500,000.

UINS = (500,000  150)0.5 = 707 The expected utility of no insurance = (1/36)(500,000  4000)0.5  (35/36)(500,000)0.5 = 726.67. A risk-averse and wealthy person does not purchase insurance. b. The loss for a wealthy person is inconsequential, and he or she behaves like a riskneutral person.

3.6

If individuals know that the government will provide subsidies to homeowners with losses, they have an incentive to purchase less insurance. In the figure, initially, the individual has an expected utility of U (w2 ), because he or she receives w0 if there is a flood, and w3 if there is no flood. This results in a risk premium of ( w2  w2 ). When the government offers the subsidy, the potential loss decreases, even though the probability of a loss does not change. The expected utility chord swings upward, resulting in a higher utility level if there is a flood [U(w1)]. The risk premium of the individual decreases to w2  w2 , decreasing the person’s willingness to pay for insurance.

3.7

They can work to obtain additional information, diversify their investments and/or purchase insurance.

3.8

This new approach to reservations shifts the risk from the restaurants to the diners. In the past if a diner needed to cancel at the last minute it was the restaurant that was harmed, now it is the diner. The most likely cost of the new system is that it might cut back on demand for dinners at the restaurant since buying a dinner is now riskier (assuming diners are risk averse). It might also create ill will between the restaurant and the diners.

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INVESTING UNDER UNCERTAINTY 4.1

If they were married, Andy would receive half the potential earnings whether they stayed married or not. As a result, Andy will receive $12,000 in present-value terms from Kim’s additional earnings. Because the returns to the investment exceed the cost, Andy will make this investment (unless a better investment is available). However, if they stay unmarried and split, Andy’s expected return on the investment is the probability of staying together, ½ times Kim’s half of the returns if they stay together, $12,000. Thus, Andy’s expected return on the investment, $6,000, is less than the cost of the education, so Andy is unwilling to make that investment (regardless of other investment opportunities).

4.2

If the case goes to trial the plaintiff will win 𝑋 7% of the time and will lose (and get zero) the remaining 93% of the time. This means that the expected return from going to trial is 𝐸𝑉 = 0.07(𝑋) + 0.93(0). This expected value needs to be compared with the settlement payment of $140,000.

Let’s answer the questions in reverse order. Set 0.07(𝑋) + 0.93(0) = 140000 and solve for the cut-off or breakeven payment of 𝑋 = $2,000,000. If the payment from winning at trial is greater than this cut-off value then the plaintiff will go to trial. If, on the other hand, the payment from winning at trial is less than this cut-off value then the plaintiff will settle.

This is the case for 𝑋 = $170,000 and 𝑋 = $250,000.

If the plaintiff is risk averse instead of risk neutral then the payment from winning will need to be even higher than $2 million to compensate for the risk involved (i.e. because it is still quite likely that they plaintiff will get zero).

4.3

a.Let’s denote E[ R(i)] as the expected profit of the retailer if it orders i copies, and E[ R(i)] as the expected profit of the studio if the retailer orders i copies. Now we have: E[ R(1)] = 7 E[ R(2)] = 0.2    2 = 12.2 E[ R(3)] = 0.2      2 = 14.7 E[ R(4)] = 0.2    21    2= 14.5.

Therefore, the optimum number of orders that maximizes expected profit for the retailer is 3.

E[ N(1)] = 7 E[ N(2)] = 0.2    1 = 12.4 E[ N(3)] = 15.4 E[ N(4)] = 16.0.

Therefore, the optimum number of orders that maximizes expected profit of the studio is 4. b. E[ R(1)] = 7 .

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E[ R(2)] = 12.26 E[ R(3)] = 16.1 E[ R(4)] = 17.5.

Now, the optimum number of orders is 4. c. As parts (a) and (b) show, the optimum does depend on who pays the shipping cost.

4.4

In the decision tree below, the individual decides to have the transplant because the expected utility from the transplant is greater than remaining on dialysis.

4.5

In the decision tree below, the individual decides to use the roundup-resistant beets because the expected utility from the roundup-resistant beet is greater than not using it.

4.6

Guatam’s expected profits (π) without advertising if he makes the investment is π = 0.4(100) – 0.6(100) π = –$20.

Thus, he will not invest and have profit of $0. The minimum probability of high demand for which Guatam will advertise and invest is p such that p(100 – 50) – (1 – p)(100 + 50) ≥ 0 50p – 150 + 150p ≥ 0 200p ≥ 150 p ≥ 0.75 Thus, advertising will have to raise the probability of high demand to at least 75 percent for Guatam to be willing to invest.

4.7

Suppose that the utility from owning a home (buying and not defaulting) is 100 in both the U.S. and Europe. In the U.S., if you default on your loan you end up with utility of 0, while in Europe you are still responsible for the balance and will receive utility of -50 if you default. Assume the utility from not buying a home is 0 in both cases. Based on the decision trees below all Americans will buy a house (expected utility is positive), but .

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Europeans will calculate the expected utility including the possible loss of utility in the case of default and will see that when the probability of default is high they could receive negative expected utility. This will cause them to buy fewer houses.

4.8

If the firm spends $5 million on electronic defenses then it lowers the chance of an attack.

The expected value of the firm’s profit after this expenditure (but not including it the calculation yet) is 0.90(200) + 0.10(120) = $192 𝑚𝑖𝑙𝑙𝑖𝑜𝑛. Subtracting out the cost of the security measures leaves an expected profit of $187 𝑚𝑖𝑙𝑙𝑖𝑜𝑛. If they don’t make the expenditure then their expected profit is 0.75(200) + 0.25(120) = $180 𝑚𝑖𝑙𝑙𝑖𝑜𝑛. Since profits are higher from undertaking the security measures they will make the investment.

4.9

No, not all risk-averse managers fail to invest in R&D. Even though R&D is risky, the degree of risk and the size of the potential reward will make a difference. In addition, not all managers – even the risk-averse ones, are risk-averse to the same degree.

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BEHAVIORAL ECONOMICS AND UNCERTAINTY 5.1

It is not consistent because the two experiments have identical payoffs. The second choice probably is more popular in Scenario B for most individuals because they are starting from a higher level. They reason that only one flip of a coin is required from them to be able to keep all of their winnings, and if they lose, they still have $10,000. In the first scenario, beginning from a lower level, the $2,500 sure thing is too tempting for many to resist.

5.2

According to prospect theory, people are concerned about gains and losses rather than the level of wealth. People start with a reference point and consider lower outcomes as losses and higher ones as gains. Evan’s and Louisa’s utility functions are consistent with prospect theory because they treat gains and losses differently, in contrast to predictions of expected utility theory.

Evan is risk-seeking with respect to gains and risk averse with respect to losses, so his utility function is the solid line.

Louisa is risk-seeking with respect to losses and risk averse with respect to gains, so her utility function is the dashed line.

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5.3

Behavioral economics is the use of insights from psychology and research on human cognition and emotional biases to augment the rational economic model in an attempt to better predict economic decision making. The gambler’s fallacy is the false belief that past events affect current, independent outcomes. Some gamblers are overconfident, overestimating their chances of winning. Some people reverse their preferences when a problem is framed in a different but equivalent way. The reflection effect is when attitudes toward risk are reversed for gains and losses, where people are risk averse when making choices involving gains and risk preferring when making choices involving losses. The certainty effect is when people put excessive weight on outcomes that they consider to be certain relative to risky outcomes. Prospect theory suggests people are concerned about gains and losses (changes in wealth) rather than the level of wealth, as in expected utility theory. According to prospect theory, people start with a reference point (a base level of wealth) and think about alternative outcomes as gains or losses relative to that reference level. In this example, Joe and Sue’s behavior can be explained by prospect theory because they are making decisions relative to a reference point, which is their wealth at the start of the day.

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MANAGERIAL PROBLEM 6.1

Halidurton is indifferent between accepting and rejecting the contract if θ is such that the expected benefits equal the expected cost: 500 = 600 θ θ = 83.333 percent.

If Halidurton is risk averse and offered fair insurance, then Halidurton will fully insure, such that it has [500(1 – θ) + (500 – 600) θ] million 500 – 100 θ million whether there is a leak or not.

Halidurton is indifferent between accepting and rejecting the contract if is such that the expected benefits equal the expected cost with the liability cap: 500 = 200 θ θ = 250 percent.

That is, the leak could occur with certainty, and Halidurton would still be willing to build the oil pipeline.

If Halidurton is risk averse and offered fair insurance, then Halidurton will fully insure, such that it has [500(1 – θ) + (500 – 200) θ] million 500 + 300 θ million whether there is a leak or not.

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SPREADSHEET EXERCISES Solutions can be found in MyLab Economics

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CHAPTER 15 ASYMMETRIC INFORMATION SOLUTIONS TO END-OF-CHAPTER QUESTIONS

ADVERSE SELECTION

1.1

This is moral hazard.

1.2

Because insurance costs do not vary with soil type, buying insurance is unattractive for houses on good soil and relatively attractive for houses on bad soil. These incentives create a moral hazard problem: Relatively more homeowners with houses on poor soil buy insurance, so the state insurance agency will face disproportionately many bad outcomes in the next earthquake.

1.3

Brand names allow consumers to identify a particular company’s product in the future. If a mushroom company expects to remain in business over time, it would be foolish for it to brand its product if its mushrooms are of inferior quality. (Just ask Babar’s grandfather.)

Thus, all else the same, we would expect branded mushrooms to be of higher quality than unbranded ones.

1.4

a. Higher repair rates on resold planes of the same vintage as one-owner planes would indicate that a lemon problem does exist. b. Higher resale volume in the first few years would indicate a lemon problem. This is especially so given that individuals selling the planes are likely to suffer significant loss of value in this timeframe due to consumer wariness regarding the lemon problem.

1.5

Consumers do not want to purchase a lemon but cannot readily distinguish lemons from non-lemons upon simple inspection. They are, therefore, very wary of a virtually new car offered for resale. Assuming that the person who purchased the car wanted it when he or she bought it (a rational assumption), it is less likely that the person would want to resell the car almost immediately after buying it unless it was a lemon.

1.6

Before eating, consumers can only gain information about the price of the meal and its general characteristics, such as the type of cuisine. They are generally unable to tell the quality of a restaurant meal until after the meal has been consumed. In a tourist environment where no consumers are likely to return to the restaurant anyway, if the restaurant owner can save money (increase profits) by serving low-quality meals, the owner has the incentive to do so.

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1.7

All sellers will sell their used cars if 𝑧 (the probability a used car is a lemon) is less than or equal to a critical value. This critical value is determined by comparing the amount buyers are willing to pay for a car selected from the population at random (i.e., the expected value of a used car) to the value that good used car owners place on their cars. The intuition is that if the percentage of lemons in the market gets too large, then buyers will reduce their willingness to pay (rightly thinking that they are likely to get a lemon), as this expected value falls it could get so low that owners of good cars find it unprofitable to sell their cars.

The expected value of a used car to buyer is 𝐸𝑉 = 𝑧(5000) + (1 − 𝑧)(11000) = 11000 − 6000𝑧. Sellers of good cars will sell as long at this expected value (willingness to pay) is greater than the $8,000 value they put on their cars. So 11000 − 6000𝑧 > 8000 1 which implies 3000 > 6000𝑧 or 𝑧 < 2. As long as the fraction of the used cars that are lemons is 50% or less, then both kinds of cars will be offered for sale.

1.8

Because buyers are risk neutral, if they believe that the probability of getting a lemon is θ, the most they are willing to pay for a car of unknown quality is p = p1(1 − θ) + p2θ. If p is greater than both v1 and v2, all cars are sold. If v1 > p > v2, only lemons are sold. If p were less than both v1 and v2, no cars would be sold. However, we know that v2 < p2 and that p2 < p, so owners of lemons are certainly willing to sell them. (If sellers bear a transaction cost of c and p < v2 + c, no cars are sold.)

1.9

With four firms in the market, three of whom are producing low-quality staplers and one that is producing high-quality ones, the chance of a consumer getting a low-quality stapler is 75%. The expected value of a consumer of buying a stapler with a 25% chance of high quality and a 75% chance of low quality is 𝐸𝐸𝑉𝑉 = 0.25(24) + 0.75(18) = $19.50.

Since this value exceeds the cost of producing a low-quality stapler ($18) but not a high quality one ($24), the new producer cannot produce high-quality staplers without losing money. If consumers value a high-quality stapler at $60 instead, then the expected value of a stapler is 𝐸𝐸𝑉𝑉 = 0.25(60) + 0.75(18) = $28.50 and the new firm could sell high-quality staplers without losing money because the price of a stapler ($28.50) exceeds the cost of producing a high-quality stapler.

1.10 a) For actuarially fair insurance, the expected profit should be zero. Therefore, if everybody buys insurance, the price should be equal to the expected payments by the insurance company, or 𝐸𝐸𝑉𝑉 = (0.5)(0.35)(11000) + (0.5)(0.35)(2000) = 1925 + 350 = $2,275. b) If only unhealthy people purchase insurance, then the price (for the firm to break even) will be 𝐸𝐸𝑉𝑉 = (0.35)(11000) = $3,850. c) If people have the option of buying insurance or “self-insuring” by not buying insurance (and paying their own bills if they get sick), then healthy people will compare the expected cost with ($2,275) and without ($2,000) insurance and conclude that they should not buy insurance, provided they are risk neutral or only mildly risk averse. Adverse selection in .

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which the healthy people do not buy insurance, causes the market outcome to change to one where insurance is more expensive and only the unhealthy people will buy it. If, on the other hand, healthy people are quite risk averse, they may be willing to buy insurance at a less than “fair” price to guard against risk.

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REDUCING ADVERSE SELECTION 2.1

a. This information prevents the lemons problem and creates a market for high-quality restaurants. b. This reduces the trustworthiness of the information. Free meals and advertising taints critics’ objectivity. c. The information that the magazine provides is a public good, and it does not get the full value of its information through sales of the magazine. Therefore, the Michelin Red Guide accepts advertising and free meals.

2.2

This policy could help students in the job market if they would have earned poor grades. It will hurt students who would have performed well. It is also likely to harm students who would have received average grades, as employers are unable to determine what their grades would have been. A risk-neutral employer would assume that all students had average grades. However, a risk-averse employer would be unwilling to make that assumption. The loss of ability to signal employers becomes less important if other signals are available to (or even preferred by) employers. An alternative viewpoint is that students feel less pressure to get good grades and spend less time taking courses designed to increase their GPAs. They study and learn more and become more productive as a result.

2.3

If education is easier to obtain for high-quality workers than for low-quality workers, then high-quality workers may signal their quality to prospective employers by getting higher levels of education than lower quality workers.

2.4

By making this commitment, the company may be trying to assure customers who cannot judge how quickly the product will deteriorate that the product is durable enough to maintain at least a certain value in the future. The firm is trying to eliminate asymmetric information to increase the demand for its product.

2.5

John Hancock Life Insurance is using modern technology to track the activity levels of the people they insure. Customers are issued a Fitbit that monitors their activity level and shares this information with the company. In return, customers receive discounts on their insurance premiums. This program reduces the degree of adverse selection between customers and the company.

2.6

Without adequate verification, all websites (trustworthy and not trustworthy) will be lumped together into a single group. Since receiving the trust certification costs the website money, it only makes sense for trustworthy sites to pay for it if it helps differentiate one site from the next. Since this will not happen, “not trustworthy” sites will chase trustworthy ones out in the same way that lemons crowd out good cars in Akerlof’s lemons model.

2.7

The problem of adverse selection is that the seller knows the quality of the good being sold (particularly the remanufactured ones) and the buyer does not. Higher feedback scores can assure buyers that the item being sold is described accurately and, to the extent that the gap between new and manufactured goods is caused by unknown differences in quality, should help reduce the price difference. It is unlikely that the price difference would ever reach zero because there could be other reasons—not related to concern over misrepresentation— .

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that buyers would prefer new products to remanufactured ones (packaging, the thrill of newness, etc.). We would expect the same effect on the price difference between used and new goods as well—though again we would not expect the gap to close completely.

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MORAL HAZARD

3.1

This arrangement would likely increase the size of the overall bill. If there are n students, then each student will incur a cost of only 1/n times the cost of any additional item that student orders. Because the student placing the order will get the entire marginal benefit but will bear only a small part of the marginal cost, an excessive amount would be ordered.

3.2

Moral hazard is opportunism characterized by an informed person taking advantage of a less-informed person through an unobserved action. If candies can be reliably labeled tested or untested, then some consumers might buy cheaper, untested goods because informed candy producers would not have the ability to take advantage of less-informed consumers by selling candies with lead that are indistinguishable from tested candies without lead.

3.3

Total expected surplus is 𝐸𝑆 = 𝐸𝜋 − 𝐶(𝑒) = 1000 + 20𝑒 − 4𝑒 2 . To maximize this expression, we take the derivative and set it equal to zero, so

𝑑𝐸𝑆(𝑒) 𝑑𝑒

= 20 − 8𝑒 and set it

20

equal to zero. This gives us 20 − 8𝑒 = 0 which implies 𝑒 = 8 = 2.5.

3.4

If Amy gets to keep the residual profit, then she will act in the best interest of the firm and maximize profit as described in Problem 3.3. This will lead her to choose e = 4. If, on the other hand, Amy is paid a fixed wage, she will likely put forth less effort since it is costly and there is no effect on her wage of putting forth higher effort.

3.5

Presumably, the promoter collects a percentage of the revenue at each restaurant. If customers can pay cash, the restaurants may lie to the promoter as to the amount of food they sold. The scrip makes such opportunistic behavior difficult.

In this case, the profit maximizing choice is to set output where marginal revenue is equal to marginal cost (or 50 − 4𝑄 = 10) which implies 𝑄 = 10. The manager, on the other hand, will want to maximize revenue as opposed to cost. This will occur where marginal revenue is equal to zero (or 50 − 4𝑄 = 0) which implies 𝑄 = 12.5. This represents a conflict of interest between the owner(s) and the manager since they want to pursue different outcomes and is a classic example of an agency problem in which the owner and the manager (acting on behalf of the owner) have different objectives. The owner will need to modify the compensation scheme in order to avoid this agency problem and bring the manager’s objective in line with her own. Check out the next problem for an idea on how to do this.

3.6

3.7

Under this new compensation scheme, the firm and the manager would both like to see profit maximized. This eliminates the agency problem and the optimal solution for both the firm and the manager is 𝑄 = 10 as shown in the answer to 3.6.

3.8

Such a system is likely to lead to over inflated claims by insurance adjusters. A better system would be to pay the adjusters a flat fee per case plus a modest hourly rate to handle .

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claims (a high hourly rate would also lead to opportunistic behavior). Another option would be to have the insurance companies provide the insurance and have the government subsidize the premiums.

3.9

The expected value (EV) for the bank from loaning to local firms is EV = 75%($100 million) + 25%($80 million) EV = $95 million.

The expected value for the bank from loaning to oil speculators is EV = 25%($400 million) + 75%(−$160 million) EV = −$20 million.

Thus, bank shareholders would prefer that Sarah loan to local firms. If Sarah loans to local firms, then she will receive 1 percent of $95 million, which is $0.95 million. If Sarah loans to oil speculators, then there is a 25 percent chance she will receive 1 percent of $400 million, which is $1 million. (If the oil speculators default on the loans, then Sarah will leave the bank.) Thus, Sarah will loan to oil speculators.

3.10 This could be a case of moral hazard in which doctors use their role as principal to generate additional revenue through ordering more testing. It could also be that labs run by doctors are not as efficient as independent labs due to economies of scale and/or learning effects.

3.11 This policy clearly creates a moral hazard problem. If a house floods and the U.S. government (via the National Flood Insurance Program administered by FEMA) pays to rebuild the house in the same, flood-prone area then the residents have no reason to consider alternative (hopefully less flood-prone) locations for their rebuild.

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USING CONTRACTS TO REDUCE MORAL HAZARD 4.1

In this case, the problem arises because a given doctor receives the same amount of revenue no matter how many or few times the physician sees a patient. Although the income variation is reduced by this scheme, it creates a moral hazard problem. Each individual doctor collects all the gains from shirking (receives the leisure) but only pays a portion of the cost, as it is shared with other doctors in the group.

4.2

There may be an incentive for investment managers to shirk with such a contract. Because the manager is paid even if no trades are executed, a manager may have more incentive to spend his or her time searching for more assets to manage than watching for ways to increase the portfolios of the individuals that he or she already manages.

4.3

A partner who works an extra hour bears the full opportunity cost of this extra hour but gets only half the marginal benefit from the extra business profit. The opportunity cost of extra time spent at the store is the partner’s best alternative use of time. A partner could earn money working for someone else or use the time to have fun. Because a partner bears the full marginal cost but gets only half the marginal benefit (the extra business profit) from an extra hour of work, each partner works only up to the point at which the marginal cost equals half the marginal benefit. Thus, each has an incentive to put in less effort than the level that maximizes their joint profit, where the marginal cost equals the marginal benefit.

4.4

a. If Arnie is paid a fixed wage of $10, then Arnie would provide low effort. Any additional effort would be costly to him and would not increase his wage and therefore be a net loss. b. Under a 50–50 profit-sharing contract, Arnie would chose medium effort. With medium effort, the expected profit is 0.5(40) + 0.5(80) = $60. Arnie gets 50 percent or $30 and subtracts the cost of effort, $10, yielding a net gain of $20. With either low effort or high effort, Arnie’s net gain is only $15. c. Arnie gets $20 under the profit-sharing contract and $10 with a fixed wage, so he prefers the profit-sharing contract. Priscilla has an expected value of 30 − 10 = $20 with a fixed wage and 0.5(60) = $30 under profit sharing, so she prefers profit sharing also.

4.5

a. If Arnie is paid a fixed wage of $10 plus 80 percent of net store income, then Arnie would provide high effort. Expected profit with high effort is $90, and Arnie would receive a fixed wage of $10 plus 80 percent of $90 (which is $72) minus the $30 cost of effort, which is a payoff of $52. b. Under a 50–50 profit-sharing contract, Arnie would chose medium effort. With medium effort, the expected profit is 0.5(40) + 0.5(80) = $60. Arnie gets 50 percent or $30 and subtracts the cost of effort, $10, yielding a net gain of $20. With either low effort or high effort, Arnie’s net gain is only $15. c. Arnie gets $20 under the profit-sharing contract and $52 with a fixed wage plus bonus, so he prefers the fixed wage with bonus. Priscilla has an expected value of 90 − 10 − 72 = $8 with a fixed wage plus bonus and 0.5(60) = $30 under profit sharing, so she prefers profit sharing.

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4.6

Here is a modified version of the spreadsheet from <LINK>Q&A<CORE>15.</CORE>4</LINK> with Amy’s effort cost at 10 instead of 0 in the case of normal effort.

Notice that the change in Amy’s effort cost changes her behavior in the 25% profit sharing case—she now wants to give high effort to earn 105 versus 100. This means that Paul’s return (given her high effort) is 585 instead of the original 330. It is also true that this new, higher return for Paul in the 25% share case is higher than his return in the 30% share case and so he will prefer to offer Amy a 25% share contract.

4.7

If the output market is competitive, the firm maximization problem is as follows: p = pq

vpq

C(q).

Differentiating and setting marginal revenue equal to marginal cost implies that the firm produces where p

vp = MC,

which results in a lower output than joint profit maximization (achieved by setting p = MC).

4.8

a. If the author receives a lump-sum payment, the solution is equivalent to a profit tax.

The firm produces the profit-maximizing quantity and price as it would if no payment were due, and then pays the author the lump sum. b. If the author is paid a share of revenue, the firm’s marginal cost curve increases to reflect the royalty paid to the author. Assume that demand is linear, p = a − bq. Total revenue is R = aq bq2. Marginal revenue is MR = a − 2bq. Total cost is vR C(Q) = v(aq − bq2 C(Q), and marginal cost is MC = v(a − 2bq) dC/dq. c. If the author receives a lump sum and a percentage, the shift in the marginal cost curve is like that described in part (b) above, causing a distortion from the joint profitmaximizing output, and the remaining lump sum is deducted from profits.

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When authors are paid a share of the revenue, then the textbook company bears the full marginal cost but receives only a portion of the marginal revenue from selling textbooks. As a result, revenue-sharing contracts are not incentive compatible because the textbook company sells fewer than the number of textbooks that would maximize joint profit. Instead, joint profit would be maximized if authors were to receive lumpsum payments.

4.9

In the figure, the quota is shown as a vertical line at q*, and initial demand is D0. Initially, the quota is exactly satisfied, the patient visits the doctor q* times, and the insurance company pays the fee p0. If the patient’s demand increases, the insurance company will not pay for more visits. If the quota were set such that no additional visits were possible, the price would increase to p1. If fees are fixed at p0, the insured must pay the difference between p1 and p0. Also (assuming perfectly elastic supply in this range), the patient can consume beyond the quota limit by paying out of pocket for the additional q1 − q* visits. In this case, the moral hazard problem of overconsumption is reduced, and some of the risk is transferred to the insured.

4.10 Moral hazard is opportunism characterized by an informed person taking advantage of a less-informed person through an unobserved action. Moral hazard results in this case because Louisa has less incentive to practice bike safety with insurance because the insurance company bears the cost if her bike is stolen. In particular, moral hazard problems are more likely to result from full insurance because Louisa bears less (actually, none) of the consequences of her actions than with partial insurance (where she would bear a percentage of the cost of the bike if it is stolen).

With full insurance, Louisa will not undertake any bike safety due to problems associated with moral hazard, so there will be a 20 percent chance the $800 bike will be stolen. To recover this cost, the insurance company will have to charge a premium of $160.

Relative to having full insurance, if Louisa purchases partial insurance, then she will take more safety precautions because she bears more of the cost of the consequences of her actions, and she will bear more risk because she is not completely insured against theft.

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USING MONITORING TO REDUCE MORAL HAZARD 5.1

The bond is posted because law firms exist and thrive primarily based on their reputations.

If a partner were to become involved in illegal activities and he or she were caught, it would seriously damage the reputation, and thus the value, of the firm. Bonds are also used to prevent shirking. If a partner knows that he or she risks losing a large bond by shirking, it reduces the probability that shirking will occur.

5.2

T he solution mentioned in the mini-case on oil and gas companies might work here as well. In that circumstances, legislation mandated that these companies post surety bonds— a type of insurance that protects buyers against the failure of the firm. The same thing could be done with condo developers, protecting potential buyers against the bankruptcy of the developer. In the absence of a surety bond, the reputation of the developer and their past performance on similar projects would be of paramount importance.

5.3

When there is full employment, workers easily find a new job at the equilibrium wage. If they are fired for shirking, their only loss may be a temporary drop in income and some psychological costs of being fired. If these costs are more than offset by the utility of shirking, then the worker shirks and risks being fired.

5.4

This is a moral hazard problem. If Medicare does not cover these costs, the hospitals will be more careful, and to prevent extra costs, they will have a motivation to come up with their own set of incentives for their doctors and nurses to be more careful.

5.5

The price difference between used rental cars and used cars owned by individuals is due to moral hazard: those who rent cars likely do not take as good of care of them as those who own cars because renters do not reap the benefits of caring for the cars they rent. So, prospective buyers are not willing to pay as much for used cars that were rented. Car rental companies could inspect the cars they rent more carefully, but they instead often only conduct a brief, cursory inspection because inspections are expensive.

5.6

Moral hazard exists in employment relationships when the employer invests in the employee through training, contributions to long-term accounts (like retirement), and so on.

By requiring a vesting period, the employer reduces the potential for opportunism on the part of the employee whereby they might stay with the company until the contribution is made and then leave immediately after. The vesting requirement incentivizes longer term, more stable relationships between employers and employees.

5.7

The potential for moral hazard exists when an employer cannot effectively monitor the actions of their employees. For an hourly employee, this takes the form of slacking off on effort and just putting in time. Amazon’s tracking technology, while potentially a bit heavy handed (ha!), would allow for more effective monitoring and would reduce moral hazard by making slacking off less likely.

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MANAGERIAL PROBLEM 6.1

Bank earnings from Leonardo only making prime loans is $160 million with certainty.

Expected bank earnings from Leonardo making prime and subprime loans is EV = 25%($800 million) + 75%(−$320 million) EV = −$40 million.

Under the original compensation scheme, if Leonardo chooses to make only prime loans, then he will receive 1 percent of $160 million, which is $1.6 million. If Leonardo makes prime and subprime loans, then there is a 25 percent chance he will receive 1 percent of $800 million, which is $2 million. (If loan recipients default on subprime loans, then Leonardo will leave the bank.) Thus, Leonardo will choose to make prime and subprime loans, and shareholder’s expected earnings will be −$40 million.

Under the new compensation scheme, if Leonardo chooses to make only prime loans, then he will receive $1.2 million plus 0.25 percent of $160 million, which is $1.6 million. If Leonardo makes prime and subprime loans, then there is a 25 percent chance he will receive $1.2 million plus 0.25 percent of $800 million, which is $0.8 million. (If loan recipients default on subprime loans, then Leonardo will leave the bank.) Thus, Leonardo will choose to make only prime loans, and shareholder’s expected earnings will be $160 million.

6.2

The profit from selling Nikon Americas cameras is $400,000 with certainty. The expected profit from selling grey market Nikons is EV = 50%($1,000,000) + 50%(−$300,000) EV = $350,000.

Thus, the store owner would prefer Curtis choose to sell Nikon Americas cameras. If Curtis chooses to sell Nikon Americas cameras, then he will receive 10 percent of $400,000, which is $40,000. If Curtis sells grey market Nikons, then there is a 50 percent chance he will receive 10 percent of $1,000,000, which is $50,000. (If consumers are unwilling to buy cameras without warranties, then Curtis will leave the store.) Thus, Curtis will choose to sell grey market Nikons.

Under the original compensation scheme, Curtis expected to receive $40,000 (10 percent of $400,000) from selling Nikon Americas cameras. Curtis would be dissuaded from selling black market cameras if his compensation were not higher from selling grey market Nikons than from selling Nikon Americas cameras. One possibility would be to pay Curtis a fixed salary of $40,000, unless the store loses money. With this compensation structure, Curtis has no incentive to sell grey market Nikons because he will gain nothing if customers are willing to buy them without a warranty and he will lose his salary if customers are unwilling to buy them.

6.3

Contracts of this type attempt to reduce the moral hazard problem that exists between principals and agents when the agent (the CEO in this case) cannot be monitored effectively. Being paid almost entirely in stock options aligns the interests of the principal (the firm and its owners) and the agent so that the agent, in acting in her own self-interest, will maximize the value of the firm. On the other hand, there is concern that some of the .

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actions that might increase the stock price of the firm in the short run are not necessarily the best for the firm in the long run. Having a variety of stock options that vest (become actionable) at different times can help mitigate this concern.

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CHAPTER 16 GOVERNMENT AND BUSINESS SOLUTIONS TO END-OF-CHAPTER QUESTIONS

MARKET FAILURE AND GOVERNMENT POLICY 1.1

A Pareto improvement is a change, such as a reallocation of goods or productive inputs, that helps at least one person without harming anyone else. An outcome is Pareto efficient if any possible change would harm at least one person. If a policy change causes a Pareto improvement, the outcome is not necessarily Pareto efficient because another change could cause another Pareto improvement. So, a Pareto improvement does not necessarily cause Pareto efficiency. If a situation is Pareto efficient, then Pareto improvements are not possible because any change from a Pareto efficient outcome would make at least one person worse off. Thus, if a situation is Pareto efficient, no further Pareto improvements are possible. If a change occurs that causes a Pareto efficient outcome, the change is not necessarily a Pareto improvement because someone could be worse off. That is, a change that leads to Pareto efficiency does not necessarily cause a Pareto improvement as there may be losers as well as winners.

1.2

A Pareto improvement is a change, such as a reallocation of goods or productive inputs, that helps at least one person without harming anyone else. A change that is a Pareto improvement necessarily passes the cost-benefit test because at least one person benefits but there are no costs.

The cost-benefit principle states that a change is desirable if benefits exceed the costs.

Because there may be costs, a change that satisfies the cost-benefit principle may not be a Pareto improvement, which is a change that helps at least one person without harming anyone else.

1.3

The cost-benefit principle states that a change is desirable if its benefits exceeds the costs.

The benefit of the bridge is $15 worth of time savings for 1,000 people, which is $15,000.

The cost of the bridge is $1 for 10,000 households, which is $10,000. Since benefits are greater than costs, the bridge passes the cost-benefit test.

A Pareto improvement is a change, such as a reallocation of goods or productive inputs, that helps at least one person without harming anyone else. Building the bridge is not a Pareto improvement because some household who do not benefit from the bridge with reduced commuting times nonetheless must pay the tax and are worse off.

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1.4

A Pareto improvement is a change, such as a reallocation of goods or productive inputs, that helps at least one person without harming anyone else. To finance the bridge, a toll of $10 per crossing would have to be charged (from a total cost of $10,000 divided by 1,000 crossings). Since the toll of $10 is less than the $15 benefit in reduced commute times, charging the toll to build the bridge would be Pareto improving.

An outcome is Pareto efficient if any possible change would harm at least one person.

Suppose a toll of $10 were charged per crossing. The outcome is Pareto efficient.

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REGULATION OF IMPERFECTLY COMPETITIVE MARKETS 2.1

Assume the figure illustrates the monopoly’s demand (D), marginal revenue (MR), and marginal cost (MC). The economically efficient market outcome is indicated (eo).

Without price regulations, the monopoly maximizes profit by producing the quantity where marginal revenue equals marginal cost. The profit-maximizing price is determined by the demand curve at the profit-maximizing price (em). Deadweight loss is equal to the area under the demand curve and above the marginal cost curve for units that are not produced by the monopoly but that would be produced at the economically efficient outcome. With the price regulation, the monopoly charges the price ceiling because it is binding (below the profit-maximizing monopoly price without the price ceiling). The demand curve indicates the corresponding quantity demanded at the price ceiling (er). Deadweight loss is equal to the area under the demand curve and above the marginal cost curve for units that are not produced by the monopoly with the price ceiling but that would be produced at the economically efficient outcome.

Deadweight loss with the price ceiling is smaller than when the monopoly maximizes profit without the price regulation because the regulated price is lower and the corresponding quantity consumed is higher.

2.2

In this case, the MR curve coincides with the demand curve. Equilibrium quantity is 100, and equilibrium price is $100. Consumer surplus is zero, and producer surplus is ($100 − $10) × 100 = $9,000. If a price ceiling of $30 is imposed, consumer surplus increases, and producer surplus decreases by area abcd. There is no deadweight loss.

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2.3

The wholesale price of milk represents the marginal cost for retailers, who sell to consumers. In the figure below, suppose prices at the wholesale level fall 30.3 percent from $2.00 to $1.394 per gallon, or $0.606 per gallon. That is, for retailers, marginal cost shifts from MC to MC. If the original retail price were $3.00 per gallon, a 30.3 percent price decrease would mean a new price of $2.09, a drop of $0.91 per gallon. However, the negative slope of the demand curve results in a price decrease that is less than $0.91. The new retail price, for the given demand curve, is $2.50. In other words, price at the retail level may not fall by the same percentage as the wholesale level due to the slope of the demand curve.

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2.4

As indicated in the diagram, the deadweight loss of pricing at AC instead of MC is $1.26 billion. If the regulator required the firm to price at MC, then that deadweight loss would be converted to consumer surplus. In addition, consumer surplus would increase by the difference between the AC pricing outcome of $7.88 and the MC pricing outcome of $5.78 (or $2.10 per unit). This gain would be realized over all 23 trillion cubic feet of natural gas.

This amounts to an additional $48.3 billion. The total increase in consumer surplus would be $49.56 billion. Unfortunately, regulators do not typically require MC pricing in these cases because the firm would lose money (and stop operating). To keep the firm operating would require a subsidy of roughly $50 billion which would eliminate any gain to consumers.

2.5

There are two potential ways for the loss in surplus to be larger than the area B+D. First, some consumers may spend time attempting to buy a unit of the good (for which their willingness to pay exceeds the price), but ultimately not be able to obtain a unit. Second, the good may be allocated in a suboptimal fashion since price cannot be used as a rationing device and other factors such as willingness to wait in line, fortunate (or unfortunate) timing, etc. may determine who gets a unit of the good. This could result in a unit being sold to someone whose willingness to pay is less than another consumer that didn’t wait in line, get the timing right, etc.

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ANTITRUST LAW AND COMPETITION POLICY

3.1

Under duopoly, each firm produces 30, so total industry output is 60, price is 40, and total profit for the two firms combined is (40 − 10)60 = 1,800. If the two firms merge to form a monopoly, industry quantity falls to 45, price rises to 55, and profit rises to (55 − 10)45 = 2,025. Thus, merging increases the combined profit of the firms. Antitrust authorities might oppose the merger because consumer surplus falls by more than profit rises, so deadweight loss rises as a result of the merger.

3.2

Under duopoly, each firm produces 30, so total industry output is 60, price is 40, and total profit for the two firms combined is (40 − 10)60 − 500 − 500 = 800. If the two firms merge to form a monopoly, industry quantity falls to 45, price rises to 55, and profit rises to (55 − 10)45 − 500 = 1,525. Thus, merging increases the combined profit of the firms.

Furthermore, antitrust authorities might be less opposed to the merger because $500 in fixed costs are avoided (the merged firm must only pay the $500 fixed cost of production once, as compared to each of the firms in a duopoly being required to pay the $500 fixed production cost). However, even when avoiding $500 in fixed costs from merging, consumer surplus falls by more than profit rises, so deadweight loss results from the merger, and antitrust authorities might oppose the merger.

3.3

A merger could reduce marginal cost if it is possible to reallocate production from higher marginal cost locations/plants to those with lower marginal cost. There also could be efficiencies that can be captured in the form of input procurement (i.e., if the newly merged firm has a stronger market position to negotiate lower input prices from suppliers). Finally, it is possible that the merger could help reduce managerial inefficiencies/slack if knowledge from one of the former firms is superior to the other.

3.4

Given the assumptions in Q&A 16.2, it is necessary for marginal cost to fall from 20 to 0 in order for the merger to result in a Pareto improvement. As long as marginal cost remains positive, consumer surplus will be reduced by the merger (and subsequent monopoly). If marginal cost goes to zero, then consumer surplus will be equal to the amount generated in the duopoly case and consumers will at least not be made worse off.

In terms of a cost-reducing merger increasing overall surplus, the answer is no. In some cases (when the cost reduction is small like 20 to 16 in Q&A 16.2), total surplus falls, while in other cases (with larger cost reductions like 20 to 12 in Q&A 16.3), total surplus rises. The intuition is that in the case of small reductions in cost, the benefit to the firm in the form of increased profit is not enough to outweigh the reduction in consumer surplus.

When the cost reduction is large, the firm benefits a great deal and their gain is larger than the loss in consumer surplus, so the net effect on total surplus is positive (though clearly not Pareto improving).

3.5

In the case of ready-mix concrete, the relevant market structure variable isn’t the total number of firms in the country, but the number in a particular geographic area. Concrete is .

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heavy and difficult to transport, so firms compete on a very localized level. It is very possible that a wave of mergers could render many local markets monopolies. Additionally, when considering the cost of mergers that create a monopoly, the speed of entry is important as well. If entry is fast, then any merger to monopoly will create incentives for entry and the market power will be short lived. If, on the other hand, entry is slow, then a newly formed monopoly may persist for a long time.

3.6

The soap manufacturer receives 20 percent of the two retail firms’ profit. Therefore, the soap manufacturer wants the retail stores to maximize their profit. Profit is maximized when the two stores maximize combined profit as a cartel or a monopoly would. The soap manufacturer can achieve this by specifying a price for the retail stores that equals the monopoly profit-maximizing price.

3.7

A dominant firm such as a monopoly may refuse to sell to one firm what it sells to others in an attempt to destroy competition. Exclusive dealing arises when a firm will sell its product only to customers who agree to buy from that firm and not from its rivals. Exclusive contracts can guarantee a source of supply, lowering transaction costs or creating dealer loyalty.

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4.10 When the tax is imposed, price increases from pM to pS. Although prices are increased, a deadweight loss of area E results. Area A  B  C  D is the reduction in social cost due to the tax, resulting in a net increase in social welfare.

4.11 a. Yes, any price between $600 and $1100 would be mutually agreeable. b. No, Aaron’s value of flying first class is greater than the value Samantha puts on quiet. c. Only values between $600 and $1100.

4.12 a. A tax increases the private marginal cost of production by an amount equal to the size of the tax. A tax will result in the same market quantity as auctioning licenses if the tax raises the private marginal cost of production to the marginal private benefit (as given by the demand curve) at the license quantity. That is, a tax will result in the same market outcome as auctioning licenses if the size of the tax is equal to the vertical difference between the demand curve and the private marginal cost curve at the license quantity. b. If political donors pay less than market value for liquor licences, they receive an economic benefit equal to the difference between the price they pay and the value of the license. This benefit increases the incentive to become a political donor and would therefore tend to increase political donations, making such arrangements attractive to many politicians.

4.13 Alyakoob and Rahman (2018) found that if activity on home-sharing platform Airbnb increases by 2%, restaurant employment in that neighborhood rises by 3%. This effect demonstrates which economic concept? (Hint: See the Managerial Implication “Disney Internalizes an Externality.”)

This example illustrates the concept of externalities. Airbnb activity creates benefits for nearby restaurants much as Disneyland creates benefits for nearby hotels and restaurants as described in the Managerial Implication “Disney Internalizes an Externality”.

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OPEN-ACCESS, CLUB, AND PUBLIC GOODS 5.1

Yes. My use of the bridge creates negative externality for others by creating congestion. A toll can internalize the negative externality.

5.2

Suppose the average value of fishing is a decreasing function of number of fish caught. In order to maximize private value, each boat continues fishing up to the point where marginal value (price in a competitive market) is equal to marginal cost; that is, as long as there is positive net gain, the fishing will continue. However, the socially optimum number of fish caught occurs where marginal value is equal to marginal social cost, which is likely to be higher than marginal private cost, thus we get the overfishing. Any tax on each fish caught that increases marginal cost reduces overfishing. However, the tax on the boat is a fixed cost and does not reduce the amount of fishing by each boat. Taxing each boat could affect the amount of fishing only if it forces some boats to go out of business, thus reducing the amount of fishing.

5.3

Yes, a charge of this type would cause the amount of spam to decline. On the other hand, it would also decrease the net benefits to non-spam email messages as well. It would likely decrease email traffic overall and decrease the proportion of email that is spam.

5.4

Pure public goods have two important characteristics. They are nonrival in consumption, as are broadcast and cable television, and they are nonexcludable. While broadcast television is nonexcludable, consumers can be excluded from cable television. Therefore, cable television is a public good and broadcast television is a pure public good. Broadcast television is privately provided (in the United States) to solve the free rider problem.

Commercials allow for payment for services given that the services are provided without exclusion.

5.5

As noted in the text, textbooks are typically owned by individuals, making them private goods, but the information in the books is public. Although copyright laws create a mechanism for exclusion, they do not cover all forms of communication (e.g., a lecture on the material in the book). Thus, the books create a positive externality and are underprovided if priced as pure private goods.

5.6

At the market price of guard service of $10 per hour, the TV store will hire four guards and the ice-cream store will hire none. Now with a $2 per hour subsidy from the mall owner, the private price of the TV store will be $8 per hour. Subsequently, the TV store will hire five guards, which makes the social marginal benefit equal to social marginal cost and therefore achieves the socially optimal outcome.

5.7

An externality occurs when a person’s well-being or a firm’s production capability is directly affected by the actions of other consumers or firms rather than indirect through changes in prices. In this example, individuals sick with swine flu do not account for the effects of their actions on coworkers (and other students). In particular, if individuals sick with swine flu report for work (or attend school), then they risk infecting their peers. Prior to the law, the marginal private benefit of staying home if sick was less than the marginal social benefit. By essentially subsidizing staying at home if sick, the law raises the .

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marginal private benefit of staying home if sick such that it is closer to (or perhaps equal) the marginal social benefit.

5.8

An externality occurs when a person’s well-being or a firm’s production capability is directly affected by the actions of other consumers or firms rather than indirectly through changes in prices. A positive externality benefits others. Flu shots generate a positive externality because when someone gets a flu shot for themselves, others benefit from being less likely to catch the flu.

A rival good is used up as it is consumed. Exclusion means that others can be prevented from consuming the good. Public goods are not rival without exclusion. Flu shots could be considered a public good because when someone gets a flu shot for themselves, others cannot be excluded from the benefit of being less likely to catch the flu. Such benefit is not rival because one person benefiting from being less likely to catch the flu does not diminish another person’s benefit from being less likely to catch the flu.

Free riding is a situation in which people benefit from the actions of others without paying.

When someone gets a flu shot for themselves, others benefit from being less likely to catch the flu without cost.

5.9

The sink and the dishes are both a form of public good for those who live in the house. If there were no one else there who might clean up, each individual would benefit from cleaning up the mess. However, the possibility that the other person might do the dishes makes it seem that an optimal strategy is to simply leave dishes and wait for the other person to do them. Unfortunately, they have the same dominant strategy, and the dishes accumulate. Each benefits the most by letting the other bear the cost.

5.10 The value of crossing the border depends on the number of cars in the special NEXUS lane (in the following, n is the number of in the NEXUS lane): 𝑉𝐴 = 4 if 𝑛 ≤ 70; 3 if 70 < 𝑛 ≤ 140; 2 if 140 < 𝑛 ≤ 210; and 1 if 𝑛 > 210. 𝑉𝐴 = 3 if 𝑛 ≤ 70; 2 if 70 < 𝑛 ≤ 140; 1 if 140 < 𝑛 ≤ 210; and 0 if 𝑛 > 210. 𝑉𝐴 = 2 if 𝑛 ≤ 70; 1 if 70 < 𝑛 ≤ 140; 0 if 140 < 𝑛 ≤ 210; and -1 if 𝑛 > 210. 𝑉𝐴 = 1 if 𝑛 ≤ 70; 0 if 70 < 𝑛 ≤ 140; -1 if 140 < 𝑛 ≤ 210; and -2 if 𝑛 > 210. a. If the cost of crossing is zero, all groups will cross the border. This is because each group does not take into account the negative externality it creates for others. b. If only cars in Group A cross the border, the total utility is 280. If Group B also crosses the border, the value will be(70 × 3) + (70 × 2) = 350. If Group C also crosses the border, the total value will be(70 × 2) + (70 × 1) + (70 × 0) = 210. With the addition of Group D, the total value is(70 × 1) + (70 × 0) + (70 × (−1)) + (70 × (−2)) = −140.

The total utility is maximized when 140 drivers (groups A and B) cross the border.

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5.11 If the industry were advertising optimally, the marginal revenue from advertising would equal the marginal cost. In this case, advertising is underfunded (MC = $1 and MR = $5.67). This is likely because some firms who get the benefit of advertising do not want to pay for it and would like to free ride—thus the agreed-upon advertising level is below the optimal. This is why the collection is mandatory.

5.12 Epidemic prevention activities such as widespread vaccination programs, etc. are an example of a club good and free riding. It is possible to exclude someone from receiving the vaccine or other kinds of disease prevention, but once these programs are in place, the benefits accrue to the entire population. This allows for potential free riding which is what is likely behind the move to cut these programs from the CDC budget. The argument is that the United States should not be involved in disease prevention outside of its borders. The difficulty, however, is that while provision by the United States of these services is subject to potential freeriding, elimination of these programs does not necessarily mean that other countries will pick up the slack. The potential for prevention to fall worldwide leads to the concern expressed in the article that some of the benefits that U.S. citizens received from overseas disease prevention (such as being protected from the spread of epidemics) will likely disappear without this funding.

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INTELLECTUAL PROPERTY 6.1

With the investment, the monopoly’s marginal revenue (MR) is MR = 50 − 4Q. A monopoly maximizes profit by producing the quantity where marginal cost (MC) equals marginal revenue: MC = MR 10 = 50 − 4Q 4Q = 40 Q = 10 units.

Plugging this back into the demand curve, the monopoly’s profit-maximizing price is p = 50 − 2Q p = 50 − 2(10) p = $30, which is not more than the competitive price (the competitive price equals the $30 marginal cost in the long run). In turn, the monopoly’s profit is π = p × Q − 10Q − F π = 30 × 10 − 10(10) − F π = 200 − F. If F = 150, the profit is $50. If F = 250, then profit is −$50. Profit equals zero when F = $200.

6.2

The monetary difference between what a consumer is willing to pay for the quantity of the good purchased and what the consumer actually pays is called consumer surplus.

Consumer surplus is a dollar-value measure of the extra economic benefit the consumer receives from a transaction over and above the good’s price. This is equal to the area under the demand curve and above the price. Initially, when the market is competitive, the equilibrium price is equal to marginal cost, which is $30. The quantity demanded is p = 50 − 2Q 30 = 50 − 2Q 2Q = 20 Q = 10 units.

Consumer surplus (CS) is equal to the area of a triangle with a base equal to the quantity demanded at the equilibrium price and a height equal to the difference in the demand curve’s vertical intercept (50) and the equilibrium price: CS = 0.5 × 10 × (50 − 30) CS = $100. .

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With the investment, the monopoly’s marginal revenue (MR) is MR = 50 − 4Q. A monopoly maximizes profit by producing the quantity where marginal cost (MC) equals marginal revenue: MC = MR 10 = 50 − 4Q 4Q = 40 Q = 10 units.

Plugging this back into the demand curve, the monopoly’s profit-maximizing price is p = 50 − 2Q p = 50 − 2(10) p = $30, which is not more than the competitive price (the competitive price equals the $30 marginal cost in the long run). Consumer surplus with the monopoly’s investment is equal to the area of a triangle with a base equal to the quantity demanded and a height equal to the difference in the demand curve’s vertical intercept (50) and the monopoly’s price: CS = 0.5 × 10 × (50 − 30) CS = $100.

Thus, the change in consumer surplus is $0.

A supplier’s gain from participating in the market is measured by producer surplus, which is the difference between the amount a good sells for and the minimum necessary for the producers to be willing to produce the good. The minimum amount a firm must receive to be willing to produce is the firm’s avoidable production cost. Competitive producers have no surplus because the competitive equilibrium price equals the constant marginal cost of $30. A monopoly maximizes profit by producing 10 units and charging a price of $30.

The monopoly’s profit is π = pQ − 10Q − F π = 300 − 100 − 150 π = $50.

Thus, the change in producer surplus is $50. Total surplus equals producer surplus plus consumer surplus. The change in total surplus equals the change in consumer surplus plus the change in producer surplus, which is $50.

6.3

With the investment, the monopoly’s marginal revenue (MR) is MR = 50 − 4Q. A monopoly maximizes profit by producing the quantity where marginal cost (MC) equals marginal revenue: .

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MC = MR 10 = 50 − 4Q 4Q = 40 Q = 10 units.

Plugging this back into the demand curve, the monopoly’s profit-maximizing price is p = 50 − 2Q p = 50 − 2(10) p = $30, which is not more than the competitive price (the competitive price equals the $30 marginal cost in the long run). However, with price regulated to be no more than $12, consumers will demand p = 50 − 2Q 12 = 50 − 2Q 2Q = 38 Q = 19 units.

In turn, the monopoly’s profit will be π = pQ − 10Q − F π = 12(19) − 10(19) − 150 π = −$112.

Woz incurs losses, but since the price is greater than the marginal (and variable) cost of production (and since the research and development fee has already been paid), it is better for Woz to stay in business. (Assuming the R&D fee is sunk, Woz’s profit is $38.)

The monetary difference between what a consumer is willing to pay for the quantity of the good purchased and what the consumer actually pays is called consumer surplus.

Consumer surplus is a dollar-value measure of the extra economic benefit the consumer receives from a transaction over and above the good’s price. This is equal to the area under the demand curve and above the price. Initially, when the market is competitive, the equilibrium price is equal to marginal cost, which is $30. The quantity demanded is p = 50 − 2Q 30 = 50 − 2Q 2Q = 20 Q = 10 units.

Consumer surplus (CS) is equal to the area of a triangle with a base equal to the quantity demanded at the equilibrium price and a height equal to the difference in the demand curve’s vertical intercept (50) and the equilibrium price: CS = 0.5 × 10 × (50 − 30) .

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CS = $100.

Consumer surplus with the monopoly’s investment is equal to the area of a triangle with a base equal to the quantity demanded and a height equal to the difference in the demand curve’s vertical intercept (50) and the monopoly’s price: CS = 0.5 × 19 × (50 − 12) CS = $361.

Thus, the change in consumer surplus is $261.

A supplier’s gain from participating in the market is measured by producer surplus, which is the difference between the amount a good sells for and the minimum necessary for the producers to be willing to produce the good. The minimum amount a firm must receive to be willing to produce is the firm’s avoidable production cost. Competitive producers have no surplus because the competitive equilibrium price equals the constant marginal cost of $30. The monopoly’s profit is π = pQ − 10Q − F π = 12(19) − 10(19) − 150 π = −$112.

Thus, the change in producer surplus is −$112. Total surplus equals producer surplus plus consumer surplus. Similarly, the change in total surplus equals the change in consumer surplus plus the change in producer surplus, which is $149, from the $261 change in consumer surplus plus the −$112 change in producer surplus. Assuming the R&D fee is sunk, the change in total surplus is $299.

In this example, the government’s price control reduces Woz’s profits, discouraging research and investment.

6.4

A trade secret is a form of intellectual property, though it remains the exclusive property of the inventor only as long as it remains secret. Patents are needed when a firm cannot rely on trade secrets to protect its innovations. Since new chemical processes are less likely to be reverse engineered, chemical companies have less need for patents. Instead, they are able to rely to a greater extent on trade secrets.

6.5 Innovation and R&D is an area rife with examples of free riding. In the absence of patent protection, a firm that invests a great deal of time, money, and effort into making an innovation will likely see the gains associated with the innovation get pirated away as other firms free ride on their efforts. Patents aim to solve this problem by correcting the free rider problem by introducing market/monopoly power. A patent gives the innovating firm exclusive rights to profit from their innovation for a certain period of time. This provides incentive to engage in R&D even though it, at the same time, restricts post-R&D competition. The United States, Europe, and most other developed economies have decided that this trade-off is worth it to ensure sufficient innovative effort. Finding the right balance between patent length (and breadth) is important, but the overall concept is strong. .

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Alternatively, it is possible for governments to support R&D and innovative activity through subsidies or innovation prizes. These methods provide a reward for the firm to engage in innovative effort, but then with the reward decoupled from the output of the R&D allows all firms to use the outcomes in a competitive fashion.

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MANAGERIAL PROBLEM 7.1

The competitive supply curve at m constrains the monopoly exactly as would a government price cap set at m: It prevents the innovating firm from charging a price above m. Thus, the innovating firm can charge the unconstrained monopoly price only if pm is less than m.

Because m is less than pm in the figure, this firm charges a price less than pm.

Given that the competitive supply curve is horizontal at m, the residual demand curve facing the innovating firm is horizontal at m until it hits the market demand curve, and then it equals the market demand curve at prices below m. Consequently, the firm’s residual marginal revenue curve, MRr, is horizontal at m up to Qc, and then, at larger quantities, it equals the marginal revenue curve that corresponds to the downward-sloping market demand curve.

The innovating firm’s marginal cost curve at 0.8m cuts MRr in the vertical section at Qc. Thus, the firm’s profit-maximizing output is Qc. The firm charges a price that is slightly less than pc so that it undercuts the competitive firms and makes all the sales. Thus, this equilibrium is virtually the same as the competitive equilibrium. In turn, the innovating firm benefits from the innovation, but the other firms and consumers do not.

The only difference between the competitive equilibrium and this outcome is that one firm sells the entire quantity and makes a profit of (m − 0.8m)Qc = 0.2mQ = c, which is 100 percent of the value of the innovation.

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SPREADSHEET EXERCISES Solutions found in MyLab Economics

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CHAPTER 17 GLOBAL BUSINESS SOLUTIONS TO END-OF-CHAPTER QUESTIONS REASONS FOR INTERNATIONAL TRADE

1.1

In South Korea, the opportunity cost of car assembly is 1.5 sets of components per assembled car. In North Korea, the opportunity cost of assembly is only one third of a set of components. The theory of comparative advantage implies that North Korea would export assembled cars because it has a lower opportunity cost of assembly.

1.2

Workers in South Korea can produce components used to make cars at the rate of 6 sets of components per worker per day and can assemble cars at the rate of 4 cars per worker per day, so 40 percent of the workers will be used to make components and 60 percent of the workers will be used to assemble cars, resulting in total output of 480 cars.

Workers in North Korea can produce components at the rate of 1 set of components per worker per day and can assemble cars at the rate of 3 cars per worker per day, so 75 percent of the workers will be used to make components and 25 percent of the workers will be used to assemble cars, resulting in total output of 150 cars.

An opportunity cost is the value of the best alternative use of a resource. South Korea’s opportunity cost of assembled cars is 1.5 component sets (from 6 component sets produced per worker per day divided by 4 assembled cars produced per worker per day). North Korea’s opportunity cost of assembled cars is 0.333 component sets (from 1 component set produced per worker per day divided by 3 assembled cars produced per worker per day).

The theory of comparative advantage says countries should specialize in producing goods and services for which they have a comparative advantage, which is the ability to produce a good or service at lower opportunity cost than other countries. In this example, North Korea’s opportunity cost of producing assembled cars is lower in terms of component sets, so it should produce and export assembled cars.

The 200 workers in North Korea can assemble 600 cars (from 200 × 3). South Korea can produce 600 components with 100 workers (from 600 assemblies divided by 6 components per worker per day in South Korea). This leaves 100 workers in South Korea to produce components and assemble cars. Workers in South Korea can produce components used to make cars at the rate of 6 sets of components per worker per day and can assemble cars at the rate of 4 cars per worker per day, so 40 percent of the remaining 100 workers (40 workers, for a total of 140 workers) will be used to make components and 60 percent of the remaining workers (60 workers) will be used to assemble cars, resulting in additional output of 240 cars. Thus, a total of 840 cars can be produced with trade.

1.3

The firm’s process for selecting the people with the strongest skills in those areas to take time off from their regular tasks and work on the renovation is based on absolute advantage: A worker has an absolute advantage over other workers if that worker can produce more output. The theory of comparative advantage says workers should specialize 352

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in producing goods and services for which they have a comparative advantage, which is the ability to produce a good or service at lower opportunity cost than other workers. In this example, it would be better for the firm to select workers for the renovation based on their opportunity cost of renovating in terms of their regular tasks.

1.4

Not necessarily, it is likely that as good as he was at programming that Paul Allen was relatively even better at managing. In other words, even though Paul had an absolute advantage in programming, he had a comparative advantage in managing.

1.5

If Carrot Patch can only sell in Malaysia and it does produce, then it will maximize profit by producing the quantity where marginal cost equals marginal revenue. Marginal cost (MC) is MC = 2.

The firm’s inverse demand curve is p = 4 − 0.001Q. Marginal revenue (MR) has the same vertical intercept as demand with twice the slope: MR = 4 − 0.002Q. Setting marginal cost equal to marginal revenue, Carrot Patch would produce MC = MR 2 = 4 − 0.002Q 2 = 0.002Q Q = 1,000 units.

The profit-maximizing price is p = 4 − 0.001Q p = 4 − 0.001(1,000) p = $3.

Since price ($3) is greater than average variable cost ($2), the firm should produce.

Demand in Malaysia and Singapore is Q + Q = (4,000 − 1,000p) + (4,000 − 1,000p) = 8,000 − 2,000p.

The firm’s inverse demand curve is p = 4 − 0.0005Q. Marginal revenue (MR) has the same vertical intercept as demand with twice the slope: MR = 4 − 0.001Q. Setting marginal cost equal to marginal revenue, Carrot Patch would produce MC = MR 2 = 4 − 0.001Q .

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2 = 0.001Q Q = 2,000 units.

The profit-maximizing price is p = 4 − 0.0005Q p = 4 − 0.0005(2,000) p = $3.

Since price ($3) is greater than average variable cost ($2), the firm should produce.

1.6

Yes, by opening up markets to its toys, Mattel (the manufacturer of Barbie dolls) is able to enjoy economies of scale by producing large numbers of each version.

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EXCHANGE RATES 2.1

An exchange rate is the price of one currency, such as the euro, in terms of another currency, such as the dollar. In this example, the exchange rate of euros for yen is one euro for 132 yen (from one euro for 1.2 dollars multiplied by one dollar for 110 yen).

Arbitrage equates prices in two countries in the absence of transaction costs. If the transaction cost is t, arbitrage moves the price in one country to within t of the price in the other country because further arbitrage is unprofitable. If the euro-yen exchange rate were higher than one euro for 132 yen, then euros should be exchanged for yen because such a trade is profitable (since one euro really equals only 132 yen).

2.2

An exchange rate is the price of one currency, such as the euro, in terms of another currency, such as the dollar. In the figure, the quantity on the horizontal axis is the number of euros that Americans want to buy using dollars. As X increases (decreases), the price of a euro in terms of dollars increases (decreases), or equivalently, the price of the dollar in terms of euros falls (rises). The price on the vertical axis is the exchange rate, X, which is the number of dollars it takes to buy one euro. If the U.S. government fixed exchange rates at X2, then there would be a shortage of euros because demand for euros would exceed supply.

2.3

Managers can often increase profits by engaging in international price competition: charging higher prices in countries where consumers have a greater willingness to pay.

However, for international price discrimination to be profitable, firms must limit resale or arbitrage across countries. If arbitrageurs can buy the good in the low-price country and sell it at a higher price in other countries without incurring transaction costs, their actions eliminate the price differential. Foreign goods shipped to the high-price country and sold outside of authorized channels of distribution are called gray market goods. One way that a firm’s managers try to prevent arbitrage is to permit only authorized dealers to handle their products. Any authorized dealer that imports the product from another country instead of buying it from the manufacturer could lose its authorization. Managers have also called upon governments to enforce their rights under patent, trademark, and copyright. They have also used country-specific warranties (warranties that are only good in the country in which the manufacturer sold the good).

2.4

At the current exchange rate, Arvind will be able to exchange the $1.5 million for 99 million Indian Rupees (INR). If the exchange rate changes to 70 INR per dollar, then Arvind will earn 105 million INR. He would break even at an exchange rate of 60 INR per dollar.

2.5

Arvind could buy a forward contract that would guarantee the exchange of $1.5 million for 99 million INR (essentially locking in the current deal and his 6 million INR profit). He might have to pay a small (relatively speaking) fee for this contract, say 1 million INR, but it may be a good idea to have this insurance against the exchange rate risk. Since Arvind’s break-even exchange rate is 60 INR to $1, he may not be interested as in hedging if he

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expects only exchange rates greater than 60. On the other hand, if he can buy a forward contract that guarantees him a rate of 66 (with a fee of 1 million INR), then he would still be interested in hedging until his expected rate is only 65 or greater.

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INTERNATIONAL TRADE POLICIES 3.1

The main winner from the ban on Russian agricultural products and the resulting retaliation

by Russia banning food imports into Russia was Russian food-producing firms who benefitted because of rising prices. The main losers were Russian consumers who were forced to pay much higher prices for food.

3.2

With trade (and a world price of pworld for sugar of 11¢), the United States consumes QD units, supplies QS units, and imports QD minus QS units of sugar.

Initially, consumer surplus (CS) in the United States is the area under the demand curve (which represents the value to consumers) and above the world price (what consumers pay for the sugar) for the units consumed (QD units). Producer surplus (PS) in the United States is the area under the world price (what producers receive for the sugar) and above the supply curve (what it costs producers to supply the sugar) for units supplied (QS).

If trade is eliminated with a quota, then the U.S. market equilibrium price is p1 (27¢) and the equilibrium quantity is Q1.

When trade is eliminated, consumer surplus decreases by A + B + C and producer surplus increases by A. The result is deadweight loss (lost economic surplus) of B + C. In the corn sweetener market, demand is increased due to the increased price of the substitute, raising prices from p1 to p2. Producers gain A + B. Consumers gain the equivalent of C + D + E. Thus, total surplus in the corn sweetener market increases by A + B + C + D + E.

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3.3

Assume the domestic supply curve hits the vertical axis at p1. The total supply curve will be the same as the foreign supply curve for prices below p1. For prices above p1, the total supply curve will be the horizontal sum of the domestic and foreign supply curves. Thus, the total supply curve will be upward sloping and kinked outward at a price of p1.

3.4

First consider the U.S. market for water. The free-trade price is pw, at which price the quantity supplied in the United States is Qs, and the quantity demanded in the United States

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is QD. Assume the Canadian water export ban eliminates U.S. water imports. The no-trade domestic price is p1, and the no-trade domestic equilibrium quantity is Q1.

The embargo reduces consumer surplus by A + B + C. The embargo increases producer surplus by A. Deadweight loss from the embargo is B + C.

Next consider the Canadian market for water. The free-trade price is pw, at which price the quantity supplied by Canada is Qs, and the quantity demanded is QD in Canada. Assume the Canadian water export ban eliminates Canadian water exports. The no-trade domestic price is p1, and the no-trade domestic equilibrium quantity is Q1.

The embargo increases consumer surplus by A + B. The embargo decreases producer surplus by A + B + C. Deadweight loss from the embargo is C.

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3.5

For the country to be a net importer, the world price must be below the domestic price without trade. The subsidy will further reduce the price consumers pay, increasing the quantity consumed and consumer surplus. At the lower price, domestic producers will supply less, and producer surplus will decrease. The increase in consumer surplus will be greater than the decrease in producer surplus. The total cost of the subsidy paid by the importing country will equal the quantity imported multiplied by the subsidy. This cost (of the subsidy) paid by the importing country will be greater than the net change in surplus, so welfare will decrease.

3.6

The figure below represents the Mexican market for corn. Assume that before NAFTA, the Mexican price is p1. Suppose the free-trade price with NAFTA is pw, at which price the quantity supplied in Mexico is Qs and the quantity demanded in Mexico is QD. Additional trade increases consumer surplus by A + B. The trade decreases producer surplus by A. New surplus from the additional NAFTA trade is B.

Next consider the market for corn in the United States. Before the additional NAFTA trade, the price in the United States is p1. The price in the United States with the additional NAFTA trade is pw, at which price the quantity supplied by the United States is Qs and the quantity demanded is QD in the United States. The U.S. supply before the subsidy is S and with the subsidy is SS. The additional NAFTA trade decreases consumer surplus by A + B. The trade increases producer surplus by A + B + C + D + E + F. New government expenditures equal the size of the subsidy (the vertical distance between the supply curve without the subsidy and the supply curve with the subsidy) multiplied by the increase in the quantity produced (the difference between the quantity supplied by U.S. producers at the original domestic price and at the new world price). The increased cost to the government is F + G. The change in surplus (the new surplus) is the difference in the change in consumer surplus and the

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change in producer surplus minus the increase in government expenditures. New surplus from the trade is C + D + E − G.

3.7

First consider the imported good. The figure below represents the U.S. market for the imported good (e.g., a manufactured good). The free-trade price is pw, at which price the quantity supplied in the United States is Qs and the quantity demanded in the United States is QD. Assume the embargo eliminates trade. The no-trade domestic price is p1, and the notrade domestic equilibrium quantity is Q1.

The embargo reduces consumer surplus by A + B + C. The embargo increases producer surplus by A. Deadweight loss from the embargo is B + C.

Next consider the exported good. The figure below represents the U.S. market for the exported good (e.g., an agricultural good). The free-trade price is pw, at which price the .

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quantity supplied by the United States is Qs and the quantity demanded is QD in the United States. Assume the embargo eliminates trade. The no-trade domestic price is p1, and the notrade domestic equilibrium quantity is Q1.

The embargo increases consumer surplus by A + B. The embargo decreases producer surplus by A + B + C. Deadweight loss from the embargo is C.

3.8

If the quota and the tariff raise the domestic price by the same amount, then the changes in consumer surplus and producer surplus are the same. The difference is that the tariff generates new government revenue, equal to the quantity imported multiplied by the size of the tariff. So, a government might prefer the tariff over the quota because it generates government revenue and the deadweight loss with the tariff is smaller (deadweight loss with the tariff is smaller than with the quota by an amount equal to the new government revenue). This is illustrated in Figure 17.3 in the text. New government revenue with the tariff is area D. Deadweight loss with the quota is area C + D + E; with the tariff, it’s only C + E.

3.9

If the payoff to each firm is 5 (rather than −5) if both enter, then entering becomes a dominant strategy for each firm, even without a subsidy to Novartis. If a subsidy of 10 is provided, then both firms enter with Ajinomoto earning 5 and Novartis earning 15.

3.10 Price discrimination is charging consumers different prices for the same good based on individual characteristics of consumers, membership in an identifiable subgroup (such as country of residence), or on the quantity purchased by the consumers. For a firm to price discriminate successfully, three conditions must be met. The firm must have market power; groups of consumers or individual consumers must have demand curves that differ and the firm must be able to identify how its consumers’ demand curves differ; and a firm must be able to prevent or limit resale. Dumping is flooding a market with goods sold at low prices to drive other firms out of business. Anti-dumping policies may limit international price discrimination by preventing companies from being driven out of business and, therefore, market competition from being reduced.

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MULTINATIONAL ENTERPRISES 4.1

Traditionally, a major motive for a firm to acquire or build foreign productive assets is to lower its cost of supplying that foreign market by producing in that market rather than exporting to it. Producing locally allows the company to reduce transportation costs and avoid tariffs or quotas on imported goods. However, as tariffs and transportation costs have fallen in recent years, and international communication has become easier, a second motive has become relatively more important: comparative advantage in the supply chain. In this example, auto manufacturers assemble cars overseas because the opportunity cost of car assembly in other countries is lower.

Chrysler’s minivans, the Ford Fusion, and the Chevy Camaro are assembled in Canada or Mexico. In 2012, the most-American car was the Toyota Camry, which is assembled in Georgetown, Kentucky; and Lafayette, Indiana. It is followed by the Ford F–150 and the Honda Accord.

4.2

To maximize combined profits, TMX Philippines should charge a transfer price equal to the marginal cost of $10. The Timex Group USA then sets its marginal revenue of 90 − 4Q equal to the transfer price (its marginal cost) of 10, which yields 90 − 4Q = 10 or Q = 20.

Price will be 90 − 40 = 50. TMX Philippines makes no profit in this case, but it could make positive profits if it raised the transfer price. However, the profit of the Timex Group USA would fall by more than the profit of TMX Philippines would rise.

4.3

Let c be the transfer price. The Timex Group USA maximizes profit such that their marginal revenue (MR) equals the transfer price (C): 90 − 4Q = c.

This is the demand for watches by the Timex Group USA. TMX Philippines’s marginal revenue is equal to demand with twice the slope: MR = 90 − 8Q. TMX Philippines will maximize profit by producing where marginal revenue equals their marginal cost (which is $10): MR = MC 90 − 8Q = 10 80 = 8Q Q = 10 thousand watches.

TMX Philippines’s profit-maximizing transfer price is c = 90 − 4(Q) c = 90 − 4(10) c = $50 per watch.

4.4

The managers of companies that produce in many countries must decide how much to trade and what prices to use when trading internationally between their units. These decisions .

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turn critically on differences in tax laws across countries. If corporate tax rates differ across countries, then a company should prefer to earn most of its profit in the low-tax country.

This is accomplished by adjusting transfer prices. In this example, if the Philippines has a lower corporate tax rate than the United States, then it should raise its transfer price above its marginal cost to shift profit from the United States, where corporate taxes are higher, to the Philippines, where corporate taxes are lower.

4.5

This change in the tax law will make it much more likely that cash held abroad will be brought back to the United States. This is true because the (reduced) tax rate applies equally to earnings held domestically or abroad.

4.6

This lower rate decreases the incentive for U.S. firms to shift profits to foreign countries since the difference between the foreign tax rate and the domestic rate is now smaller.

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OUTSOURCING 5.1

Outsourcing work to India by American firms will shift the Indian labor demand curve to the right (to D2). The new equilibrium, where the original Indian supply curve intersects the new Indian labor demand curve, will be at a higher wage (w2) with more employment (L2).

5.2

Before VIOP, the cost per hour of service in the United States was $50 and the cost per hour of service in India was $55, from $20 per hour in wages plus $35 per hour in telephone costs. Initially, it was optimal for Hewlett-Packard to provide service based in the United States. After VIOP, the cost per hour of service in the United States is $50, and the cost per hour of service in India is $45, from $20 per hour in wages plus $25 per hour in communication costs. Now, it is optimal for Hewlett-Packard to provide service based in India.

5.3

If the value of the rupee rises such that it costs more than $50 per hour to provide service for printers in India, then it will be optimal for Hewlett-Packard to keep its service support operations in the United States. Specifically, the hourly wage in India would have to rise from $20 per hour to at least $25 per hour, which would be possible if the Indian rupee rose in value by 25 percent.

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MANAGERIAL PROBLEM 6.1

The price of the perfume in France is 61.54 euros, from $80 divided by $1.30. International firms can often increase profits by engaging in international price competition: charging higher prices in countries where consumers have a greater willingness to pay. It might be profitable for Chanel to charge lower prices in the United States if consumer demand for the perfume in the United States is lower than in France.

If the value of the euro rises by 25 percent in terms of the dollar, then one euro will equal $1.625, from $1.30 multiplied by 1.25. Thus, the price of the perfume in France (assuming the price of the perfume in the United States does not change) will be 49.23 euros, from $80 divided by $1.625.

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