Solution Manual For Microeconomics and Behavior, 10th Edition Robert Frank Chapter(1-18)

Solution Manual For Microeconomics and Behavior, 10th Edition Robert Frank Chapter 1-18

Chapter 1 Thinking Like an Economist Answers to Review Questions 1. The opportunity cost of reading a novel this evening is not being able to do whatever you would have done instead. If you would have watched TV, then your opportunity cost is not watching TV; if you would have studied economics, then your opportunity cost is not studying economics.

2. The tuition is a sunk cost and so your roommate should consider only costs and benefits relevant now and in the future. If he will be better off in life by leaving school now, he should not let the tuition make the rest of life less meaningful.

3. Driving an automobile (which pollutes the atmosphere) imposes an external cost on others.

Building a house which others admire presents an external benefit. Inventing something which is new and useful, but which cannot be patented presents another external benefit.

4. A 50-year-old presumably is in a higher pay bracket than a 20-year-old so the opportunity cost of leaving the job is greater for the older person.

5. By definition, a sunk cost is a cost that is incurred regardless of one's current decisions.

6. Economists generally argue that people act in their own self-interest even if they do not consistently evaluate costs and benefits. The analogy most frequently used (from Milton Friedman) is that of a pool player who knows how to sink his shots without having studied physics.

Answers to Chapter 1 Problems 1. Let $X be the amount Jamal earns in a day on his job. The cost to Jamal of going to the park is then $15 (admission fee) + $5 (gas & parking) + $10 (the lost satisfaction from not working) + $X (lost salary) = $30 + $X. The benefit of going to the park is $45. He should go to the park if his salary is $10/day, and shouldn't go if his salary is $20/day. At a salary of $15/day, he is indifferent between going and not going.

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2. If Tom kept the $200 and invested it in additional mushrooms, at the end of a year's time he would have an additional $400 worth of mushrooms to sell. Dick must therefore give Tom $200 of interest in order for Tom not to lose money on the loan.

3. It is reasonable to assume that everybody has decreasing satisfaction from each pound of food as consumption level increases. In University A, everybody will eat until the benefit from eating an extra pound of food is equal to $0, since this is the cost of each pound of food.

In University B, people will eat until the benefit decreases to $2. Thus, everybody will eat less if they are at University B. So, not just average consumption but also each individual‘s personal consumption will be lower. Note that to reach this conclusion we need the assumption that the students at both universities have the same appetites.

4. The only costs that vary with mileage are fuel, maintenance, and tires, which are average $0.25/mile (cost of driving for fuel $1,200/10,000 = $0.12, for maintenance $1,100/10,000 = $0.11, and tires $200/10,000 = $0.02). The cost of driving will thus be $250 (= $0.25 × 1,000), and since this is less than the cost of the bus, you should drive.

5. The band and hall rental fees are fixed costs. The caterers charge at the rate of $7/guest ($5 catering bill/$2 drink). So, an extra 10 guests will increase total costs by only $70.

6. You gave up the $60 (= $1,000 × 0.06) you would have earned if the money was in your savings account. This assumes that your tax rate on interest earned is zero.

7. Monica has already bought her ticket, so her cost-benefit calculation when it is time to go is as follows: benefit of seeing game vs. cost of the drive + time costs, etc. Rachel, not having bought her ticket, faces a different calculation: benefit of seeing game vs. $30 + cost of the drive + time costs, etc. Since the benefits are the same in each case, but the costs are larger for Rachel at the moment of decision, she is less likely to go.

8. A plane of either type—large or small—should use the state-of-the-art device if the extra benefits of that device exceed its extra costs. Because the device will save more lives in large planes than in small planes, its benefits are larger in large planes than in small ones.

Your original recommendation was presumably based on the calculation that the benefits for the larger planes justified the extra cost but did not do so in the case of the smaller planes.

Airline passengers are like other people insofar as their willingness to invest in extra safety is constrained by other pressing uses for their scarce resources. Where extra safety is relatively cheap, as in large planes, they will rationally choose to purchase more than when it is relatively more expensive, as in small planes.

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9. With more than a week to go, the $100 driver's fee and the $50 bus cancellation fee are sunk costs. If the trip takes place, the additional costs will be the remaining $450 of the bus fee plus the $75 in tolls, for a total of $525 in additional costs. If at least 30 tickets will be sold, it makes sense to continue the trip, since total revenue ($540) will exceed the additional cost.

10. Assuming that residents are required to recycle cans, they simply cannot put them with the regular trash. In the first case, the fixed cost of $6/week is a sunk cost. Therefore, for the residents, the cost of disposing an extra can is $0. In the tag system, the cost of disposing an extra can is $2, regardless of the number of cans. Therefore, since the costs are higher and the benefit of setting out a can is assumed to be the same in both cases, you expect less cans to be collected in the tag system.

11. The benefit of the 1st gigabyte is $32, the 2nd is $16, the 3rd is $8, the 4th is $4, the 5th is $2, the 6th is $1, the 7th is $0.50 and the 8th is $0.25. At a cost of $8, you should purchase 3 gigabytes. At higher levels of benefit, the benefit is less than the cost. At lower levels, benefit exceeds the cost.

Price 32.00

16.00

8.00 4.00 1

2

3

4

5

6

7

8

9 Memory (GB)

12. The benefit of the 1st gigabyte is $1,600, the 2nd is $800, the 3rd is $400, the 4th is $200, the 5th is $100, the 6th is $50, the 7th is $25, and the 8th is $12.50. At a cost of $50 and your willingness to pay $800 for the first gigabyte, you should purchase 5 gigabytes. When your benefit rises to $1,600 for the first gigabyte, you consume 6 GB of RAM. Price 32.00 The curve to the right shows the new benefit function.

16.00

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8.00 4.00 1

2

3

4

5

6

7

8

9 Memory (GB)

13. False. The fact that Dana would have chosen the party before she bought her ticket means that she prefers a party to an event that costs $40. Now her choice is between two events that she can attend with no further payment.

14.

Benefit Cost (initial) Cost (final)

Taylor Swift Bp

Bruno Mars Br

$75

$75 $75

$50

In the problem, we are given that Bp – $75 > Br – $75 or Bp > Br (*) Now, we need to find out whether the following is true or not: Bp – $75 > Br – $50 which is the same as Bp > Br + $25 (**) Notice that (*) does not necessarily imply (**). For example, if Bp= $80 and Br= $60, then (*) holds while (**) does not. So we can conclude that you should not go to the Taylor Swift concert in the above scenario if you are a rational utility maximizer.

Your decision will depend on the relative values of Bp and Br. The fact that you would have bought a Taylor Swift ticket means that the benefit of attending the Taylor Swift concert, denoted Bp, must be greater than $75. Let Bs denote the benefit of going to the Bruno Mars concert. The fact that you would have chosen the Taylor Swift concert before receiving your Bruno Mars concert ticket means that Bp > Bs. But this does not imply that you should go to the Taylor Swift concert. Suppose Bp = $80 and Bs = $60. When you now choose between the two concerts, the opportunity cost of attending the Bruno Mars concert is $50, so the net benefits of attending each concert are given by Bd – $75 =$5 and Bs – 50 = $10, which means you should go to the Bruno Mars concert. So FALSE.

15. Safari provides $10,000+/yr more enjoyment than a business job. $70,000 = gross benefit of business job salary.

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50,000 lost salary as safari leader 10,000 + lost enjoyment from safari job $70,000 + total cost of taking of business job > benefit, so don't take the job.

If business salary was $70,001/yr, he would have taken it.

16. True. If you got $20,000 for the Equinox and paid that plus $5,000 more for the Explorer, the entire Explorer expense would have cost you $25,000. Since you have already shown that you did not want the Explorer for $25,000, why would you spend that for it now?

Chapter 2

Supply and Demand

Answers to Review Questions 1. A shortage occurs when, at a given price, quantity demanded exceeds quantity supplied.

Scarcity implies that not everyone can consume as much of a good as he wants. A good can be scarce without a shortage occurring if the price of the good is set at the market equilibrium.

2. The supply curve would be a horizontal line where the price equals zero. The demand curve would be a typical demand curve. If the price is greater than zero, then the market system is acting to allocate resources; not everyone can have as much as they want.

3. Some examples: Parking places for the president of the college; giving seniors priority in class assignments. Shortage of parking spaces and students being bumped from preregistration.

4. A reduction in supply implies a shift in the supply curve whereas a reduction in the quantity supplied implies a movement along the supply curve.

5. a. Change in demand b. Change in the quantity demanded (shift in supply) c. Change in the quantity demanded (shift in supply) d. Change in demand

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6. Because consumers prefer to pay a lower price. When there is excess supply, the price is above the equilibrium price. So as the price falls, the quantity supplied falls, while the quantity demanded increases

7. The allocative function of price is not important with vertical, or nearly vertical, supply curves, e.g., land.

8. For the tax burden to fall mostly on consumers rather than producers (buyers rather than sellers), you want to find a product (or products) for which the quantity supplied is very responsive to price but quantity demanded is less responsive to price. Addictive goods like cigarettes and alcohol may fit this description.

9. If a poor person were given $50,000 in cash, it is unlikely she would spend it on a Mercedes, since she probably has other, more pressing wants. Since the gift Mercedes would fetch less than the cash gift, most poor persons would choose the cash.

Answers to Chapter 2 Problems 1. a. The imposition of the ceiling price on tea causes a reduction in the quantity of tea bought, from Q1 to Q2 (left panel). The result is a leftward shift in the demand for lemons, resulting in a reduction in both price and quantity (right panel).

b. The ceiling price for tea lowers the quantity people are able to buy from Q1t to Q2t.

There is excess demand for tea at the ceiling price P2t, and some of this excess demand spills over to substitute products such as coffee. The result is that the equilibrium price of coffee rises.

(Note: This result may seem inconsistent with the claim that a fall in the price of a good's substitute reduces the demand for that good. But this claim refers to a fall in the equilibrium price of the good, not a price reduction caused by a ceiling. Because of the 6 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

quantity reduction caused by the ceiling, tea buyers would be willing to pay P3t for tea.

So the price ceiling actually raises the opportunity cost of additional units of tea.)

Pcoffee

P tea

St

Sc

P3t P1t

Pc 2 c P 1

Pt 2 D Qt Qt 1 2

D 1 Qc Q c 1 2

Qtea

D2

Qcoffee

2. a. The given supply and demand curves suggest that 16.15 million LPs would have been sold in 2018 at a price of $25.50. b. Total revenue is 16.15 million × $25.50 = $411,825,000. c. A possible graph is

Price of Vinyl LPs

The US Market for New Vinyl LPs - 2018 $30 $29 $28 $27 $26 $25 $24 $23 $22 $21 $20 10

11

12

13

14

15

16

17

18

19

20

Millions of LPs LP Demand

d. Technology, as represented by music streaming services, and the low price of streaming services as a substitute, may represent the fall in demand for CDs. Since, vinyl LPs face the same headwinds, their success is more likely attributed to a change in consumer tastes or, since tastes in music are strongly generational, an actual turnover in consumers. The price difference of vinyl LPs may reflect higher per unit production costs, but the relative price strength of LPs could have many explanations. Commentators have speculated that consumers value LPs (and their covers) as artwork as well as means

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of listening to music. When it comes to music, ―collectibles‖ may command higher prices than consumables.

3. a. A reduction in the price of hardware would raise demand for software and thus cause equilibrium price and quantity of software to rise. b. A rise in the price of software would reduce demand for hardware and thus cause the equilibrium price and quantity of hardware to fall.

4. a. Both price and quantity drop.

b.

Both quantity and price drop.

c. Both price and quantity go up.

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5. a.

b.

The price goes up, the quantity goes down.

The price and the quantity go down.

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c.

The price and the quantity go up.

d.

The price and the quantity go down.

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e.

6. a. b. c. d. e.

The price goes down, the quantity goes up.

Change in quantity demanded.

Change in demand.

Change in demand.

Change in demand.

Change in quantity demanded.

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7. a. The equilibrium quantity is Q = 90,000 seats and the equilibrium price is P = 1,900 – (1/50)(90,000) = 1,900 – 1,800 = $100. b. At a price ceiling of P = $50, quantity demanded is found by solving 50 = 1,900 – (1/50)Q for Q = 92,500 seats. Since the stadium only holds Q = 90,000 seats, there will be 92,500 – 90,000 = 2,500 dissatisfied fans who want to buy a ticket at P = $50 but cannot find one available. c. Quantity demanded for the higher demand is found by solving 50 = 2,100 – (1/50)Q for Q = 102,500 seats. Now there will be 102,500 – 90,000 = 12,500 dissatisfied fans who want to buy a ticket at P = $50 but cannot find one available. The excess demand is 12,500 – 2,500 = 10,000 seats more than for the not so big game. d. Normally a price ceiling both raises quantity demanded and lowers quantity supplied.

Here, only the first effect is present because the stadium capacity is fixed.

8. a. Under the original demand curve, quantity demanded was Q = 900 units and quantity supplied Q = 300 units, so excess demand was 900 – 300 = 600 units. With the larger demand, quantity demanded becomes Q = 1,100 units, so excess demand becomes 1100 – 300 = 800 units. Excess demand has grown by 800 – 600 = 200 units. b. Quantity demanded is Q = 1400 – P; quantity supplied is Q = P. Subtracting quantity supplied form quantity demanded gives excess demand of 1,400 – 2P units. Set excess demand equal to the original level of 600 and solve 600 = 1,400 – 2P for the required price floor of P = $400. If the government accommodates the increase in demand by raising the rent control from $300 to $400, the degree of excess demand will be unchanged.

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9. a. With a price support of P = $500/ton and the original supply of P = Q, quantity supplied must be Q = P = 500 tons. Meanwhile, quantity demanded is Q = 100 tons, so excess supply is 500 – 100 = 400 tons. With the expanded supply of P = (1/2)Q, quantity supplied grows to Q = 2P = 1,000 tons. Quantity demanded is still Q = 100 tons, so excess supply grows to 1,000 – 100 = 900 tons. b. The extra 500 tons (= 900 – 400) the government has to buy of excess supply costs the government $500/ton, so the added expenditure is 500 × 500 = $250,000.

10. a. Set the supply for each area equal to the demand and solve for P and Q.

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Nimbyville: Qd = 2,000 – 0.75Ps = Qsn = 100 + 2Psn; 1,900 = 2.75Psn; Psn = $691; Qsn = 1,481 apartments Yimbyville: Qd = 2,000 – 0.75Ps = Qsy= 400 + 2Psy; 1,600 = 2.75Psy; Psy = $582; Qsn = 1,564 apartments b. We would expect that the restrictions in Nimbyville would cause some residents to move to Yimbyville, in search of housing bargains. The population increase would cause the demand curve to shift for apartments in Yimbyville to shift to the right and—absent any new supply—apartment prices would rise. In Nimbyville, the loss of population might cause apartment prices to fall. c. No. The given equations, if solved in terms of P for the demand equation would be P = 1,600 – 0.8Q would yield the same equilibrium figures.

11. The supply curve becomes P = 2 + 2Q and the demand remains P = 8 – 2Q. By setting the two equations equal to each other and solving for Q we have Q = 1.5. Substituting 1.5 into the demand equation results in a price of 5.

Answers to Appendix Problems 1. The supply curve after the tax is shown as S' in the diagram. The new equilibrium quantity will fall to 2. The equilibrium price paid by the buyers is now $4/oz. The price received by the sellers is now $2/oz.

Price ($/ounce) 6

S' S

5 4 3 2 1 D 1

2

3

4

5

6

Quantity (tons/year)

2. The supply curve tells us that at a quantity of 2 tons/yr. suppliers will be willing to supply additional titanium at a price of $2/oz. At that same quantity, buyers are willing to pay $4/oz. Suppose a supplier sells one ounce to a new buyer at a price of $3. This will make the supplier better off by $1. The buyer will also be better off by $1.

3. With the tax of T = $2/oz on sellers, the supply curve shifts up by the amount of the tax from

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curve is found by solving 8 – Q = 2 + Q for Q = 3 tons. Inserting the quantity into the demand curve yields a price buyers pay of P = 8 – 3 = 5 an ounce and hence a price sellers receive of P = 5 – 2 = 3 an ounce. The government collects revenue of TQ = 2(3) = $6. Prior to the increase in demand, the government collected the tax on only 2 ounces, so its total revenue collected was $4. Thus, government revenue has grown by 6 – 4 = $2 due to the expansion in demand for titanium. See the graph below

4. At a price floor of P = $4/oz, quantity supplied would be Q = 2 tons. Using demand P = 6 – Q and P = $4/oz, quantity demanded is also Q = 2 tons. Thus, the reduction in supply raises the equilibrium price to the level of the price floor, so the price floor is no longer binding.

5. a. 13.85 million LPs in equilibrium b. Buyers will pay $27.00 c. See graph.

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The US Market for New Vinyl LPs - 2018 $3.00 Tax imposed on Seller $32

Price of Vinyl LPs

$30

$28

$26

$24

$22

$20 10

11

12

13

14

15

16

17

18

19

20

Millions of LPs LP Demand

LP Supply 1

LP Supply 2

d. Buyers will now spend a total of $373.95 million. e. The government will collect $41.55 million in taxes.

6. a. The seller bears 50%. b. The buyer bears 50%. c. The supply and demand curve have equal 0.65 responses to a change in price. d. If the ―real life‖ effect of the $3 tax were smaller than we have modeled, it would suggest that our supply or demand curve was too steep. On the demand side, a smaller effect would suggest that consumers substitute for vinyl LPs at a lower rate than 0.65 per dollar in price. Similarly, a larger-than-expected effect of a $3 tax on sales would suggest that consumers are more sensitive to the price of LPs than we have modeled.

7. In the diagram below, P* and Q* are the original equilibrium price and quantity of Japanese cars sold in the U. S. If a quota of Q1 is imposed, Japanese car makers will be able to charge P1 for their cars. To get the same quantity reduction by means of a tax, the after-tax supply curve must intersect the demand curve at Q1. The result is a price to the U. S. buyer of P1, the same as in the quota case. The difference in the two policies is that in the quota case the price increase goes to Japanese car makers, while in the tariff case it goes to the U. S. government.

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S'

Price

S

P1 P* P -T 1

D Quantity Q*

Q1

8.

Price

S(tax) S

120 90 60 45 30 D

Quantity 15

30

60

a. Before tax: 120 – 2Q = 30 + Q (in equilibrium) Q = 30 P = 60 b. After tax supply curve: P = 60 + 2Q Equilibrium: 120 – 2Q = 60 + 2Q Q = 15 Price, including tax = 90 Price received by seller (net of tax) = 45. c. Sellers share = 60 – 45 = 15 Buyer‘s share = 90 – 60 = 30 9. a-c. With the tax on sellers, supply rises by the amount of the tax to P = 4 + 4Q. the equilibrium is found by solving 20 = 4 + 4Q for Q = 4 units. Buyers pay P = $20 and sellers receive 20 – 4 = $16. Sellers pay the full tax because demand is perfectly elastic, which means that buyers cannot be forced to pay any of the tax.

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10. a-c. With the tax on buyers, demand falls by the amount of the tax to P = 24 – Q. The equilibrium is found by solving 20 = 24 – Q for Q = 4 units. Sellers receive P = $20, and buyers pay 20 + 4 = $24. Buyers pay the full tax because supply is perfectly elastic, which means that sellers cannot be forced to pay any of the tax.

Chapter 3

Rational Consumer Choice

Answers to Review Questions 1. You will be as well off as a year ago; your budget line will remain the same.

2. False. The slope of the budget constraint tells us only the ratio of the prices of the two goods.

3. False. Diminishing marginal rate of substitution explains the convexity of the indifference curve, but not the downward slope.

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4. You prefer Coke to Diet Coke, Diet Coke to Diet Pepsi, but prefer Diet Pepsi to Coke.

5. The slope of an indifference curve indicates how much of a good one is willing to give up to get one unit of another and be at the same level of satisfaction. Thus the more of one good that one is willing to give up, the less important is that good relative to the other.

6. One bundle may be within the individual's opportunity set while the other is not.

7. If the relative price of the two goods is not the same as the slope of the indifference curve, then one will always get a corner solution.

8. True. The corner solution (a) is on a higher indifference curve than the corresponding tangency (b). Which corner becomes the solution depends on the slope of the budget constraint. There can be a solution in either corner, as shown in the graphs below. Quantity discounts will not change this outcome scenario.

Y

a

Y

B

b a X

X

9. Suppose that Monique's current consumption bundle is given by the point A in the diagram.

The information given tells us that on the budget with M + 10 units of income, Monique would consume at the point B, and that B is equally preferred to C. This can happen only if the indifference curve passing through B and C does not have the usual convex shape. Her indifference curve through B and C could, for example, be a straight line, indicating that tuna fish and Marshallian money are perfect substitutes in this region. (If the indifference curve through B and C were convex, then Monique's optimal bundle would lie between B and C, which means that he would spend some of the extra $10 on tuna fish.)

Y M + 10 M

B

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Answers to Chapter 3 Problems 1.

Y($/wk) 100 80 60 40 20 Seeds (lbs/wk) 20

40

60

80

100

40

60

80

100

2.

Y($/wk) 100 80 60 40 20 Seeds (lbs/wk) 20

3. a. Pecans are equally preferred to macadamias, which are preferred to almonds, which are preferred to walnuts, so by transitivity it follows that pecans are preferred to walnuts. b. Macadamias are preferred to almonds and cashews are preferred to almonds. Transitivity tells us nothing here about the preference ranking of macadamias and cashews.

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4. True. Each price increases by 15%, so that – Px/Py is unchanged.

Y M/80 M/92

slope = 120/80 = 3/2

Slope = 138/92 =3/2

M/138 M/120

X

5. a.

Y 150

60

Milk Balls

b. The opportunity cost of an additional unit of the composite good is 1/2.50 = 0.4 bags of milk balls.

6. a.

Y 150

100

60

Milk Ball

b. The opportunity cost of a unit of the composite good is now 0.6 bags of milk balls.

7. a.

Y 150

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90 Milk Balls b.

The opportunity cost of a unit of the composite good is again 0.6 bags of milk balls.

8. a. To get any enjoyment from them, Picabo must consume skis and bindings in exactly the right proportion. This means that the satisfaction Picabo gets from the bundle consisting of 4 pairs of skis per year and 5 pairs of bindings will be no greater than the satisfaction provided by the bundle (4, 4). Thus the bundle consisting of 4 pairs of skis per year and 5 pairs of bindings lies on exactly the same indifference curve as the original bundle. By similar reasoning, the bundle consisting of 5 pairs of skis per year and 4 pairs of bindings lies on this indifference curve as well. Proceeding in like fashion, we can trace out the entire indifference curve passing through the bundle (4, 4), which is denoted as I1 in the diagram. b.

Skis (pairs/yr)

20 16

I4

12

I3

8

I2

4

I1 0

4

8

12

16

18

20 Bindings (pairs/yr)

9. Picabo's budget constraint is B = 15 – 2S. Initially, she needs the same number of pairs of skis and bindings S = B. Inserting this consumption equation into her budget constraint yields B = 15 – 2B, or 3B = 15, which solves for B = 5 pairs of bindings (and thus S = 5 pairs of skis). As an aggressive skier, she needs twice as many skis as bindings S = 2B. Inserting this consumption equation into her budget constraint yields B = 15 – 4B, or 5B = 15, which solves for B = 3 pairs of bidings (and thus S = 6 pairs of skis). She consumes more skis and fewer bindings as an aggressive skier than as a recreational skier. See graph below.

Pairs of Bindings per Year (B) 15

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B = 15 – 2S

B+S 5 B = S/2 3 0

5 6 Pairs of Skis per year (S)

7.5

10. Alexi's budget constraint is T = 75 – (3/4)C. Her perfect substitute preferences yield linear indifference curves with slope equal to negative one, such as T = 75 – C and T = 100 C. By consuming 90/0.90 = 100 cups of coffee each month, she reaches a higher indifference curve than consuming 90/1.20 = 75 cups of tea (or any affordable mixture of coffee and tea). Thus Alexi buys 100 cups of coffee and no tea. Any increase in the price of coffee would force Alexi to a lower indifference curve, and thus lower her standard of living.

Cups of Tea/month (T) 100 T = 100 – C 75 T = 75 – (3/4)C

0

100 Cups of Coffee per month (C)

11. In the diagram, suppose we start at bundle A and then take away P units of pears. How many more units of apples would we have to give Eve to make her just as happy as at A? The answer is none, because she didn't care about pears in the first place, and therefore suffered no loss in satisfaction when we took P units of pears away. Bundle B is thus on the same indifference curve as bundle A, as are all other bundles on the horizontal line through A. All of Eve's indifference curves are in fact horizontal lines, as shown.

Apples (lbs/wk)

Increasing satisfaction 

B A P

Pears (lbs/wk) 23

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12. Again start at a given bundle, such as A in the left panel of the diagram below. Then take

away a small amount of food, F, and ask what change in smoke, S, would be required to restore Koop's original satisfaction level. In the standard case, when we take one good away we need to add more of the other. This time, however, we compensate by taking away some of the other good. Thus, when we take F units of food away from Koop, we must reduce the smoke level by S in order to restore his original satisfaction level. This tells us that the indifference curve through A slopes upward, not downward. Koop would be just as happy with a smaller meal served in a restaurant with a no-smoking section as he would with a larger meal served in a restaurant without one.

It is usually possible to translate the consumer's indifference curves into ones with the conventional downward slope by simply redefining the undesirable good. Thus, if we might focus not on smoke, an undesirable good, but on cleanliness (the absence of smoke), which is clearly desirable. So doing would recast the indifference map in the left panel of the diagram as the much more conventional-looking one in the right panel.

Food (lbs/wk)

Increasing Satisfaction 

I3 I2 I1

Food

Increasing Satisfaction 

B A F

I3 I2

S

I1

Smoke (micrograms/wk)

Cleanliness

13. You would want to choose the option where customers consume the least electric power.

Depending on demand, this could be either option. But, option 2 is the one most likely to cause lower consumption. With option 2, a customer will consume electricity until the point where they are willing to pay $0.08/kWh. With option 1, a customer who consumes more than 1,000kWh, will consume until the point where they are willing to pay $0.05/kWh. Given that the cost of using electricity is lower with option 1 the customer will consume more. So, if most customers use more than 1,000kWh per month the best option to reduce electricity usage is option 2.

14. a.

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Movies 36 30 24 21 15

B0

B 1 5

7

10

12 Plays

b. If plays cost $12 and movies cost $4, the budget line is Bo, which has exactly the same slope as Paula's indifference curves. She will be indifferent between all the bundles on B0. c. On B1, she will consume 10 plays.

15. a- b) Y

Increasing satisfaction

Y Increasing Satisfaction

Garbage

Garbage

16. Let C = coffee (ounces/week) and M = milk (ounces/week). Because of Boris's preferences, C = 4 M. At the original prices we have: 4M(l) + M(0.5) = 9 4.5M = 9 So M=2 and C=8

Let M' and C' be the new values of milk and coffee. Again, we know that C'=4M'. With the new prices we have: (4M')(3.25) + M'(.5) = 9 13M' + 0.5M' = 9, 13.5M' = 9, M' = 2/3 C = 8/3

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17. An unrestricted cash grant would correspond to the budget B1 in the diagram. On B1 the university would want to spend more than 2M on non-secular activities anyway, so the restriction will have no effect. This result is analogous to the result in the text concerning the restriction that food stamps not be spent on cigarettes. Provided the recipient would have spent more on food than he received in stamps, such a restriction has no effect.

Non-secular Activities 14 12 10

B0

B1

8 6 4 2 0

2

4

6

8

10

12

14

16 Secular Activities

18.

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19 a.

10(0) + 10(0.25) = 2.50

b. 10(0.25) + 10(0.50) = 2.50 + 5.00 = 7.50.

20. Your budget constraint is Y = 360 – 40C for 0 < C < 5 days of car rental (when you pay the daily rate), constant at Y = 160 for 5 < C < 7 days of car rental (when you switch to the weekly rate and thus additional days up to one week are free), and then Y = 160 – 40(C – 7) = 440 – 40C for 7 < C < 11 (when again you have to pay by the day for each day beyond the one week).

a. If y = 140C, then inserting this equation into the first leg of the budget constraint yields 140C = 360 – 40C or 180C = 360, which solves for C = 2 days of car rental and thus Y = 280 worth of other goods.

Composite Good per trip (Y) 360

Y = 140C Y = 360 – 40C

280

Y = 160 160 Y = 440 – 40C 0

2

5 7 11 Days of Car Rental per trip (C)

b. If instead you will trade a day of car rental for $35, then you would consume a week's rental C = 7 and thus Y = 160 worth of other goods. Your seven days of car rental are equivalent to 7(35) = $245 according to your preferences, which when added to the $160 remaining, yields $405. This 27 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

beats the $360 if you consume no rental days and also beats the 11(35) = $385 if you consume the maximum rental days you can afford (as well as beating any other affordable combination of C and Y. Composite Good per trip (Y) 360 Y = 405 – 35C Y = 360 – 40C Y = 160 160 Y = 440 – 40C 0

5 7 11 Days of Car Rental per trip (C)

21. With diminishing MRS, to decrease pizza consumption from 3 to 2 slices, Tony has to be given more than 1 beer (since that was the amount needed to decrease pizza consumption from 4 to 3 slices and stay on the same indifference curve). So he would be indifferent between the bundles (3 slices of pizza, 2 beers) and (2 slices of pizza, X beers) where X > 3.

However, we know that he prefers (1 slice of pizza, 3 beers) to (3 slices of pizza, 2 beers), so he should also prefer that bundle to (2 slices of pizza, X beers). But this violates the more-isbetter assumption.

22. Budget set under Plan A:

composite($/week)

12

calls(number/wk) 240 Budget set under Plan B:

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composite($/week)

12 .

10

.

calls(number/wk) 30

230

Notice that Plan A is superior to Plan B since its budget constraint is above the budget constraint of Plan B. 23.

Note that the budget constraint is not a line but rather the set of points that are shown in the diagram and the ones that are below them. To construct this, for each level of composite good, from 0 to 12, determine the maximum number of bottles you can buy with the leftover money. For example, for Y = 4, you have $8 left. The best you can do is 1 large and 1 small,

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which gives 11 tickets. Remember that you can't buy a fraction of a set. Notice that point (0,12) is also on the budget constraint.

24. Assume that the quality of the food is the same in both restaurants, so that price is the only difference that matters to consumers. In the first restaurant, the $15 flat tip is a fixed cost: it does not affect the cost of additional items ordered from the menu. In the second restaurant, by contrast, the price will be 15 percent higher for each extra item you order. The marginal cost is higher. The average meal is $100 in the first restaurant, which with tip comes to $115.

The same amount of food would cost the same in the second restaurant. But because the cost Y (1000s) of each additional item is higher there, we expect that less food will be consumed in the 16 second restaurant. Note the similarity of this problem to the pizza experiment described in Chapter 1. 14 10

25. Bo is Plane's budget constraint last year. By selling all his grapes he would have an income of $14,000. By spending all his income on grapes he would have 7000 bu. This year's budget constraint is B1. It starts at 16 on the Y axis and IC0 hits the grapes axis at 16/3, passing through Y = 10, G = 2, last year's bundle.

B1 Since B0 last year's indifference curve (ICo) was tangent to B0 at Y = 10, G = 2, and since this year's budget constraint is steeper than last year's, we know that some part of last year's a part of ICo that lies above Y = 2 IC lies 5.33within 7 B Grapes (1000 bu/yr) 1. In particular, 10, G = 2 is within B1. This means that Plane will consume more Y and less G than he did last year. (See graph.)

Answers to Chapter 3 Appendix Problems 1. Solve the budget constraint, 100 = 4X + l0Y, to get Y = 10  0.4X, then substitute into the utility function to get U = X(10  0.4X ) = 10X  0.4X2. Equating aU/aX to zero we have 10  0.8X = 0, which solves for X = 12.5. Substituting back into the budget constraint and solving for Y, we get Y = 5.

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2. The result of solving the budget constraint for Y and substituting back into the utility function is now U=X1/2(10  0.4X)1/2. ¶U / ¶X = (1/2)X-1/2(10  0.4X)1/2 + X1/2(1/2)(10  0.4X)-1/2( 0.4) = 0 Rearranging terms, we get (10  0.4X)/X = 0.4, which solves for X = 12.5. Plugging back into the budget constraint, we get Y = 5. Thus the optimal bundle is (12.5, 5), the same as in problem 1.

3. Note that the utility function in Problem 1 is simply the square root of the utility function in Problem 2. Since the square root function is an increasing function, it follows that the values of X and Y that maximize utility in Problem 1 will also maximize utility in Problem 2.

4. Since we are given the marginal utility per last dollar spent on each good, the prices, per se, do not matter. If Aria spent $1 less on clothing and $1 more on food, her total utility would change by 9 + 12 = 3. So, no, she cannot be maximizing utility.

5. For Miguel to be a utility maximizer, he must allocate his allowance so that the extra utility per dollar is the same for both the last book he purchased and the last movie he rented. As shown in the table, this condition is satisfied when he purchases 2 books and rents 3 movies.

And since this bundle costs exactly his weekly allowance (2 × 4 + 3 × 3 = 17), he is maximizing his utility.

N U(N) MU(N) MU(N)/PN M U(M) MU(M) MU(M)/PM __________________________________________________________________ 0 0 0 0 12 3 21 7 1 12 1 21 8 2 12 4 2 20 2 33 4 1 6 2 3 24 3 39 4 1 3 1 4 28 4 42

Chapter 4

Individual and Market Demand

Answers to Review Questions 1. Salt is generally considered a necessity. As the text points out, the income effect for salt is extremely small.

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2. Unlike salt, education at a large private university has a large income effect.

3. See Figure 4-5 in the text. If a good exhibits a stable Engel curve, we may then define its income elasticity of demand, which is a formal measure of the responsiveness of purchase decisions to variations in the average market income. A negative slope of an Engel curve means a good is inferior and income elasticity of demand is less than 0. A positive slope of Engel curve means a good is normal and income elasticity of demand is also positive.

4. Some examples: hamburger, generic beer, bus tickets, almost anything purchased at stores selling "as is" damaged or discontinued merchandise.

5. Yes. A downward-sloping PCC simply implies that as the price of a good falls, the consumer purchases so much more of the good that the proportion of income spent on the good actually increases.

6. When we sum horizontally, we determine the total quantity demanded at every price.

Horizontal summation means each person consumes their commodity and excludes others from it. Vertical summation would mean that each good could be jointly consumed.

7. An elastic demand leads to revenue increases if price falls. An inelastic demand leads to revenue increases if the price increases. A unitary demand curve results in constant revenue no matter what price does. If price goes the opposite direction from that listed above, the revenue moves in the opposite direction also.

8. The slope of the demand will give only an absolute change number. It does not give a proportionate change. Since price sensitivity has little meaning apart from the proportion of change, elasticity is far better than slope at showing a useful responsiveness of demand to price.

9. If the elasticity is smaller in absolute value than 1, then revenue is increased by increasing price. If the elasticity is greater in absolute value than 1, then revenue is increased by decreasing price.

10. Since other good substitutes abound, a school will likely have a fairly elastic demand curve.

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11. If income is shifted from the rich to the poor, those products consumed by poor people and not by rich will increase in demand and those goods consumed by the rich and not the poor will have a decrease in demand.

12. Companies that produce more necessary items rather than luxuries would be better to invest in than companies that produce luxury items since people will be paring down their expenditures.

13. False. In the diagram below, an increase in the price of X leads to a reduction in the amount of X consumed, but an increase in the quantity of Y. Y

Positive income effect for both X and Y because the quantity of both X and Y increase when income is increased.

Change in Y

X Change in X

14. The demand for tennis balls is elastic. When its price goes up, the total expenditure on the balls goes down. Thus, the share of income available for tickets increases. Since their price is constant, he consumes more tickets.

15. False. Look at Figure 4-13 in the text. Both individuals have linear demand curves, but the aggregate demand curve is kinked, not straight.

16. No. If bread is an inferior good, then as income increases, quantity demanded of bread decreases. If butter were an inferior good also, then likewise, quantity demanded of butter would decline as income grows. However, spending on both goods cannot decline, because there would be no way of spending the added income. Thus, not all goods can be inferior.

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Answers to Chapter 4 Problems 1. Sam‘s budget constraint is 2OJ + AJ = 6 or OJ = 3 – (1/2)AJ. Sam‘s indifference curves are straight lines with constant MRS = 1/3. Sam‘s optimal bundle is to consume no apple juice and three cups of orange juice. When the price of apple juice doubles, Sam would not need any additional income to afford his original consumption bundle, since he does not consume any apple juice.

2. Sunil‘s budget constraint is the same as Sam‘s, but his indifference curves have constant MRS = 1. Thus, Sunil‘s optimal bundle is to consume six cups of apple juice per week and no orange juice. To afford his original consumption bundle, Sunil would need additional income (P‘AJ – PAJ)AJ = (2 – 1)6 = $6/wk. At his new income of $12/wk and facing the higher price of apple juice, Sunil‘s budget constraint would become OJ + 2AJ = 12 or OJ = 6 – AJ, which contains Sunil‘s original consumption point of six cups of apple juice and no orange juice.

Orange Juice in cups/week 6

ICB = BB‘ 3 B1

B0 34

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0

3 Apple Juice in cups per week

6

3. Anke‘s budget constraint is the same as Sam and Sunil‘s but her indifference curves are right angles (L-shaped) at bundles where the cups of orange juice and apple juice consumed are the same. Setting OJ = AJ in her budget constraint gives OJ = AJ = 2 as her optimal consumption bundle: two cups of orange juice and two cups of apple juice per week. To afford her original consumption bundle, Anke would need additional income (P‘AJ – PAJ)A = (2 – 1)2 = $2/wk. At her new income of $8/wk and facing the higher price of apple juice , Anke‘s budget constraint would become OJ + 2AJ = 8 or OJ = 4 – AJ, which contains Anke‘s original consumption point of two cups of apple juice and two cups of orange juice per week.

Orange Juice in cups/week 4 OJ = AJ 3 2 1

B0 B1

0

BM‘

1 Apple Juice in cups/week

2

4. First solve the demand curve for Q and multiply the result by 10. Then solve back in terms of P to get P = 101 – Q for the market demand. At price $1/cup the individual consumes 10 cups and the market consumes 100 cups.

Price 101

10.1

101 Cups

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3

5. a.

P = 10, Q = 100; So Elasticity = (P/Q)(1/slope) = (10/100)[1/(-0.5)] = -0.2

b.

P stays the same, Q increases, and the slope stays the same. Therefore, elasticity decreases.

6. a.

b. At (1, 50), total revenue is maximized since this is the unit-elastic point. At higher prices, revenue decreases since it is the elastic region. At lower prices, revenue again decreases since it is the inelastic region.

7. a. When P = $30, Q = 10,000 – 3,000 = 7,000. So, revenue is ($30) (7,000) = $210,000 b. The demand curve can be rewritten as P = 100 – Q / 100. This has a slope of –1/100. The elasticity = (P/Q) (1/slope) = ($30/7,000) (–100) = –0.43 c. A price increase will increase revenue since current price is in the inelastic region. d. Since substitution chances are increased, demand for the bridge will become more elastic.

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8. We can‘t know. We are only given that income elasticity of demand for safety (Ei) is positive. For necessities, we have 0 < Ei< 1, and for luxury goods we have Ei> 1.

We need more information to determine whether Ei> 1 or not.

9. QA = 25 – 0.5P, QB = 50 – P, so Q = QA + QB = 75 + 1.5P and hence P = 50 – (2/3)Q.

10. Elasticity at A = (PA/QA)(  Q/  P) = (400/300)(-20/200) = 40/300 = 2/15. Elasticity at B = (PB/QB)(  Q/  P) = (600/280)(-20/200) = 60/280 = 3/14.

Price B

600

Change in P = 200 A

400

Change in quantity = 20 280 300

Quantity 11. Price elasticity = -CE/AC = 3/7 (using segment-ratio method). Because demand is inelastic with respect to price, total revenue will go up with an increase in price.

Price ($/calculator) 100

A total revenue = $2100/mo.

30

C A Q (calculators/mo.)

37

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12. Total expenditure = PQ = 27Q – Q2, which is shown in the diagram below. It attains its maximum value, 54, when Q = 3.

Total Expenditure 54

Quantity 1

2

3

4

5

For students who have had calculus, an easier approach is to set d(PQ)/dQ = 0: d(PQ)/dQ = 27 – 3Q2 = 0, which solves for Q = 3.

2

Plugging Q = 3 back into the equation for the demand curve, we have P = 27 – 3 = 18, and this is the price that maximizes total expenditure.

13. a. 300 = 1,800 – 15P, so P = 100, which gives TR = 100(300) = 30,000 cents/day. b. Expressing the demand curve in terms of price, we have P = 120 – Q/15. Price elasticity = (P/Q) (1/slope) = (1/3)(-15) = -5 . c. Since demand is elastic with respect to price, a reduction in price will increase total revenue. d. Maximum total revenue occurs where price elasticity = -1.

(P/Q)(1/slope) = (P/Q)(-15) = -1, so maximum TR will occur when P = Q/15.

Substituting P = Q/15 back into the demand curve we get Q/15 = 120 – Q/15, or 2Q/15 = 120, which solves for Q = 900. At Q = 900, we have P = 60.

14. In absolute value terms, where price elasticity = Ep Ep A = Q2A/AP2 = 2 Ep B = Q2B/P2B = 1 Ep C = Q1C/P1C = 1 Ep D = Q1D/P1D = 3 38 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Ep E = Q1E/P2E = 1 So Ep D > Ep A > Ep B = Ep C = Ep E

15. The income elasticity for food is positive but less than 1; for Hawaiian vacations, greater than 1; for cashews probably greater than 1; and for cheap sneakers, less than 0. These elasticity values are reflected in the Engel curves shown below.

16. a. Tennis balls and tennis racquets are complements, so cross-price elasticity of demand is negative. b. Peanut butter and jelly are complements, so cross-price elasticity of demand is negative. c. Hot dogs and hamburgers are substitutes, so cross-price elasticity of demand is positive.

17. In 2001, the cross-price elasticity of good X with respect to good Y is – 4/5. This is calculated by taking the location and slope of a function representing the quantity of X in terms of the price of Y and putting that data into the standard elasticity equation. Accordingly, EpXY = (Py/X)(dQx/dPy) = (Py/X)(1/slope) = 10/400)[1/(–1/50)] = – 5/4.

The graph below illustrates this situation, but it is an unusual graph which cannot be interpreted as a typical demand curve since the price of the vertical axis is not for the product on the horizontal axis.

Py 12 14

300 400

Quantity of X

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18. Wheat and rice are perfect substitutes for Luisa, and her indifference curves are shown as the heavy downward-sloping 45° lines in the diagram on the next page.

The lighter downward-sloping straight lines, B1_B4, are the budget constraints that correspond to four arbitrarily chosen prices of wheat, namely, $12/lb, $4/lb, $2/lb, and $1.50/lb, respectively. The first two of these prices exceed the price of rice, so Luisa ends up spending all of her food budget on rice. Bundle A denotes the optimum purchase of wheat when the price of wheat is $12/lb (budget constraint B1); and bundles C, D, and F are the corresponding bundles for the remaining prices (budget constraints B2, B3, and B4, respectively).

As noted, the amount of wheat in both A and C is zero. Once the price of wheat falls below the price of rice, Luisa does best to spend all of her food budget on wheat.

When wheat costs $2/lb, for example, she will buy ($24/wk)/($2/lb) =12 lbs/wk (bundle D on B3); and at $1.50/lb, she will buy 16 lbs/wk (bundle F on B4). The heavy line labeled PCC is Luisa's price-consumption curve.

To construct Luisa's demand curve for wheat, we can retrieve the price-quantity pairs from her PCC and plot them in a separate diagram, just as before. But an even easier way is available in this particular case. It is to note that her behavior may be summarized by the following purchase rule: when the price of wheat, PW, is below the price of rice, she will buy $24/PW pounds of wheat, and when PW is above the price of rice, she will buy no wheat at all. The demand curve that corresponds to this purchase rule is plotted as the heavy line in the diagram below 40 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

P ($/lb) W Demand curve for wheat

6 5 4 Price of rice =

3 2 1.5 1

D

Wheat (lbs/wk)

0 4

8

12

16

20

24

.

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19.

Rice (lbs/wk) 12 PCC

10 8 6 4 2 0

24/9 2

24/5

24/3

Wheat (lbs/wk)

24/2

3 4 5

Price of Wheat ($/lb)

D

9 8 7 6 5 4 3 2 D

1

Wheat (lbs/wk)

0 1

2

3

4

5

6

7

20. a. The new policy represents a decline in the price of cappuccino by less than 20 percent (the nominal price, including the $0.50 for the milk, declines by exactly 20 percent but the implicit cost of the effort of buying the milk separately must now be added to the nominal price), accompanied by a quantity increase of 60 percent. It follows that the absolute value of the price elasticity of demand for cappuccino is greater than 3. So false.

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b. The policy has the effect of making milk more valuable to those users who supply their own milk to receive the discount. At a given price of milk, the quantity demanded will rise, and hence total revenue will rise, no matter what the value of the price elasticity of demand for milk. So false.

21. All Giffen goods are inferior. For a Giffen good, the income effect must be negative; that is a

fall in income increases demand, or a rise in income decreases demand. This effect must, furthermore, be strong enough to outweigh the substitution effect whereby higher prices induce consumers to switch away from this good. There is a theoretical possibility of a Giffen good, one for which the total effect of a price increase is to increase the quantity demanded. There have been no documented examples of Giffen goods. For a Giffen good, which is an inferior good, the income and substitution effects move in opposite directions.

Chapter 5

Applications of Rational Choice and Demand Theories

Answers to Review Questions 1. Because gasoline is relatively more expensive than other goods after the tax, consumers substitute away from it and will spend only part of the tax rebate on gasoline. Consequently the consumption of gasoline does fall, but not as much as it would if the rebate were not given.

2. A two-part pricing scheme exists when a seller charges an initiation fee or cover charge and then a per unit charge as well. This is an attempt on the part of the seller to capture as much consumer surplus as possible.

3. The demand of each individual will be different, but the industry demand for education will surely be more inelastic than the demand facing any given school.

4. Heavy drinkers generally spend a sizable portion of their budget in alcohol. Therefore, the income effect is exacerbated by their limited budget.

5. The interest rate is the premium required to move future income to the present. Since future goods are on the vertical axis and present goods are on the horizontal axis the budget line becomes an exchange rate between future and present income.

6. The most important reason is the increase in income. Assume that, 30 years ago, the budget constraint was b and the optimal consumption was q0. Although the price of gas has increased, so has income. The budget constraint (a) has become steeper, but it has also shifted outward. Optimal consumption increases to q1, despite the increase in price.

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other goods ($/year)

b q0

a

gas (gal/year)

q1

7. According to the permanent income hypothesis, consumption in each year is a constant proportion of the present value of lifetime income, or permanent income. Jennifer's lottery winnings more than double her current income, but have a much smaller proportional effect on her permanent income. So the proportional increase in her current consumption should be smaller than the proportional increase in her current income.

Answers to Chapter 5 Problems 1. The rich family has income (Yr), the poor family has income (Yp), where Yr > Yp. The two families have the same indifference maps. The rich family's budget constraint is the heavy line, and the poor family‘s budget constraint in the thinner one. The poor family maximizes utility by purchasing only public education (i.e., 1 unit of quality), but the rich family buys Y* >1 units of private education.

Other goods ($/year) Yr - Pe

Yr - 2Pe Yp - Pe

Yp - 2Pe

1

Y* Quality of Education

(Yr - Pe)/Pe

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2. Assume the consumer's original income was M. His original budget constraint is a; after the gas price increase, it is b; and after the money from his uncle it is c. At the very end, he can afford the original bundle he bought. But his indifference curve at the original optimum is below his new budget constraint. By decreasing his gas consumption and increasing other goods consumption, he can reach a higher indifference curve. (See dotted indifference curve.)

Other goods ($/year) M + 1000

M

a b 1000

M/2

c (M + 1000)/2 Gas(gallons/year)

M

3. The loss in consumer's surplus is 5, the area of the shaded trapezoid in the diagram:

4. P = $4/movie, Q = 8 movies/year, consumer surplus = (20 – 4) × (8 – 0) / 2 = $64. So maximum he will pay for membership is $64.

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5. Since her demand for caviar is inelastic at all prices, the increase in the price of caviar will cause her total spending on it to go up. The money left over for hot dogs will decrease. Since their price stays the same, consumption of hot dogs will decrease.

6. The two budget lines and last year's optimal bundle are shown in the diagram. A closer look at the tangency point for last year's bundle shows that this year Jordan can afford a bundle she prefers to last year's.

Y 42

Last year's bundle This year's bundle

34 30

Last year's budget

0

20

This year's budget

70

170 X

7. When r = 0.05: PV = 210 + 210/1.05 = 210 + 200 = 410.

FV = $410 × 1.05 = $430.50 When r = 0.20: PV = 210 + 210/1.20 = 210 + 175 = $385.

FV = $385 × 1.20 = $462.00

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C2 Budget constraint when r = 0.20

462 430.5

Budget constraint when r = 0.05 210

C1 210

385

410

8. 1-for-1 substitutes means MRTP = 1 (slope of indifference curves = -1). In this case, Yanni will consume all of his resources in the next period.

9. From Problem 7, Yanni‘s intertemporal budget constraint is C2 = 430.5 – 1.05C1. Since Yanni views current and future consumption as one-to-one complements, he will consume equal amounts in both periods C1 = C2. Setting C1 = C2 in his intertemporal budget constraint C2 = 430.5 – 1.05C1 yields C2 = 430.5 – 1.05C2, which solves for C1 = C2 = 210.

10. a. Facing an interest rate r = 0, Karen's intertemporal budget constraint is C2 = 150,000 C1. Her constraint has endpoints (C1 = 150,000, C2 = 0) and (C1 = 0, C2 = 150,000).

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b. Facing an interest rate r = 0.1, Karen's new intertemporal budget constraint is C2 = 157,500 – 1.1C1. Her new constraint has endpoints (C1 = 143,182, C2 = 0) and (C1 = 0, C2 = 157,500).

Future Consumption ($000) 157.5 C2 = 157,500 – 1.1C1 75

0

75 Current Consumption ($000)

143.2

11. a. $50,000/1.08 = $46,296 b.

$50,000/1.1 = $45,455

c.

$50,000/1.12 = $44,643

12. a. The highest attainable indifference curve passes through the bundle (100, 100).

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b.

Now the optimal bundle is to consume everything in the future. The bold line is the budget line and the normal line is the indifference curve with a 0.8 MRTP.

C2 Optimal bundle 190

100

100

237.5

13. Sureka's intertemporal budget constraint is C2 = (1 + r)55,000 + 60,000 – (1 + r)C1. Her maximum current consumption would occur by setting C2 = 0 and solving for C1 = 55,000 + 60,000/(1 + r). To achieve C1 = 105,000, then 55,000 + 60,000/(1 + r) = 105,000 implies 60,000/(1 + r) = 50,000, which solves for r = 0.2 (20% interest). Similarly, her maximum future consumption would occur by setting C1 = 0 and solving for C2 = (1 + r)55,000 + 60,000. If C2 = 1200,500, then (1 + r)55,000 + 60,000 = 120,500, and so (1 + r)55,000 = 60,000, which solves for r = 0.1 (10% interest).

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14. True

b

a

100

A

B 100

The enlarged picture would look like the one above. The original intertemporal budget constraint is A (with slope -1.1), and the new constraint is B (with slope -1.2). The original decision was point a. The new budget constraint also passes through a. But she can do much better by choosing point b. The increase in interest rate causes her to save today and consume more next period.

15. Because Chris's initial bundle (A in the diagram) was given to her, as opposed to having been chosen by her, there is no presumption that it was optimal for the initial prices. Indeed, it may be that the initial bundle turns out to be optimal for the new budget constraint, as shown, in which case Chris is not better off as a result of the price change. So false.

Price 100 75 A

50

1

2

3 Quantity

16. The original budget constraint and the post-change budget constraint are shown as B1 and B2, respectively. Hector curtails his mileage from M1 to M2. The heavy line is the extra revenue Antonio and Isabella collect from the higher mileage charge, which is less than $10/wk.

Y Y0 + 10 50 © 2021 by McGraw-Hill. This is Y proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This 0 document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

 Extra revenue from 40 cent fee < $10

Y2

C A

B1 M1 M2

B2

Y0/.2 (Y0 + 10/.4)

B miles/wk

17. a. Let R be the buyer's reservation price for the right to use the book for one year.

Let U be the price of a used book. Then the reservation price for a new book is R + U/(1 + r) = R + $20 = $50 => R = 30. Reservation price for book with disappearing ink = R= 30 b.

Profits with normal ink: (N/2)(R + 20 – m) = 25N – mN/2 = A Profits with disappearing ink: N(R – m) = 30N – mN = B B – A = N(5 – m/2) > 0 if and only if m < 10.

18.

The opportunity cost of Christina's time is the $6/hr she can earn in the library.

Her optimal 2-part tariff for tutoring is thus a $6/hr fee plus a fixed fee given by the 8 units of consumer surplus each tutee would receive if there were no fixed fee. Thus, her tutoring fee is $8 + $6/hr. Confronted by this fee schedule, each graduate student will want to purchase 4 hr/wk of tutoring. This gives Christina her desired 12 hr/wk, with total earnings of $96/wk. She should not spend any time clerking in the library.

10

 area = 8 6

4

10 Quantity

19. If P0 is the tuition of other universities and Eastern provides a subsidy of kP0, CFCs will have to pay only (1 – k)P0 after the subsidy. The quantity (in 1000s) of CFCs attending other universities in the absence of any subsidy is Q0 = 2 – (P0/5). With the subsidy, this

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quantity goes up to Q' = 2 – ((1 – k)P0/5). The extra revenue Eastern will get (in $1,000s) by being able to sell the extra slots is DTR = 15(Q' – Q0) = 15(kP0/5) = 3kP0.

Each subsidized CFC costs Eastern kP0. Since there are Q' students subsidized, the total subsidy cost is equal to S = kP0Q' = kP0 [2 – ((1 – k)P0/5)] = 2kP0 – kP02/5 + k2P02/5 .

Eastern's goal is to choose the value of k that maximizes D = DTR – S = kP0 + kP02/5 – k2P02/5.

The first order condition is dD/dk = P0 +P02/5 – 2kP02/5 = 0, which solves for k* = (5 + P0)/2P0.

Thus, if tuition at other universities (in $1,000s) is P0 = 24, we have k* = 0.6.

20. For P0 = 12, we have k* = 0.71, which means that Eastern should pay 0.71% of the outside tuition. If the tuition of other schools was low enough, (For example, k* = 4) then Eastern should pay all the tuition and also give a cash bonus of $500 to each CFC who attends an outside university.

21. Her optimal strategy is to sell popcorn at marginal cost and then add the consumer surplus from popcorn to the consumer's reservation price for the movie ticket. Thus, the price of popcorn should be $1/qt, which yields a consumer surplus of $4.50 from popcorn. The ticket price should be $5 + $4.50 = $9.50.

Price 30

P0 (1-k) P0

2-P0/5 2-(1-k)P0/5

6

Q0 (1000)

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Chapter 6

The Economics of Information and Choice Under Uncertainty

Answers to Review Questions 1. If anyone can fake the signal, it will cease to be a signal at all since it would be meaningless information.

2. If nobody is advertising, it must be not profitable to advertise. If someone is advertising, they must find it profitable. If the product is of credibly better quality, it makes more sense to advertise it. Hence, if some sellers advertise, their products must be of better quality. Now consider the incentives of the seller who is indifferent between advertising and not advertising. That indifferent seller can advertise, revealing the quality of their product, or be mixed with sellers of worse quality, facing the market that perceives that that seller‘s expected quality is lower than that seller‘s true quality. This difference in the market‘s perception creates an incentive to advertise. The full disclosure principle means that advertisers will be eager to separate their products from products with lesser qualities.

3. Interviewees will have an incentive to tell information about which the employer may have concern even if the employer is not allowed to ask for the information. Employers may expect the worst, so the applicant will make sure that the employer knows that the worst is not true.

4. The low-risk types subsidize the high-risk people in the group, because the insurance company will charge a premium to cover the average claim.

5. The rate will be higher than it should be because those who are the best risks leave the pool and self-insure. That raises the rates for those left, and the best risks left are again inclined to self- insure. Thus the average premium keeps climbing.

6. It is logical that there are diminishing returns to wealth, and therefore risk aversion is normal.

7. Gambling and bungee jumping might help you start your list.

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8. Insurance companies need to cover their risk and make profits. This means they offer unfair gambles. It is better to self-insure your small losses instead of taking an insurance against them. For example, instead of insuring your mobile phone against theft, you could pay the equivalent of the insurance premiums into a bank account and buy a new phone in the case of theft.

9. The service contracts on small appliances and credit card insurance when the maximum loss is only $50 are two of the obvious ones.

Answers to Chapter 6 Problems 1. If the general threshold for denying admission is 80, and if those who deny admission are uniformly distributed between 80 and 100, then our best estimate of the messiness index of someone who denies admission will be 90.

The threshold will not be stable. Someone whose messiness index is between 80 and 90 has good reason to let people in rather than be assumed to have an index of 90. A threshold of 90 should be unstable for similar reasons, as indeed will any disclosure threshold less than 100.

In practice, the fact that some people do refuse to let others see their messy apartments seems to indicate that actually seeing the mess firsthand will be more damaging than having people conclude in the abstract that the apartment is messy.

2. One salient fact about teenage males is that they have much higher car accident rates than other groups. A company that charged the same rates to teenage males as it changes to all other groups would therefore have to have higher premiums than those other companies charge members of all other groups. There would then be no reason for these other group members to remain with the company. In the end, the company with uniform rates for all groups would have to charge a premium high enough to cover the expected losses of members in the highest risk group.

3. If all consumers value nondefective cars at $6,000 and used cars sell for only $1,000, then no nondefective cars will be offered for sale in the used market. The only used cars for sale will be defective, so we know that the value consumers place on a defective car must be exactly 1,000. Since consumers are risk neutral, the expected value of a new car, En, is simply the sum of the expected values of nondefective and defective cars: En = (1 – d)(6,000) + d(1,000) = 4,000, which solves for d = 0.4.

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4. The expected value of a new motorcycle, En, is equal to En = 9,000 = (1– d)1,000 + dX, where X is the price of a nondefective one and d is the proportion of defective motorcycles.

Therefore, 9,000 = 0.8X + 0.2(1,000), which solves for X = $11,000.

5. You know your car is not a lemon; but if you try to sell it, the market will assume it is, and you will be unable to get full value for it. This makes it more worth your while to fix the car.

6. Because social workers receive very low salaries relative to the amount of education they have, it is a reasonably safe inference that most of them chose that line of work for reasons other than money. Therefore, if the primary motive for cheating at cards is monetary gain, it follows that a social worker is not very likely to cheat. Further, social workers usually exhibit a high level of altruism and attention for societal matters. This typically implies that they find any form of cheating reprehensible, especially if cheating for one‘s personal gain only.

7. The college degree is a signal to the employer about the ―smartness‖ of an employee.

Assume that the smartness of an employee is distributed between 0 and S. The only costs to education are monetary costs and the difficulty of passing courses, which is lower for smarter students. Thus, for any two people with the same wealth, the smarter one is likely to have more education. At the beginning of the century, let‘s say that the average high-school graduate had smartness level of Sh and the average college graduate had Sc, where Sc > Sh. Since the monetary costs of education went down, more people are getting education, especially the ones who were smart but could not afford it before. Also, smarter high school graduates will now be getting college degrees. Assume the average smartness level of a high school graduate now is Nh and of a college graduate is Nc. Then Nh < Sh and Nc < Sc. Of these four quantities, Sc is the highest and Nh is the lowest, but we do not exactly know the relationship between Sh and Nc. If Nc < Sh, then banks might raise their education criterion.

8. The expected value of one toss of a six-sided die is: EV = (1/6)(1 + 2 + 3 + 4 + 5 + 6) = 21/6 = 3.5 .

9. The expected value of the gamble is given by: EV = (1/4)(20) + (1/4)(9) + (1/4)(-7) + (1/4)(-16) = +1.5 .

10. EU = (1/4) + (1/4) + (1/4) + (1/4) = 6/4 + 5/4 + 3/4 = 3.5.

Your utility without the gamble is = 4.0; so you will not accept the gamble.

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E(interest rate) = 0.3(0.4) + 0.2(-1) + 0.5(0.1) = -0.03 = -3% b. EU(govt. bond) = (1.08 × 10,000)2 = 116, 640,000 EU(junk bond) = 0.3(1.4 × 10,000)2 + 0.2(0)2 + 0.5(1.1 × 10,000)2 = 119,300,000 Since EU(junk bond) > EU (govt. bond), you will invest in the junk bond. c. EU(govt. bond) = = 103.92 EU(junk bond) = 0.3 + 0.2 + 0.5 = 87.94 .

Since EU(junk bond) < EU (govt. bond), you will invest in the govt. bond.

12. Expected Utility (with ticket) = 0.25(110)2 + 0.75 (100)2 = 10,525.

The wealth level to give the same utility for sure is w = √ = 102.59.

Thus, you would be willing to sell the ticket for 102.59 – 100 = 2.59.

13. EU (without insurance) = 0.99999 = 632.449 .

The wealth level to give the same utility is w = (632.449)2 = 399,992 .

So you would be willing to pay $400,000 – $399,992 = $8 for this insurance.

14. With one trip, EU1 = (1/2) + (1/2) =5 With two trips, there are four equally likely outcomes:

1.

2.

3.

4.

EU2 = (1/4)

First Trip 0 break 500 break 0 break 500 break + (1/4)

Second Trip 0 break 0 break 500 break 500 break + (1/4)

+ (1/4)

Income 100 50 50 0

Probability 1/4 1/4 1/4 1/4

= 2.5 + 1.77 + 1.77 = 6.04

As there is a 50 percent chance that the farmer will break the eggs each time he takes a trip, we have four possible outcomes to consider: 1. No egg broken overall: This happens only if the farmer breaks no eggs in either trip, which happens with probability (1 – 1/2) × (1 – 1/2) = 0.25 2. 500 broken eggs: This happens if the farmer breaks eggs in the first trip but not in the second OR breaks no eggs in the first trip but does break them in the second; the first possibility happens with probability (1/2) × (1 – 1/2) = 0.25; the second possibility happens with probability (1 – 1/2) × (1/2) = 0.25; thus overall the probability of breaking 500 eggs is 0.25 + 0.25 = 0.50 56 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

3. All eggs end up broken: This happens if the farmer breaks the eggs in both trips, which happens with probability 0.5 × 0.5 = 0.25.

So, it is better to take two trips than one, even though the expected number of eggs broken is the same either way. Moral: Don't put all your eggs in one basket!

15. a. EV = (1/2)15 – (1/2)13 = 1 b. EU = (1/2)

+ (1/2)

=4+3=7

c. EV = 0 EU = (1/2) + (1/2) Without gamble U = 7.

= 4 + 5.83/2 = 6.91

d. Let x = the most you would pay to get out of the gamble. Then 49 – x = 47.75 x = 1.25

16. a. EU = ( )/2 + ( make the investment.

)/2 = 12/2 + 9/2 = 10.536 <

= 6.91

, so Jane will not

b. With 2 equal partners, the three must share wins (11) and loses (10), thus EU = [ ] /2 + ( ) /2 = 10.55 > , so Jane will make the investment.

17. Expected utility without info = max[ , (.2 + .8 So without info, she will choose to become a lawyer.

Suppose info costs P;

)] = max (9, 10) = 10.

Expected utility with info = 0.2√ + 0.8√ Set EU with info = EU without info = 10 and solve for P: P = $53.68. For any price less than this amount, she should pay Ellis for his evaluation.

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18. If Amanda becomes a professor her expected utility is 9. If she becomes an attorney her expected utility is 0.2 . Without being interviewed by Ellis, she will become a lawyer. If a fee of p is charged when Ellis believes Amanda will become partner and a fee of q is charged when Ellis believes Amanda will not become partner, Amanda's expected utility is EU = 0.2√ + 0.8√ . Amanda will pay to be interviewed by Ellis as long as EU > 10. If p = q then the maximum Ellis will pay is p = q = $53.68. If q = 0 then Ellis will pay up to p = $704. Clearly, Ellis is better charging for the interview only if he believes Amanda will become a partner.

19. a. For group 1, the reservation price of insurance is found by solving = 0.5 + 0.5 = 9, which yields x1 = 19. √ For group 2, we get √

= 0.9

+ 0.1

= 9.8, which yields x2 = 3.96.

b. If members of the two groups are indistinguishable, an insurance company will have to charge the same premium to each. If its policyholders consisted of equal numbers of people from each group, this premium would have to cover the expected loss, which is [(0.5)(36) + (0.1)(36)]/2 = 10.8. Since this exceeds the reservation price of members of group 2, nobody from that group would buy insurance. And with only group 1 members remaining in the insured pool, the premium would have to rise to 18 in order to cover the expected loss for members of that group. c. If a company has the test described, and the test says a person is a member of group 2, then the expected benefit payout from insuring that person is x(0.1)(36) + (1 – x)(0.5)(36) = 18 – 14.4x = E(L). Setting E(L) equal to the reservation price for group 2 we get 18 – 14.4x = 3.96, or x = 0.975. The test would have to be accurate 97.5% of the time in order for a member of group 2 to find insurance an acceptable buy.

20. a. Let X1 denote the reservation price for members of group 1. X1 must satisfy the equation √

= 0.5

+ 0.5

= 11, which solves for X1 = 23. The reservation

price for group 2 must satisfy √ for X2 = 4.76.

= 0.1

+ 0.9

= 11.8, which solves

b. The most an insurance company can charge and still include group 2 members is X2 = 4.76. Let p be the proportion of group 1 members in the potential client pool. If the price is low enough to attract group 2 members, it will necessarily also attract members of group 1. The expected benefit payouts for members of the two groups, denoted B1 and B2, are given by B1= 0.5(44) = 22 and B2 = 0.1(44) = 4.4. The expected benefit payment per client, B, is thus a weighted average of

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these expected payouts, where the weights are the respective population shares in the client pool: B = p(22) + (1 – p)(4.4) = 4.4 + 17.6p. Equating this expected benefit payment to the reservation price X2, we have 4.4 + 17.6p = 4.76, which solves for p = 0.36/17.6 = 0.02. Thus, if more than 2 percent of the potential client pool consists of members of group 1, it will be impossible to include members of group 2.

21. Let m be Sejal‘s initial wealth, and u be her utility function.

Picking A over B => uA = u(m + 100) > EuB = 0.8u(m + 150) + 0.2u(m) Picking D over C => EuD = 0.4u(m + 150) + 0.6u(m) > EuC = 0.5u(m + 100) + .5u(m) Rearranging terms of the last inequality, we have 0.5u(m + 100) < 0.4u(m + 150) + 0.1u(m).

Dividing both sides by 0.5 gives u(m + 100) < 0.8u(m + 150) + 0.2u(m), which is the reverse order of the inequality implied by the choice of A over B, hence the inconsistency.

Answers to Chapter 6 Appendix Problems 1. If the current wage offer is w, the probability of getting a better offer on the next draw is (8 – w)/3. If you do get a better offer, its expected value is (8 + w)/2, which is (8 – w)/2 better than the current offer. So the expected gain from sampling another offer is [(8 – w)/3][(8 – 2 w)/2] = (8 – w) /6. Setting this equal to the cost of sampling another offer we have (8 – 2 w) /6 = 0.06, which solves for W* = $7.40. So, the rule should be to keep searching until you get an offer at least as high as $7.40.

2. The expected value of the largest of 100 estimates is (100/101)(C). If you win the auction, your estimate will be the largest of the 100. If its value is 50, your best estimate of C will be C* = (101/100) 50 = 101/2. Since the expected value of the money is C/2, you should bid C*/2 = 101/4 = $25.25.

3. If your company bids P and X is greater than P, then Bumbler will refuse the offer and the deal is off. Your company earns zero profit in that case. If Bumbler accepts your company's offer, then we know that X < P. Since X is uniformly distributed between 0 and 100, the expected value of X, given that X < P, is P/2. This means that the expected value of Bumbler's oil field to your company is P/2 + 40. a. If your company bids P and Bumbler accepts, then the expected profit of your company will be P/2 + 40 – P = 40 – P/2. Equating this expression to zero, we see that the most your company can bid without expecting to make a loss is $80. b. The probability your company acquires Bumbler at a bid of P is equal to the probability that X is less than P, which is P/100. If your company fails to acquire Bumbler (i.e., if X > P), then your company's profits from transaction will be zero.

Expected profit from a bid of P is thus given by: 2 E = (P/100) (40 – P/2) + (1 – P/100) (0) = 40P/100 – P /200.

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The first-order condition for maximum expected profit is given by: dE/dP = 40/100 – P/100 = 0, which solves for P* = $40.

4. Assume the offer you have is w. The probability of getting a better offer is (150 – w)/75. The expected value of the offer will be (150 + w)/2, which is (150 – w)/2 bigger than the current 2 offer. The expected gain is EG = (150 – w)/75 × (150 – w)/2 = (150 – w) /150. At the optimum, EG = cost of a search = 2, which solves for w = 150 – = $132.68.

5. Assume the current date you have has an index v. The probability of getting a better date is (100 – v)/100. The expected index of the new date, if better, will be (100 + v)/ 2, which is (100 – v)/2 bigger than the current date. The expected gain is: EG = (100 – v)/100 × (100 – v)/2 = (100 – v)2/200.

Thus, the expected gain in terms of dollars will be EG($) = EG × 50 = (100 – v)2/4.

At the optimum, EG($) = cost of a search = 100, which solves for v = 100 – = 80.

6. The expected value of the largest of 20 estimates is (20/21)C. If yours is the largest, your best estimate of C is C = 200 × (21/20) = $210. Since the expected value is C/2, you should bid $105.

Chapter 7

Departures from Standard Rational Choice Models (With and Without Regret)

Answers to Review Questions 1. The present-aim standard takes individual interests as given even if these interests appear to be irrational. The self-interest standard argues that people are purely egoistic.

2. Rational calculations can affect feelings and hence actions.

3. Typical examples students might come up with: commitment in a relationship; commitment to getting an A in class.

4. If one observes someone with a disposition toward, say, anger, one will assume that the person will commit to a strategy of retaliation.

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5. You would be willing to pay more if case 1 were true. If people behave in strict accordance with rational choice theory, the course would tell you all you need to know to maximize profit. For instance, it would tell you how to make the most money from customers, while paying as little as possible to suppliers. Thus, you should be willing to pay more if case 1 were true. If case 2 were true, behavior would depart systematically from the predictions of rational choice theory. It would then be less useful to attend the course, and your willingness to pay for a course that only focuses on rational choice theory would be lower. You would rather attend a course that covers both the traditional theory of rational choice and departures from rational choice.

6. Gathering information is costly, and at some point the costs outweigh the benefits.

7. No. If the marginal utility of wealth decreases with wealth, then weighing gains less heavily than losses is consistent with utility maximization, and therefore rational.

8. The policy of punishing students would be more effective because losses are felt more than gains of the same size. This policy may not be a good one if you are interested in more than just attendance.

Answers to Chapter 7 Problems 1. For a given total income for the two, Alphonse's utility function, UA = MAMG, is maximized when MA= MG, as shown in Example 7.1. Given Alphonse's budget constraint (see diagram), this happens when MA= MG = 60. So Alphonse will give Gaston 40 of his initial 100.

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2. If they do not do the project, each person will have a utility level of 102/10 = 10. If they do the project and Abdul gets P, Bindi will get 10 – P. Bindi's total wealth will then be 10 + P, Bindi's 20 – P. The minimum acceptable value of P for Abdul will satisfy UA = (10 + P)2/(20 – P) = 10. Solving for P, we have P = $3.028.

Since the problem is symmetric, this is also the minimum payment that would be acceptable to Bindi. And since the total gain from doing the project is more than enough for each person to get $3.028, they will do it. (Verify, for example, that if each takes 5, each will be better off than before.)

3. If Bindi accepts Abdul's 1-unit offer, his utility will be UB = (10+1)2 = 121. If he refuses, his utility level will be only 102 = 100, so she will accept Abdul's offer. There is no point in refusing in hopes of a better bargain, since if Abdul gives Bindi more than 1 unit, the contract will require her to give 20 to a cause she opposes, which would lower her utility below her original level.

4. The advantage is that if opposing nations know this leader's preferences about retaliation, they are less likely to commit aggression in the first place. One disadvantage of having such a leader is that he or she may engage in costly retaliation even after an unintended act of aggression by an opponent.

5. Let t represent the length of the line at the polls, measured in hours. Then the total time required to vote, including travel time, is equal to (t + 1/3) hours. Given that she can earn $30/hr at her job, the opportunity cost of her voting is thus (30t + 10) dollars. And since she gets 3 units of utility from each unit of consumption of the composite good, the opportunity cost of voting in utility terms is equal to 90t + 30 units. On the benefit side, she stands to gain 60 units of utility by voting. The maximum length of the polling line is the value of t that equates the costs and benefits of voting in utility terms: This value of t is found by solving the equation, 90t + 30 = 60, which yields t = 1/3 hour, or 20 minutes.

6. a. Combine small loss with the larger gain, because V(450) > V(500) + V(-50). b. Segregate the small gain (the silver-lining effect): V(50) + V(-500) > V(-450). c. Reckon the gains separately: V(500) + V(600) > V(1,100). d. Combine the losses: V(-1,100) > V(-500) + V(-600).

7. (1) If the machine normally costs $4,000, they could raise the price to $4,500 and offer a "$500 cash rebate." If buyers code the rebate as a separate event, the Kahneman-Tversky 62 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

value function says it will more than compensate for the negative effect of the higher price (the "silver-lining effect").

(2) Combine the all-terrain vehicle into a package with the new Honda Recreational Vehicle.

The resulting small percentage increase in the price of the RV will seem insignificant [Psychophysics of perception (Weber-Fechner law); also principle of combining losses.].

8. Suppose a disease will claim 600 lives if we do nothing. Given a choice between program A, which would save 200 lives with certainty, or program B, which would save 600 lives with probability 1/3 and zero lives with probability 2/3, most people pick A. But given a choice between program C, under which 400 people would die, or program D, under which there is a 1/3 chance no one will die and a 2/3 chance that all 600 will die, most people pick D. These choices are inconsistent because the two pairs of alternatives are exactly the same.

As a second example, consider the following three apartments, which are identical expect for monthly rent and distance from campus a. $600/mo, 2 blocks from campus b. $400/mo, 1.5 miles from campus c. $405/mo, 1.6 miles from campus Because C is unambiguously worse than B, its availability should not influence the likelihood that a person chooses B over A. And yet when people are given a choice between A, B, and C, they are much more likely to choose B than if they are given a choice between only A and B.

9. Increased subway patrols are likely to be assigned in years following unusually high crime rates. Regression effects alone would lead us to expect crime rate reductions in the year following an unusually bad year. So it is difficult to conclude that the reduced rates are the result of increased patrols.

10. A ―superb‖ meal at any restaurant is likely to be an unusually good one compared to the meals usually served there. On her next visit, Claiborne is likely to encounter a ―normal‖ meal. This is the regression-to-the-mean effect.

11. Out of every 100 people Dalgliesh interviews, 60 are liars, 40 are truthful. Of the 60 liars, Dalgliesh identifies 48 correctly. Of the 40 truth tellers, Dalgliesh mistakenly calls 8 liars.

So out of every 56 people he says are lying, 48 really are. The probability that Jones is lying is thus 48/56 = 6/7. In this problem, taking base rates into account raises the accuracy of Dalgliesh's prediction, because there was a better than even chance that a randomly chosen person would be lying.

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12. For every 100 taxis in a dark alley, 15 will be green, 85 blue. The witness will identify 0.8(15) = 12 of the green taxis as green, the remaining 3 green taxis as blue. Therefore, the witness will identify 0.8(85) = 68 of the blue taxis as blue, the remaining 17 blue taxis as green. The probability that the cab in question was green given that the witness said it was is thus equal to 12/(12 + 17) = 0.413, and since this is less than half, the Green Taxi Company should not be held liable.

13. You view the loss of the original deal as a loss of $400, the amount you would have saved.

The next deal is seen as a gain of $360. If you have a value function similar to the one described in the text, V(-400) is much bigger than V(360), so you end up ―feeling‖ you are worse off. But this is irrational, since the regular ticket is $1,067 and you should compare your purchase of $708 to this amount and feel better off.

14. No. Since you would choose the initial offer on Hawaii to this one in any case, this new offer is an ―irrelevant‖ alternative. It should not even be considered, much less be allowed to affect your decision about the two initial offers.

15. Eun should drive across town if and only if the amount she saves is greater than the cost of the drive. In the 10 percent off computer sale she would save $100. She would save only $16 in the 40 percent off sale on the blouse. And yet she makes the trip in the latter case but not in the former. Her behavior is thus irrational.

16. Racquet C is dominated by racquet B, which has more control and the same amount of power. The rational choice model says that adding C should not affect how people choose between A and B. As an empirical matter, Tversky has shown that the availability of an alternative like C tends to make people more likely to choose B over A. 17. Wilson may know that he is sorely tempted to get some coconuts before he should if his plan is to use them in the spring. Having the bears in the way acts as a commitment device to help him live up to his plans.

Chapter 8 Production Answers to Review Questions 1. Examples may include: 1) an opera singer performing an aria; 2) Usain Bolt running the 100 meters; 3) an economics professor teaching intermediate micro.

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3. The person hiring wants to know how much an additional worker will add to total production which is the marginal product of the labor.

4. The official‘s IQ was below average for New York, but above average for California.

5. They are equivalent mathematically except for the fact that one can measure production numerically but utility is a subjective value which can be discerned only ordinally.

6. Decreasing returns is a long-run phenomenon; diminishing returns is a short-run phenomenon. Diminishing returns to a variable input concerns an increase in just that input, keeping all else constant. Decreasing returns to scale concerns a proportionate increase in all inputs.

7. As shown in the diagram, MP is decreasing from L1 onward, whereas AP does not begin to decline until L2. So false.

8. False. For the average product to increase, the new worker should contribute more than the existing average. Thus, his marginal product should be more than the average product before his/her arrival.

9. Under constant returns the output will be 2, under decreasing returns to scale the output will be less than 2 and under increasing returns to scale the output will be greater than 2.

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1. The short run product curve for (a):

The short run product curve for (b):

2. The production function in (1a) has a constant marginal product of labor for all levels of labor input, and the production function in (1b) has an increasing marginal product of labor for all levels of labor input. So neither production function obeys the law of diminishing returns.

3. The marginal product of labor equals its average product at the maximum value of AP. The MP of the next worker hired will thus be less than his AP. The next worker should thus prefer to be paid his AP. The employer would prefer to pay MP.

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4. Total product (TP) equals average product (AP) multiplied by the amount of labor. This makes it possible to fill in TP and AP for all amounts of labor except 2. Marginal product (MP) of a unit of labor equals the difference between the total product with and without the laborer. With this we can fill in the values for MP and find TP and AP when labor is 2.

5. The marginal product of the second hundred teams sent to Development is only 35 tickets per week, and this amount is less than the 40 tickets per week they could achieve in Support.

They should instead be sent to Support. The allocation is 1 team to the Development and 4 teams to Support.

6. All 5 teams should be sent to Support because the marginal product there is more than it can possibly be in Development.

7. a. See graph below:

b. Maximum production (Q = 9) occurs at L = 6. [Calculus trained students: To find the

maximum, take the first derivative and set it equal to zero and solve for L: dQ/dL = 3 – (1/2)L = 0, which yields L = 6, Q = 9.] c. For 0 < L < 2, MPL is increasing. For 2 < L < 7, MPL is decreasing.

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d. MPL < 0 for L > 6.

8. With an optimal allocation of time, the extra points earned from the last minute devoted to each question will be the same. Someone who earned 2 extra points from the last minute devoted to Problem 10, and 4 from the last minute devoted to Problem 8, ought to have spent less time on Problem 10 and more on Problem 8. This is true irrespective of the total points earned on each question.

9.

Q Q=4L

12

3

L

AP, MP 4

AP=MP=4 L

Total product is Q = KL. Substituting in K = 4 we get Q = 4L. The average product of labor is Q/L = KL/L = K. Given that K = 4 we get AP = 4.

The marginal product of labor is dQ/dL = K. So, MP = 4. Any line drawn as y = 4 is correct on the basis of this.

10. This production function shows constant returns from A to C, increasing returns from C to E, and decreasing returns from E to G. Total product is Q = KL. Substituting in K = 4 we get Q = 4L. The average product of labor is Q/L = KL/L = K. Given that K = 4 we get AP = 4. The marginal product of labor is dQ/dL = K. So, MP = 4. Any line drawn as y = 4 is correct on the basis of this.

From C to D, inputs go up by 33 percent and output by 67 percent. This is increasing returns to scale. From D to E, inputs go up by 25 percent and output by 60 percent. This is increasing returns to scale.

From E to F, inputs increased by 20 percent and output by 13 percent. This is decreasing returns to scale. From F to G, inputs go up by 100/6 percent and output by 50/9 percent, which is less than 100/6 percent. This is decreasing returns to scale.

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11. The overall average of the population need not change if physics was on the high side of average and economics on the low side of average. For example, if 3 economists each have an IQ of 150 and 2 physicists have IQs of 155 and 160 respectively, then if the 155 physicist becomes an economist, both groups have higher IQ averages but the population average has not changed.

Answers to Chapter 8 Appendix Problems 1. a. F(K,L) = 4 K1/2 L1/2 ; F(cK,cL) = 4 (cK)1/2 (cL)1/2 = cF(K,L), so constant returns.

MPL = 2 K1/2 /L1/2, MPK = 2 L1/2/K1/2, both of which decline, so this production function satisfies the law of diminishing returns (LDR). b. F(K,L) = aK2 + bL2 ; F(cK,cL) = a(cK)2 + b(cL)2 = c2F(K,L), so increasing returns to scale. MPK = 2aK, MPL = 2bL, both of which are increasing, so neither satisfies the LDR. c. F(K,L) = min(aK,bL) ; F(cK,cL) = min(acK,bcL) = cF(K,L), so constant returns. MPL = b when K > (b/a)L , 0 when K < (b/a)L. MPK = a when K < (b/a)L, 0 when K > (b/a)L. Here the marginal product of each variable input drops precipitously at K = (b/a)L then remains constant at 0, so this production function does not satisfy the LDR. d. F(K,L) = 4K + 2L ; F(cK,cL) = 4cK + 2cL = cF(K,L), so constant returns. The marginal products of both inputs are constant, so this production function does not satisfy the LDR. e. F(K,L) = K.5 L.6 ; F(cK,cL) = (cK).5 (cL).6 = c1.1F(K,L), so increasing returns. Both marginal products decline, so satisfies LDR. f. F(K,L) = K1.3K2.3L.3 ; F(cK1,cK2,cL) = (cK1).3(cK2).3(cL).3 = c.9F(K,L), so decreasing returns. All MPs decline, so satisfies LDR. 2. For K = 27, we have Q = 6L1/3, so MP = dQ/dL = 2L-2/3.

3. Take the Cobb-Douglas production function of the form Q = F(K,L) = m Ka Lb. F(cK, cL) = m (cK)a (cL)b = ca+b m Ka Lb = ca+b F(K, L) Since ca+b is fixed for all levels of output, we will have decreasing returns if a + b > 1, increasing returns if a + b < 1. But we can‘t have both with the same production function.

4. Q = F(K, L) = min (2K, 3L) and K = 6, L = 5 Then Q = min(12, 15) =12.

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MPK = F(7, 5) – F(6, 5) = 14 – 12 = 2.

MPL= F(6, 6) – F(6, 5) = 12 – 12 = 0.

5. The team's objective is to maximize its total yardage, which is the same as maximizing average yards gained per play, G. G is the following weighted average of the yardage gained on passing and running plays: G = (1 – r) (8 + 12r) + r (10 – 8r) = 8 + 14r – 20r2.

The first-order condition for a maximum is: dG/dr = 14 – 40r = 0, which yields the optimal value of r: r* = 14/40 = 0.35. At r*, the average gain per pass is 8 + 12(0.35) = 12.2 yards.

The average gain per run is 10 – 8(0.35) = 7.2 yards.

6.

If f represents the proportion of fastballs, your opponents' batting average against fastballs, denoted Af, is given by Af = 0.100 + 0.200f. Their average against curves is Ac = 0.300 – 0.050f.

Their overall average against both types of pitches is the weighted average A = fAf + (1 – f)Ac = 0.100f + 0.200f2 + 0.300 – 0.050f – 0.300f + .050f2, which reduces to A = 0.250f2 – 0.250f + 0.300. The first order condition for a minimum value of A is given by dA/df = 0.500f – 0.250 = 0, which solves for f = 1/2.

At f = 1/2, we have Af = 0.200, Ac = 0.275. Note that these are the averages assumed in the baseball scenario discussed in the chapter. If more than 50 percent fastballs are thrown, the effect will be to raise the opponents' overall batting average.

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Chapter 9

Costs

Answers to Review Questions 1. The law of diminishing returns implies that eventually the TVC curve will begin to rise at an increasing rate.

2. As soon as diminishing returns set in, the MC curve will slope upward.

3. Book publishing because the marginal labor cost of one book is a very small part of the cost of a book while landscape work is labor intensive.

4. If MC is less than average costs (total or variable), then each additional unit produced should pull down average cost. If MC is more than average costs (total or variable), then each additional unit produced should increase average cost. If you have an average score in this class of 90 and your next test (the marginal test) score is 85, your average is pulled down. If the marginal test score is 95, the average for the class is pulled up.

5. We have decreasing returns to scale.

6. If MC is greater for one production activity than for another, then total cost can be reduced by shifting some production to the lower marginal cost operation. In this way that last unit is produced at less cost and so total costs for the output fall.

Answers to Chapter 9 Problems 1.

Quantity Total Fixed Variable ATC AVC AFC MC of output cost cost cost ___________________________________________________________ 0 24 24 0 ---_____ ______________________________________________________________ 16 1 40 24 16 40 16 24 _____ ______________________________________________________________ 34 2 74 24 50 37 25 12 _____ ______________________________________________________________ 34 3 108 24 84 36 28 8 _____ ______________________________________________________________ 52 4 160 24 136 40 34 6 _____ 71 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

______________________________________________________________ 60 5 220 24 196 44 39.2 4.8 _____ ______________________________________________________________ 62 6 282 24 258 47 43 4 _____ ______________________________________________________________

2. With K fixed at 2, we have Q = 6L, which solves for L = Q/6. So we have: VC = wL = wQ/6 = Q/3; AVC = 1/3; FC = 3K = 6; AFC = 6/Q; TC = 6 + (Q/3); ATC = (6/Q) + (1/3); MC = 1/3 $/t TC

12

VC 6

FC

Q 18

$/Q

2.0 AFC ATC

AVC=MC 1/3 18

Q

3. When MP = AP, marginal cost and average variable cost will be the same. To see this, note first that MC =  VC/  Q = w  L/  Q = w/MP. Similarly, AVC = wL/Q = w/AP. So when AP = MP, it follows that MC = AVC. 4. a. The firm minimizes costs when it distributes production across the two processes so that marginal cost is the same in each. If Q1 denotes production in the first process and Q2 is production in the second process, we have Q1 + Q2 = 8 and 0.4Q1 = 2 + 0.2Q2, which yields Q1 = 6, Q2 = 2. The common value of marginal cost will be 2.4.

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b. Note that for output levels less than 5, it is always cheapest to produce all units with process 1.

MC1 $/Q

MC2 5

2 Qi 5 5. If K and L are perfect substitutes, only one of the inputs will be used for any given isocost line. No matter what the isocost line's slope, we will always get a corner solution (except where the slope is exactly -1).

K

Q1 Q2

Q3 L

6. If K and L are perfect complements, the two inputs will be used in fixed proportion, no matter what the slope of the isocost line.

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K

Q3 Q2 Q1 L

7. The necessary condition for cost minimization is MPK/PK = MPL/PL. Here, MPK/PK = 2

and MPL/PL = 4.5. Since this firm gets more output from the last dollar it spends on labor than from the last dollar it spends on capital, it should buy less capital and more labor.

8. For this production function, as long as the input price ratio (PK/PL) remains 2:1, the optimal input bundle will always have 2 units of capital for every 3 units of labor, i.e., K = 2L/3. For a total cost of 70, we thus have PKK + PLL = 2(2L/3) + L = 70, which solves for L = 30 and K = 20. (See diagram.)

Capital 35 Output Expansion Path (slope = 2/3)

20

3.5 7

30

70

Labor

9. At the minimum-cost input bundle for producing Q*, we know that the extra output obtained from the last dollar spent on labor is the same as the extra output obtained from the last dollar spent on capital. Thus, the two short-run marginal cost curves will take the same value at Q*.

10. The LAC curve is the outer envelope of the firm's two SAC curves, as shown by the locus ABC in the diagram. The two curves cross when Q = 3.

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11. The LMC and SMC curves coincide at the output level for which LAC and ATC are equal. If

LMC is not equal to SMC, it follows that ATC > LAC.

12. LRAC = LRTC/Q = Q2 – 20Q + 220 LRMC = dLRTC/dQ = 3Q2 – 40Q + 220

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13. ATC = LTC/Q = Q + 10/Q AVC = Q AFC = 10/Q MC = dLRTC/dQ = 2Q

Answers to Chapter 9 Appendix Problems 1. We can use the Lagrangian technique. The Lagrangian is:

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Rearranging gives:

Inserting this expression for L into the production function and setting Q = 2, we get 2 = = 2K, so K = 1 and L = 4 are the cost-minimizing input values.

2. The problem is to find min (3K + 2L) subject to Q = 3KL. K,L If we solve the production function for L = Q/3K and substitute back into the total cost expression, the problem becomes min [3K + (2Q/3K)].

K The first order condition for a minimum is d[3K + (2Q/3K)]/dK = 3 – (2Q/3K2) = 0, which solves for the cost-minimizing value of K, K*= √ . Substituting this expression into the production function, we get L*= .

The least costly way of producing Q is thus given by LTC = 3K*+ 2L*= √ +√ = 2√ ; LAC = LTC/Q = (2 / .

LMC = dLTC/dQ = √

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This production function has increasing returns to scale.

3. a. Optimality requires that MPL/MPK = w/r = 2/4. (*) MPL = Q / L = 2 K MPK = Q / K = L/( ) MPL/MPK = (2 K )/(L/ ) = 2K/L (**) From (*) and (**), we can say that K/L = 1/4. b. Since K/L = 1/4, we have L = 4K. When we substitute this into the production function, we have Q(K, L) = 2L = 8K = 1,000.

This implies K3/2 = 125, which implies K = 25 and L = 100.

4. Optimality requires MPL/MPK = PL/PK .

MPL/MPK = K/L = PL/PK. This implies PL/PK = 2/8 or PK = 4PL. (*) We also have that LxPL + KxPK = 16. (**) Substituting (*) into (**) yields 8PL + 2x4/3PL = 16, or PL = 1.5 and PK = 2.

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5. Optimality requires MPL/MPK = PL/PK .

MPL = = 2/L. MPK = = 3/K. MPL/MPK = (2/L)/(3/K) = 2K/3L = PL/PK = 6/4.

Thus the optimal ratio is K/L = 9/4

Chapter 10 Perfect Competition Answers to Review Questions 1. Economic profit includes all costs (including opportunity or implicit costs), while accounting profit looks only at cash flow. The firm should consider economic profit only.

2. Unless firms act as though their pricing decisions affect other firms, we should assume that firms act as price takers. Firms behave as price takers when it is easy for new firms to enter the industry and/or prices are determined before firms have produced the good. Each firm knows that a rival firm could ‗undercut‘ and capture the market. A firm‘s ability to set a price above marginal cost is thus constrained.

3. The dry cleaning markets would be nearly perfect except that many people do not want to drive far for their clothing pickups and dropoffs. In small towns there may only be one or two cleaners so less competition will be present.

4. Price = TR/Q, so this firm's demand curve is given by P = a – 2Q. Since its price is a declining function of output, it cannot be a perfectly competitive firm.

5. No, because managers often relate to their competition by trial and error actions moving in the direction of what succeeds for them. This moves the firm to the quantity of output that is consistent with perfect competition outcomes.

6. The firm should shut down if and only if its price is below AVC. MC can lie below AFC at the same time price lies above AVC (see diagram). So false.

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P AVC

P* AFC

MC Q Q*

7. The value of the last unit to consumers (the price) equals the opportunity cost of resources necessary to produce that unit.

8. The effect of such a tax is to produce a parallel upward movement in each firm's long-run average cost curve. The output level for which the minimum value of LAC occurs will thus be the same as before, which means that firms in long-run equilibrium will each have the same amount of output as before. So true.

9. A firm will have a long-run marginal cost function that is above average cost for all points past the minimum point on the long-run average cost curve. If demand causes price to be above the minimum average cost in the short-run, then firms could be operating where price equals long-run marginal cost and they could be making economic profits. When entry occurs in the long-run the price will fall and price will equal long-run marginal cost at the long-run equilibrium output level. Thus the statement is false. See the diagram below.

SMC

$/Q LAC

SAC

P0 P* LMC

Q 0

Q*

Q

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10. Consumer surplus in a competitive industry is the area between the price line and the market demand curve, not the individual firm's demand curve. Since the market demand curve is downward sloping, there will in general be positive consumer surplus. Indeed, compared to other market structures, perfect competition creates the maximum consumer surplus. So false.

11. Pecuniary economies and diseconomies are industry wide concepts that are operative when all firms act similarly to put pressure on input prices. Since many inputs effect all industries it is less likely that any one industry will impact input prices substantially cause pecuniary effects.

12. Yes, in the short run, firms that innovate first will reap economic profit until other firms catch up and compete away the economic profit. Thus, intensive innovation efforts are consistent with the perfect competition model.

Answers to Chapter 10 Problems 1. Reading from the table and graph, price equals marginal cost at Q = 4. For a quantity of 4, average total cost is ATC = 26. Thus  = (P – ATC)Q = (32 26) × 4 = 24.

Price 64 48

ATC

MC profit (6x4) AVC Price

32 26 16

0

2

4

6 Quantity

8

10

2. Setting price P = 10 equal to marginal cost of SMC = 2 + 4Q, solve for quantity 10 = 2 + 4Q or 8 = 4Q or Q = 2. The fixed cost that leads to zero economic profit is calculated by solving  = (P – AVC)Q – FC = 0, or (10 – 6)2 – FC = 0 for FC = 8.

3. SR supply = ∑ MCi = 4 + Qi Qi = MCi – 4  Qi = Q =  MCi – 4,000 Q = 1,000 MC – 4,000 81 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

MC = P, so Q = 1,000 P – 4,000, which means that industry supply is given by P = 4 + Q/1,000.

SR equilibrium Q: 4 + Q/1,000 = 10 – 2Q/1,000 3Q/1,000 = 6, Q = 2,000, P = 6.

P

Consumer surplus

10

Producer surplus S

6 4

D

Q 2000 Consumer surplus = area of upper triangle = 4,000.

Producer surplus = area of lower triangle = 2,000.

Total loss in surplus = 6,000.

4. In the long run, both the demand and supply curves will be more elastic than in the short run, making the loss in both consumer and producer surpluses smaller.

5. Since P = SMC > AVC, the firm should continue at its current level of output in the short run. In the long run, it should select the plant size for which P = LMC = SMC. As indicated in the diagram below, this means it should switch to a smaller plant size in the long run. $/Q LAC

SAC

12 AVC

10 8

LMC

SMC

Q0

Q*

Q

6. Long-run equilibrium price for this industry will occur at the minimum value of LAC. LAC = LTC/Q = Q2 – 10Q + 36 dLAC/dQ =2Q – 10 = 0, which solves for Q = 5.

At Q = 5, LAC = 25 – 50 + 36 = 11.

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7. The LAC curve for firms in this industry is given by LTC/Q = Q + 4. The minimum value of LAC now occurs at an output level of 0, where LAC takes the value 4. As a practical matter, the notion of an infinitesimally small firm has no meaning. Because of indivisibilities, a firm's LAC curve will increase beyond some point as Q shrinks toward zero.

8. The taxi industry supply curve for Metropolis is a horizontal line at P = $0.20/mile. The demand schedule intersects it at Q = 80,000 miles/yr, which means 8 taxis. The equilibrium fare will be $0.20/mile.

P 1.0

AC=MC

0.20

Q (10,000s) 8 10 9. If the total number of taxis is reduced from 8 to 6, the equilibrium fare will rise to $0.40/mile. Ignoring the opportunity cost of the medallion, each medallion owner will earn a profit of $(0.40 – 0.20)10,000 = $2,000/yr. If the annual interest rate is 10 percent, a person would need $20,000 in order to earn as much interest as a medallion holder earns each year in profit. So medallions will sell in the market for $20,000 each. A person who buys a medallion at this price will earn zero economic profit.

10. The short-run MC curve for firms in the industry is dSTC/dQ = 10 + 2wQ. The equilibrium output is found by equating P and MC: 10 + 2wQ* = 28, which yields Q*= 9/w. For firms with normal managers, w = 2, so Q* = 9/2 = 4.5. Profit of normal firms = ∏ = 28(4.5) – 2 (4.5)2 – 45–M = 40.5 – M. For the firm that hires Amanda, w = 1, so Q* = 9. Profit of firm with Amanda as manager = ∏ = 28(9) – 92 – 90 – Mm = 81 – Mm, where Mm is Amanda's salary. The premium paid to Amanda in equilibrium will be exactly the amount required to equate her firm's profits with those of other firms, because with a smaller amount, another firm will try to headhunt Amanda away, and with a bigger amount, the firm employing Amanda will earn a negative profit. ∏ = 81 – Mm = ∏ = 40.5 – M, so Mm – M = 81 – 40.5 = 40.5.

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11. a. With the new process your costs, excluding your payment for use of the patent, will be TC' = 4 + Q + Q2. To find your profit maximizing output level, we equate your new marginal cost, MC' = 1 + 2Q, to the industry price, which, as before, will be the minimum value of the average cost curve associated with the prevailing technology: LAC = 8/Q + 2 + 2Q => dLAC/dQ = 2 – 8/Q2 = 0 => Q* = 2 => LAC = 10 = P*. If we use Q' to denote the patent holding firm's profit-maximizing output level, we have MC'=10 = 1 + 2Q' => Q' = 4.5. The patent holder's economic profit will thus be TR – TC = 45 – 4.5 – 20.25 = 16.25. So the most you would be willing to pay for the patent is 16.25. b. Because the patented process can reduce the costs of each of the 1001 firms by half, it is

worth considerably more than 16.25; thus the investor would not be willing to sell exclusive rights to its use to one firm at that price. For example, he could sell the patent to two firms for 16.24.

12. a. MC = Similarly, AVC= wL/Q = w/AP. So when AP = MP, it follows that MC = AVC. b. Since the firm is perfectly competitive, its output price is equal to marginal cost, which

here is equal to AVC. So all of the firm's revenue is paid out to its workers, leaving none for its cost of capital. Thus, if the firm stays open in the short run, its loss will be equal to its fixed capital costs of $40/day, which is the same loss it would suffer if it were to shut down. So the firm is indifferent between shutting down and remaining open in the short run.

13. TC = 0.2Q2 5Q + 30. Taking the derivative yields MC = dTC/dQ = 0.4Q − 5.

MC = dTC/dQ = 0.4 Q – 5.

In equilibrium MC = P, which implies 0.4Q – 5 = 6, which solves for Q = 27.5.

Profit = revenue – cost = 27.5 × 6 – [0.2(27.5)2 – 5(27.5) + 30] = 121.25. Since the firm earns positive profit, it should stay open.

14. Demand is given by P = 5 – 0.002Q, and supply is given by P = 0.2 + 0.004Q. In equilibrium, sale and purchase prices are equal. Thus, we get 5 – 0.002Q = 0.2 + 0.004Q, which solves for Q = 800 and P = 3.4. With tax, assume the supply curve shifts upward by 1 unit, which makes it: P = 1.2+ 0.004Q. When we solve 5 – 0.002Q = 1.2 + 0.004Q, we get Q = 1,900/3 and P = 56/15.

This is the price paid by the consumer. The supplier gets P = 41/15 as it has to pay the tax worth $1 (=15/15).

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The incidence of tax on the supplier is [(41/15) – 3.4]/1 = [(41/15) – (51/15)/1] = 10/15 = 2/3, and on the consumer it is [(56/15) – 3.4]/1 = [(56/15) – (51/15)/1] = 5/15 = 1/3.

The consumer surplus before tax is [(5 – 3.4)800]/2 = 640.

The producer surplus before tax is [(3.4 – 0.2)800]/2 = 1280.

The consumer surplus after tax is [(5 – 56/15) × (1,900/3)]/2 = 401.11.

The producer surplus after tax is [(41/15 – 0.2) × (1,900/3)]/2 = 802.22.

Lost consumer surplus is 238.88.

Lost producer surplus is 477.77.

15. (1) Since the supply curve faced by the individual firm is elastic, the advertisement (which shifts the demand curve out) will increase quantity increase but leave price unchanged, as shown on the diagram.

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(2) The result will be a shift in the long-run supply curve. Price will increase and quantity will decrease.

16. a. LAC = TC/Q = 4Q + 100 + 100/Q. The minimum point on LAC is found either by graphing the LAC curve or by taking the first derivative and setting it to zero. dLAC/dQ = 4 – 100/Q2 = 0, which yields Q = 5.

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In the long run P = LAC = 140 b. If demand is Q = 1,000 – P, then at P = 140, we get Q = 860. So in long run equilibrium, there will be 860/5 = 172 firms. c. Now LAC = (TC – 36)/Q = 4Q + 100 + 64/Q. Again, the minimum point on LAC is found either by graphing the LAC curve or by taking the first derivative and setting it to zero. dLAC/dQ = 4 – 64/Q2 = 0, which yields Q = 4. In the long run P = LAC = 132.

17. a. At a world price of 30, domestic demand is 35 million bushels per year.

Domestic producers supply the 20 million bushels of this total, foreign producers the remaining 15 million (left panel.) b. With a tariff of $20/bu, the import price becomes $50/bu. Because the domestic market clears at $40/bu (center panel), this means that no beans will be imported. Since no beans are imported, the tariff raises no revenue. c. Consumer surplus and producer surplus with the tariff is the area of triangle ABC (center panel), which equals $1350/yr. Consumer surplus and producer surplus before the tariff-the shaded area in the right panel-- was $1425/yr, which means that the tariff has reduced consumer and producer surplus by $75/yr.

18. (i) Costs will fall for all existing firms. At existing prices the firms will make positive economic profits and increase output. (ii) New firms will enter the industry because of profits. (iii) The industry supply curve will shift out until profits are again driven down to zero. The final result is that prices fall, quantity increases, and there are more firms than before. In other words, consumers reap all the surplus from this innovation.

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Chapter 11 Monopoly Answers to Review Questions 1. The five factors include exclusive control over inputs, economies of scale, patents, a network economy, and government licensing or franchising. Economies of scale derive from technological conditions rather than institutional arrangements that can change anytime.

2. Yes, if the transportation costs of cement from the next town make the competing cement more expensive than the monopoly price of the local cement.

3. Since the demand curve slopes downward, marginal revenue will always be less than price, because for each additional unit sold one must lower the price for all other goods sold.

4. A profit maximizing monopolist will never produce on the inelastic portion of the curve.

This is because raising prices will always increase revenue and since output will be lower, it also lowers costs. The monopoly equilibrium will not be reached. On the inelastic portion of the curve, raising price will always increase revenue and (since output will be lower) it also lowers costs. Therefore, the firm should always move up the demand curve to where it is not inelastic if profit maximization is a goal.

A revenue-maximizing monopoly would also never produce where demand is inelastic, since lowering quantity and raising prices will raise total revenue.

5. If MR intersects MC from below, then MC must be downward sloping; more output will lower MC. 6. There will be no effect. The firm‘s objective is still to maximize economic profit—even though it only gets 50 percent of the profit. The same combination of price and quantity maximize profit before and after the tax on profits.

7. (P – MC) /P = 1 – MC/P = 1/3. In perfect competition P = MC. A perfectly competitive firm faces a horizontal demand curve and hence does not have a price mark-up.

8. The price-quantity pair that maximizes profits will also maximize the profits minus a lumpsum tax. Such a tax is equivalent to any other fixed cost since it leaves the optimal pricequantity pair unaffected.

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9. With a perfectly horizontal market demand curve, any attempts to increase the price by decreasing the supply will be futile. Because of that, there can be no mark-up. Therefore, there will be no deadweight loss because of the monopoly. So true.

10. X-efficiency is the degree of efficiency maintained by firms under conditions of imperfect competition. As per the efficiency, prices are equated with marginal cost. The monopoly firm has a falling average cost and AC always lies above marginal cost. This implies a loss to a natural monopoly.

11. The hurdle model gives the lower price only to those willing to jump the hurdle so the markets are more easily segregated. Deadweight losses are reduced.

Answers to Chapter 11 Problems 1. a. Increase output because MR > MC and P > AVC. b. Reduce output because MR < MC (we know that MR < P and P = MC here). c. Remain at current output. MR = MC, and P = TR/Q = 11 > AVC. d. Figures can't be right (P < MR). e.

Figures can't be right (P = TR/Q = 3.99, which is clearly not equal to 35.00).

2. MC = 2Q = MR = 100 – 2Q 100 – 2Q = 2Q, so Q* = 25, P* = $75.

TR = $1,875; TC = $641  = TR – TC = $1,234

3. The profit maximizing level of output for a single-price monopolist occurs where MR = MC. The linear demand curve P = 100 – Q has a marginal revenue of MR = 100 – 2Q. By equating marginal revenue and marginal cost (100 – 2Q = 2Q) we get a quantity of 25. The price charged for this quantity is read off the demand curve so P = 100 – Q = 100 – 25 = 75.

The monopolist‘s price and quantity are unaffected by fixed costs. However, the monopolist earns lower profits:  = TR – TC = 75Q – (32 + Q2) = 1,875 – 657 = 1,218. The difference in profits equals the increase in fixed costs.

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4. The profit-maximizing level of output for a single-price monopolist occurs where MR = MC. The linear demand curve P = 100 – Q has associated marginal revenue of MR = 100 – 2Q. Setting marginal revenue equal to marginal cost, MC = 8Q, we have 100 – 2Q = 8Q, which solves for Q = 10. The price charged for this quantity is read off the demand curve: P = 100 – Q = 100 – 10 = $90. The monopolist‘s price rises and quantity falls due to the increase in marginal costs. The monopolist earns lower profit than before:  = TR – TC = 90Q – (16 + 4Q2) = 900 – 416 = $484. See graph below.

Price 100 90

MC

ATC

D 42 MR

0

10

20 Quantity

30

40

50

5. MR should be equal in both markets. Since the price is fixed at 60 in the foreign market, MR is also fixed at 60 in that market. This means that MR at home should also be 60. We have MRhome = 100 – 2Q = 60, which solves for Qhome = 20. Also MC should be equal to 60.

MC = 2Q = 60 solves for Qtotal = 30. Therefore Qforeign = Qtotal-Qhome = 10. Price in the home market = 100 – 20 = $80.

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6. The profit-maximizing level of output for a single-price monopolist occurs where MR = LMC, The linear demand curve P = 100 – Q has associated marginal revenue of MR = 100 – 2Q. Setting marginal revenue equal to marginal cost, LMC = 20, we have 100 – 2Q = 20, which solves for Q = 40. The price charged for this quantity is read off the demand curve: P = 100 – Q = 100 – 40 = 60. A perfectly competitive industry would produce the quantity such that P = LMC = 20 so that Q = 100 – 20 = 80. The total surplus generated by perfect competition would be TS = (1/2)80(100 – 20) = 3200.

By comparison, the monopoly generates producer surplus PSm = 40(60 – 20) = $1,600 and consumer surplus CSm = (1/2)40(100 – 60) = $800 for a total surplus of TSm = 160 = 80 = $2,400. The efficiency loss due to monopoly is the amount by which total surplus under monopoly falls short of the total surplus under perfect competition. (TS = $2,400 – $3,200 = $800) The efficiency loss is the triangular area between the demand curve and marginal cost (supply) with base equal to quantity by which ouput under perfect competition exceeds output under monopoly.

Price 100

60

MC MR 0

40

D

50

100 Quantity

7. A perfectly discriminating monopolist sells the quantity where marginal cost intersects the demand curve P = MC or 100 – 10Q = 20 or 10Q = 80 or Q* = 8. The monopolist‘s economic profit is the area under the demand curve down to average cost out to quantity. PS = (1/2)(100 – 20)8 = 320. The government could charge the firm any fixed fee up to 320. See graph below.

Price 100

20

MC D

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0

8

10

Quantity

8. MR = P(1 – 1/||) = MC, which implies that P = MC/(1 – 1/||) Senior citizens: PS* = 1/(1 1/4) = 4/3, or $1.33 Adults: PA* = 1/(1 – 1/2) = $2.

9. Iraq: P = 400 – 0.5Q => MR = 400 – Q, or Q = 400 – MR. Iran: P = 300 – Q => MR= 300 – 2Q, or Q = 150 – MR/2.

When we add these horizontally, we get Q = QIraq+ QIran = 400 – MR for 0 < Q < 100, 550 – (3/2) MR for Q >100.

MC = Q will intersect MR when Q >100.

In equilibrium, MR = MC= 1,100/3 – (2/3)Q = Q, which solves for Q = 220 and MR = 220.

Iraq: Q = 400 – MR = 180; P = 400 – 0.5Q = 310.

Iran: Q =150 – MR/2 = 40 and P = 300 – Q = 260.

10. Since they have lower income, their demand is more price elastic than regular customers'. So they are more willing to jump the hurdle to get a lower price. The hurdle is the coupon in this case, and it is used to sort people according to their price elasticities of demand.

11. || =2, so MR = P(1 – 1/||) = 10(1 – 1/2) = $5.

12. If demand is inelastic at the price ceiling, we know the monopolist could increase its profits by raising its price. So false.

13. See footnote in text associated with this problem.  = PH QH + PL QL – 5(QH + QL) – 15 a. PH = 20 – 5QH,

PL = 20 –5QH – 5QL

max [(20 – 5QH) QH + (20 – 5QH – 5QL) QL – 5QH – 5QL – 15] QH,QL First-order conditions: (1) QH = 20 – 10QH – 5QL – 5 = 0 (2) QL = 20 – 5QH – 10QL – 5 = 0, which may be restated as (1') 15 10QH = 5QL, so 3 – 2QH = QL 92 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

(2') 15 – 5QH – 10 (3 – 2QH) = 0, so -15 + 15QH = 0 Thus QH = 1; QL = 3 – 2QH = 1; PH = 15; PL = 10 b. Profit = 15 + 10 – 5(2) – 15 = 0 c. MR = 20 – 10Q = MC = 5, so Q* = 1.5 P* = 20 – 5(1.5) = 12.5 = (12.5)(1.5) – 5(1.5) – 15 = -3.75 d. With a single price, Harry would be forced out of business in the long run, and consumers would lose the surplus they enjoy under the two-price arrangement.

14. The publisher's net income from the project comes when it sets the price that corresponds to the quantity for which marginal revenue and marginal cost are equal. The author's net income from the project is maximized when the price is set at the level that maximizes total revenue. The author's best price thus corresponds to the quantity for which marginal revenue equals zero. As long as marginal production costs are positive, it follows that the publisher will prefer a higher price than the author. So false.

15. The studio's maximum net income from the project comes when it sets the rental price that corresponds to the quantity for which marginal revenue and marginal cost are equal. The director's net income from the project is maximized when the price is set at the level that maximizes total revenue. The director's best price thus corresponds to the quantity for which marginal revenue equals zero. As long as marginal production costs are zero (which follows from the assumption that all costs are fixed), it follows that the studio will also prefer the price that equates marginal revenue to zero. So false.

Chapter 12

A Game-Theoretic Approach to Strategic Behavior

Answers to Review Questions 6. In the prisoner‘s dilemma the two strategy choices are cooperate and defect. The defining condition of the game is that each player receives a higher payoff when each cooperates than when each defects. To say that the costs of failing to cooperate are high in prisoner‘s dilemmas is simply another way of saying that there are powerful financial incentives to find some way to hold collusive agreements together. Both parties would be better off without nuclear arms.

2. Each knows that the other will have nothing to lose by defecting on the last round. This robs each party of an effective threat of retaliation on the third round, which means each also has nothing to lose by defecting on round 3. The same reasoning extends backward to the second and first rounds as well.

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3. When three or more are interrogated for a crime they committed or when multiple firms in an industry are contemplating advertising.

4. Typical examples students might come up with: commitment in a relationship; commitment to getting an A in class.

5. Strategic preferences are ones that help people solve problems of social interaction. ―Evolutionary game theory,‖ is a branch of game theory that provides a structured way of thinking about how strategic preferences might have emerged. An early example comes from the biological literature‘s approach to the origin of a preference for aggressive behavior. If one observes someone with a disposition toward, say, anger, one will assume that the person will commit to a strategy of retaliation.

Answers to Chapter 12 Problems 1. A dominant strategy can only be determined if the severity of the punishments are

rated.

Assume expelling is the worst and withdrawing is worse than a C. Then there is no dominant strategy. However, if a C is worse than withdrawing, then both have a dominant strategy to sign and take the F because if only one signs the other is expelled and fearing that they both sign.

Bob signs Bob doesn‘t sign

Beth doesn‘t sign Beth expelled Bob withdraws Bob = C Beth = C

Beth signs Beth = F Bob = F Beth withdraws Bob expelled

2. a. Kiplinger has a dominant strategy to go comprehensive and Intuit does not have a dominant strategy. But knowing that Kiplinger will go comprehensive, Intuit then goes simple. Because neither one has incentive to change because changing will make them worse off, there is a Nash equilibrium in the northeast box.

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b. This has now become a sequential game. If Kiplinger goes first they will pick a comprehensive plan and get 200. Intuit would then follow with a simple plan and make 110. If Intuit goes first they will pick a comprehensive plan and make 220. Kiplinger will then follow with a comprehensive plan and make 100. Because Intuit has 110 to gain by going first and Kiplinger has only 100 to gain, Intuit bids 101 and gets the services of the programmer. All of this assumes that the profit numbers in the matrix do not change because of the unique talents of the programmer.

3. a.

Neither firm has a dominant strategy. If one firm chooses to produce a big car, the other has an incentive to produce a small car, and vice versa.

b. One firm producing a big car and the other producing a small car is a Nash equilibrium.

4. a.

D Big car Big car

400 for Firm 1 400 for Firm 2

B Firm 2 Small car

E 1000 for Firm 1 800 for Firm 2

Big car

F

800 for Firm 1 1000 for Firm 2

Small car

G

500 for Firm 1 500 for Firm 2

A Firm 1

Small car

C Firm 2

b. If firm 1 chooses the big car, firm 2 will choose the small car (point E). If firm 1 chooses the small car, firm 2 will choose the big car (point F). Since profits for firm 1 are higher at E than at F, firm 1 will choose big car to begin with. So the Nash equilibrium for this game occurs at point E.

5. If Zuri goes Rohan will not go because 15 is better than 10. That leaves Zuri at -5. If Zuri does not go Rohan will not go either because 0 is better than -5 for him. Knowing this, Zuri doesn‘t go because zero is better than her alternative at -5 so both stay home. This is not a good outcome for the class. Maybe Zuri should go and bride Rohan with 6 so he goes for 16 and she goes with a net gain of 4.

6. Chris has a dominant strategy to go to Joe‘s. Knowing this, Taylor will go to Joe‘s where they meet.

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7. a. False. If MCI has a discount plan AT&T should not offer one because -6 is better than -8. If MCI has no discount plan AT&T should offer one because 15 is better than 6. b. False. Neither firm has a dominant strategy. c. False, - 8 is better than -12 d. False. There are not dominant strategies. e. True.

8. At first glance the waiter will not give good service because 80 is better than 20 so the diner gets only 30. A binding commitment will eliminate the ―don‘t tip‖ portion of the game tree leaving both with 100. Gaining 70 will mean that is the most he would spend.

9. a. True. Raj has a dominant strategy for A and if he is there Adhira will go to A also. Neither has incentive to move to B. b. False. Adhira will gain by moving to A. c. False. Both Raj and Adhira will have incentive to change. d. False. Raj will have incentive to change.

10. The population will be 33.33% friendly. The equations are payoff for aggressives = 0.05(%F) and the payoff for friendlies = 1 + .02(%F). Equating the two leaves %F = 1/3 of the population friendly. Below that the friendlies thrive and above that the aggressives get higher payoffs.

11. a. The population of Cs will be 83.3%. (5 = .06%C) so C = 5/6. b. The population will be all Ds because their expected payoff is higher at all levels of Cs.

Chapter 13 Oligopoly and Monopolistic Competition Answers to Review Questions

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1. The models differ in their assumptions about firm behavior. The Cournot model assumes firms choose quantities simultaneously (taking as given the other firm's quantity.) the Bertrand model assumes firms choose prices simultaneously (taking as given the other firm's price.) The Stackelberg model assumes one firm (the leader) chooses its quantity before the other firm (the follower) chooses its quantity before the other firm (the follower).

2. Like the prisoner‘s dilemma, members of the cartel will be better off if none of them cheat, but the option to cheat is a dominant strategy for each.

3. If there are more than two firms, the enforcer (who detects cheating and punishes it) will have higher costs; all compliant firms have an incentive to shirk that duty.

4. No; the assumption that one firm makes about the other firm's strategy is naive.

5. The extra utility that consumers get from product variety must be weighed against the higher prices that result from product differentiation and monopolistic competition.

6. A greater population density can sustain more product variety ceteris paribus. Greater transportation costs also increase product variety. The higher the fixed cost of offering new products, the fewer new products will be offered.

Answers to Chapter 13 Problems 1. Shared monopoly: MR = 15 – 2Q = MC = 3 2Q = 12, Q = 6, P = 9, Q1=Q2=3  = 54 – 18 = 36,  1 =  2 = 18.

Cournot: P1 = 15 – Q1 – Q2 = (15 – Q2) – Q1 MR1= (15 – Q2) – Q1 = MC = 3 2Q1 = 12 – Q2 Q1 = 6 – Q2/2 1's reaction function.

Q2 = 6 – Q1/2 2's reaction function.

Q1 = Q2 = 4. Q = 8. P = 15 – 8 = 7 TR1 = 7(4) = 28 = TR2  1 = 28 – 4(3) = 16 =  2;  1 +  2 = 32.

Bertrand:

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TR = 36 TC = 36  =0 Stackelberg: Firm 2's Cournot reaction function: Q2 = 6 – Q1/2 Firm 1's demand: P = 15 – (6 – Q1/2) – Q1 = 9 – Q1/2.

MR1 = 9 – Q1 = MC = 3 => Q1 = 6 Q2 = 6 – Q1/2 = 3 Q=6+3=9 P=6 TR1 = 36  1 = 36 – 18 = 18 TR2 = 3(6) = 18  2 = 18 – 9 = 9.  1 +  2 = 27.

2. P1 = 36 – 3Q = 36 – 3 (Q1 + Q2) = (36 – 3 Q2) – 3 Q1.

MR1 = (36 – 3Q2) – 6 Q1 = MC = 18.

1‘s reaction function: Q1 = 3 – (1/2) Q2.

Similarly, for 2: Q2 = 3 – (1/2) Q1.

This solves for Q1 = Q2 = 2.

P = 36 – 3Q = 36 – 3(4) = 24.  1 = TR – TC = 2(24) – 2(18) = 12 =  2.  =  1 +  2 = 24.

3. P = MC = 18.

Since P = 36 – 3Q, we have Q = 6.

Thus, Q1 = Q2 = Q/2 = 3.

TR1 = TR2 = 3(18) = 54.

TC1 = TC2 = 3(18) = 54.

And so  1 =  2 =  = 0.

4. P2 = 36 − 3Q = 36 − 3 (Q1 + Q2) = (36 − 3Q1) − 3Q2.

MR2 = (36 − 3Q1) − 6Q2 = MC = $18.

2‘s reaction function is the same as in the Cournot case: Q2 = 3 – (1/2) Q1.

1‘s demand is P = 36 – 3(Q2) – 3Q1 = 36 – 3(3 – (1/2)Q1) – 3Q1 = 27 – (3/2) Q1.

MR1 = 27 – 3Q1 = MC = 18.

This solves for Q1 = 3 and Q2 = 3/2.

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Therefore Q = Q1 + Q2 = 9/2 and P = 36 – 3(9/2) = 45/2. Õ 1 = 3 (45/2 – 18) = 27/2. Õ 2 = (3/2) (45/2 – 18) = 27/4.

5. As a monopolist, MR = 140 - 2Q = 20 implies Q = 60: P = 140 – 60 = 80: so  = (80 – 20)60 = 3600. Then as Cournot duopolists, MRA = 140 – QL – 2A = 20 = MC implies QA = 60 – (QL/2) and QL = 60 – (QA/2), QA = QL = 40, Q = QA + QL = 80, P – 140 – 80 = 60,  = (60 – 20)40 – 1600,  = 2 = 200. Therefore the change in profit = 3,200 – 3600 = -400.

6. a. Suppose firm 1 produces Q1. Firm 2's residual demand curve will then be P = (100 – Q1) – Q2, and its marginal revenue will be MR = (100 – Q1) – 2Q2. And since marginal cost is zero, firm 2 will maximize its profits by choosing the Q2 for which MR = 0: Q2* = 50 – (Q1)/2 . Anticipating this response from firm 2, firm 1 can thus anticipate that its demand curve will be given by P = (100 – Q2*) – Q1. Substituting for Q2*, firm 1 thus sees the demand curve P = 50 – (Q1/2), and the corresponding marginal revenue curve, MR = 50 – Q1. Firm 1's best output level is thus given by Q1* = 50. So Q2* = 25 and total quantity = Q1* + Q2* = 75. The market price is therefore P = 100  75 = 25. So firm 1's profit is Õ 1= 50(25) = 1,250. Firm 2's profit is 25(25) = 625. b. Firm 2 is willing to pay at most Õ 2 = 625 for the license that gives the right to move second. Firm 1 is willing to pay at most Õ 1 = 1,250 for the license that gives the right to move first.

7. The expected profit for firm 1 is given by E( Õ 1) = [I1/(I1 + I2)]R – I1 . Assuming Nash-Cournot behavior, the first-order condition for maximum expected profit for firm 1 is given by dE( Õ 1)/dI1 = [RI2 – (I1 + I2)2]/(I1 + I2)2 = 0, which solves for the optimizing value of I1 conditional on I2: I1* = (RI2)1/2 – I2. Because the problem is symmetric, the value of I2, conditional on I1, is given by I2* = (RI1)1/2 – I1. In equilibrium, it follows that I1* = I2* = R/4.

8. The condition for profit maximization in a perfectly competitive market is P = MC on a rising portion of the MC curve. To sell additional units at the current market price would thus mean to earn lower profits if the firm were in equilibrium in a perfect competitive market. So true.

9. Suppose we have N garages. Following the example in the text, the distance between two adjacent garages will be 100/N. The average towing distance will thus be 100/4N. Average round-trip distance is 100/2N. There are 5,000 towing incidents with a cost of $50/mile each.

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Total direct towing cost is thus (5,000) (50) (100/2N) = $12,500,000/N. Total cost of the garages is 5,000N. Overall total cost is TC = 5,000N + 12,500,000/N. To find the optimal N, we could graph this function. Alternatively, taking the first derivative and setting it to zero will give the minimum. dTC/dN = 5,000 – 12,500,000/N2 = 0. This solves for N = 50.

10. Suppose we have N ports. Following the example in the text, the distance between two adjacent ports will be 10/N. The average travel cost will thus be 10/4N. Average round-trip distance is 10/2N. There are 1,000 fishermen. The total travel cost is (L) × (t) × (10/2N) = 1,000t(10/2N) = 5,000t/N. Total fixed cost is 1,000N. Total cost = 5,000t/N + 1,000N. For the moment, assume that t is known and you are finding the optimal N. So take the first derivative, set it equal to zero, and solve for N. dTC/dN = 1,000 – 5,000t/N2 = 0 so 5,000t/N2 = 1,000 or t = 1,000N2/5,000 Since N = 2, t = 4/5.

Chapter 14 Labor Answers to Review Questions 1. In the VMPL curve, the firm is a price taker. In the MRPL curve, the firm is a price maker.

2. It would be reduced because monoplists restrict output to raise price and therefore need less workers.

3. Other firms in the area could bid away workers.

4. Employers who discriminate will be driven out of the market by those who do not discriminate.

Answers to Chapter 14 Problems 1. Wages = $4/hr which equals VMP at L = 30 hours. The VMP column numbers are 16, 12, 8, 4, and 0.

Wage ($/hr) 16 VMP

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4

w=4 MP

0

30

40

Labor (person-hrs/day)

2. The new budget constraint shares M = $0 at h = 24 hours, but has twice the slope due to the wage being twice as high. The M‘ column numbers are 288, 216, 144, 72, and 0.

Income ($/day) 288 M‘

216 144 M 72

0

6

12 Leisure (hrs/day)

18

24

3. The monopsonist hires L = 20 units of labor, where VMP = MFC = $8, and pays the wage: w = AFC = $4/hr.

Wage ($/hr) 16 VMP MFC 8 AFC 4

0

20

30

Labor (person-hrs/day)

4. The value of the marginal product of labor is price times the marginal product of labor. VMP = P(MPL) = 5(22 – L) = 110 – 5L. A perfectly competitive firm hires labor until the point 101 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

where w = VMP, which in this case occurs at 10 = 110 – 5L or 100 = 5L or L = 20 units of labor.

Wage ($/hr) 60

VMP

10 0

20

22

Labor (person-hrs/day)

5. ABC = budget constraint for current job; E1 = current job; Income ($/day)

48

CD = budget constraint for new job E2 = new job

A D

I1

36

E1

E2 B

I2

8

C 12

16

24

Leisure

Since the new budget constraint also contains E1 (the current job), and since Smith's indifference curve was tangent at E1 with a slope of 2.5, it follows that he will accept the new job; at E1, he values extra leisure at $2.50/hr and the new job lets him get it for only $1.50/hr.

6. Program 1 is more likely to reduce hours worked, assuming leisure is a normal good, because it provides more income while leaving the price of leisure unchanged. Program 2, by contrast, makes leisure more expensive than before.

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Income ($/day) 115.2 106 96

Program 2 budget constraint

Program 1 budget constraint

initial budget constraint 10 leisure 24

11.5

7. a. Equilibrium occurs where MFC = demand: 4L = 12 - 2L, which solves for L* = 2 W = 2L* = 4

($/L) 12

MFC

AFC

7 4 L 2 2.5

6

b. With a minimum wage of 7 in effect: 7 = 12 –2L, which solves for L** = 5/2; W = 7 c. 12 – 2L = AFC = 2L, Lc = 3, Wc = 6 With min wage: L = 5/2; W = 7 8. The monopolist's demand curve for labor is his marginal revenue product curve, the product of marginal revenue and the marginal product of labor: MRP = (100 – 2Q)(4) = (100 – 8L)(4) = 400 – 32L. Acme's marginal factor cost curve is given by MFC = 40 + 4L. Equating MRP and MFC, we have 400 – 32L = 40 + 4L, which solves for L = 10. The wage is given by W = 40 + 2L = 60.

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9. a. MFC = 3 + 2L = Demand = W = 35 – 6L, which solves for L = 4 and W = 7 as shown from the supply supply curve for L = 4. b. At W = 17, we get L = (35 – 17)/6 = 3. $/L 35 D MFC 17 11 AFC 74 7

3 4

L 32/7 35/6

10. Since MR < P for a monopolist, we know that MR < $5, which means that MRPL = (MR)(MPL) is less than (5)(2) = $10/hr. And since w = 10, this means that she should hire less labor.

11. a. MRPL = (MR)(MPL). So MRPL = 5 × 8 = 40 and MFC = 10 + 2L. Since MFC = MRP, L = 15 and W = 10 + L = 25. Output = 15(5) = 75. b. MRPL = (102 – 3.92Q)(5) = 510 – 19.6Q. Since the production function is Q = 5L (because of constant marginal cost), when we substitute we get, MRPL = 510 – 98L. MFC = MRPL implies 510 – 98L = 10 + 2L which solves for L = 5 and W = 10 + L = 15 and Q = 5L = 25 and P = 102 – 1.96Q = 53. c. From part (b) MRPL = 510 - 98L. At L = 5, MRPL = 20 At L = 6, MRPL = -78.

Since MRPL becomes negative, no matter what the wage is an extra worker will decrease profits. So Ajax will not increase its labor force.

12. Comparing VMP with marginal willingness to pay for additional vacation time, we see that the optimal vacation lengths for the two types of worker are V*young = 2 weeks; V*old = 4 weeks.

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Compared to the current arrangement (in which all workers get 5 weeks vacation), older workers would be willing to cut their vacation to 4 weeks for only 150/yr more in pay. Since the older worker's VMP is 175/wk the firm can meet this requirement with 25/yr left to spare.

Younger workers would be willing to switch to 2 weeks vacation for an increase in pay of only 325/yr, and since the VMP of each younger worker is 150/wk, the 3 week/yr cut in vacation time will generate 450/yr additional revenue, or 125/yr more than necessary to meet the required pay hike. So the extra profit will be 25/yr for each older worker and 125/yr for each younger worker.

13. a. E(VMP) given that test = 9 and applicant is blue: (1/3) (9) + (2/3) (6) = 7. b. E(VMP) test = 9 and applicant is green: (1/3) (9) + (2/3) (12) = 11. c. No. Statistical discrimination pulls members within each group toward the respective group averages. It says nothing about why the group averages differ.

14. a. The wage schedule described in the diagram below pays the worker less than VMP in the early years, more than VMP in the later years. A shirking employee will be reluctant to work under such a schedule, because of the risk of getting caught and fired for shirking before having a chance to cash in on premium wages. The non-shirker, by contrast, does not have this reason to worry about being fired. Of course, if the probability of being caught were zero, the threat of losing future premium wages would lose all force. $/hr Wage Value of marginal product

time

b. Workers run not only the risk of being fired for shirking but also the risk of being fired because the firm doesn't want to pay the promised wage premiums. Any firm with a reputation for not making good on such promises would have a very difficult time finding workers to agree to work under a future-oriented pay schedule.

15. a.

The equilibrium condition for sector 1 is that its expected wage equals the wage in sector 2: (5/N1)100 = 10, so N1 = 50 and N2 = 80 – 50 = 30.

b. GNP = 5(100) + 30(10) = 800, which is the same as if sector 1 didn't exist!

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c. If we tax in sector 1 at the rate 0.5, the new equilibrium condition is that the expected

value of the after-tax wage in sector 1 be equal to the wage in sector 2: (5/N1) (0.5) 100 = 10, so N1' = 25 and N2' = 80 – 25 = 55. GNP= 5(100) + 55(10) = 1,050.

16. MPL = Q / L = (1/2) ( K / L ) = 1/ L VMPL = P MPL = 10/ L 17. MRPL = MR × MPL = (20 – 2Q) (1/ L ) = (20 – 4 L )/ L

Answer to the Appendix Problem 1. The utility functions lead to the following payoff matrix: A

Safe Mine

Unsafe Mine

Safe Mine

400 each

150 for B 500 for A

Unsafe Mine

500 for B 150 for A

300 each

B

a. These payoffs confront A and B with a prisoner's dilemma. The dominant strategy is to choose the unsafe mine, yet each gets only 300 utils when that happens, as compared with the 400 each would have gotten had each chosen the safe mine. b. Accordingly, it is in their interests to enter a binding agreement to work in the safe mine.

Chapter 15 Capital Answers to Review Questions 1. Real capital represents the actual physical capital used in production. Financial capital refers to the monetary assets whose rate of return explains the opportunity cost of real capital. To determine how much physical capital to use, one must think in financial terms.

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2. Depreciation represents a cost to the firm since it would have to replace the asset at the new current price.

3. Higher interest rates reduce the present value of any given nominal income stream. In other words we will attach a lower weight to future events.

4. Lenders and borrowers are concerned with real rates, not nominal rates. To keep real rates constant when prices rise, one must raise nominal rates an amount equal to the level of the increase in inflation. This will happen when the incomes of both borrowers and lenders rise proportionately with inflation.

5. Example: Suppose a $1,000 bond pays 10 percent in perpetuity, or $100 a year. If interest rates fall to 5 percent, then any new bond issued for $2,000 will yield $100 a year. Thus, the price of the old bond will rise to $2,000. In short, bond prices = (dividend/interest rate).

6. Any advice published is available to all; as soon as it is published, the market will take any new information into account and the price of stocks and bonds will change accordingly.

Only the few early birds will cash in their worms.

7. Telephone companies charge lower rates at night. Video rental stores charge lower rates on weekends. Rental car firms charge less on weekends.

8. Because it is rational for people near retirement to choose low-risk assets, which have lower expected returns, young people should experience higher expected returns.

Answers to Chapter 15 Problems 1. The rental rate of the first computer is (0.09 + 0.01 + 0.10)4,000 = (0.20)4,000 = $800/yr.

The rental rate on the second computer must obey (0.09 + 0.01 + 0.30)P = $800/yr, so its price must be P = 800/0.40 = $2,000.

2. The present value of the returns plus scrap value of the machine is given by PV = 30/1.1 + 30/(1.1)2 + 30/(1.1)3 + 30/(1.1)3 = 97.15 < 100.

Thus, the machine is a bad investment.

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3. The price of the bond at 5 percent interest would be P = 3,000/0.05 = $60,000. The price of the bond at 6 percent interest would be P' = 3,000/0.06 = $50,000.

4. The interest rate on taxable government bonds will adjust so that the after-tax returns are the same as for nontaxable government bonds. So the interest rate for nontaxable government bonds will be 4 percent.

5. The interest rate on tax-exempt consoles would have been 5 percent when everyone's marginal tax rate was 50 percent. It will rise to 7 percent when the marginal tax rate falls to 30 percent. If C denotes the console's annual coupon payment, its original price was given

by Po = C/.05. Its new price will be P1 = C/.07, which tells us that P1 = (5/7) Po, or that the price of the tax-exempt console will fall by 2/7 of its original value.

6. The rates of return should be the same for the two types of companies. If the return on companies that did business in China were higher, investors who don't mind that would bid for their stocks, and the resulting market pressures would eventually equalize returns.

7. The economically efficient price for a haircut at any moment is the amount it would cost to produce another one at that moment. This marginal cost will be different at different times of the day and week. On Saturday mornings and at other times when all four barbers and chairs are busy, the marginal cost of a haircut is the labor time of the barber plus the additional chair, shop space, clippers, and related capital equipment needed to serve another customer.

During less busy periods, by contrast, an additional haircut can be provided without incurring these additional resource costs. And so for this reason, the price of haircuts should be higher during busiest times.

8. The price should increase at the rate of interest. Therefore, Pn = Po (1 + i)n = 2,000 (1 + i)n.

Answer to Appendix Review Question 1. If the interest rate rises the opportunity cost of not extracting the oil goes up. Therefore the return on the asset must rise also which means the price level must rise on the resource

Answers to Chapter 15 Appendix Problems 1. If the price of oil rises at the real rate of interest, its price will reach $2 in t* years, where t* is found by solving (1.80)(1.05)t* = 2. This solves for t* = 2.16 years. Even without solving the equation explicitly, it is clear that if the price of oil starts at $1.80 and grows at 5% 108 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

annually, it will reach $2.00 well before 10 years have passed. This means that at current usage rates, there will still be oil left when its price reaches $2.00. No one will want to hold oil once that happens because its price will never rise again, given the availability of the solar substitute. Owners will attempt to get rid of their oil at the current price, which will drive that price downward.

2. The first step is to trace the price and stock-exhaustion paths under current beliefs about stocks. To do this, note first that the last drop of offshore oil will be used when its price, including the $6 extraction cost, reaches $12 per unit of energy. If resource markets were in equilibrium, the net price of offshore oil (the price exclusive of extraction cost) will have grown exponentially at the real rate of interest r. Tracing backward along that path from t2* (see diagram), we proceed to t1*, the point at which use of offshore oil begins. To find t1*, we proceed as follows: each time we move a small amount leftward on the time axis, we look at the price of offshore oil at that moment [P0Ser(t -t1*) + 6]; we then plug that price into the demand curve for oil, and add the resulting quantity onto the amount of offshore oil remaining. Moving leftward along the time axis in that fashion, we stop once the total stock of offshore oil reaches S2, its initial value. The amount of time that has elapsed in the process (t2*– t1*) is the length of the offshore oil age. In similar fashion, we work backward to determine the length of the underground oil age, t1*. If time = 0 denotes the current moment, it follows that underground oil will begin at a price of P0U (excluding extraction costs). The net and gross prices of underground and offshore oil will follow the paths shown in the diagram.

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Price ($/unit of energy) 12 P er(t-t1*)+6 0S P ert +2 0U 6

P e rt 0U

P ert 0S

P +2 0U P

P 0U

(t-t1*)

0S time

Stocks remaining (barrels) S 1 S2

t* 1

t* 2 offshore oil

underground oil

time

0 Underground oil age

t* 1

t* 2 Offshore oil age

Now, what happens when an additional  barrels of underground oil are discovered? We use the same method as before to calculate the price and stock exhaustion paths. The stock of offshore oil hasn't changed, nor has the price of the backstop technology. These values, together with extraction costs and the real rate of interest, thus lead to the same length of offshore oil age as before. Working backwards along the underground oil stock exhaustion path, we see that as before there are S1 barrels of oil when we have moved t1* units leftward into the underground oil age. But since the initial stock of underground oil is now S1+  , that means we must keep moving leftward along the time axis to find the starting point for the underground oil age. Once we move an additional  t units, the stock of underground oil reaches S1+  and that is where we stop.

Thus the effects of the underground oil discovery are (1) to reduce the current price of underground oil (in the diagram, from P0U to P'0U); (2) to extend the underground oil age by  t units; and (3) to postpone the onset of the offshore oil age by  t units.

Neither the price at which offshore oil is first extracted nor the length of the offshore oil age is affected by the discovery of the additional underground oil.

3. An exhaustible resource is an asset much like capital. If interest rates rise, then the future stream of payments from the resource is worth more; hence the price rises. (dB/dt)/B = r, 110 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

(dB/dt)/B = (10/_t)/(20_t) = 1/2t = 0.05, so t* = 10 years.

4. Suppose people extracted the shale oil first. By switching to the underground oil, we could then save on current extraction costs. If we put those savings in a bank account, we would get back enough to extract the shale oil later, and in addition we would gain all the interest payments. So we clearly do better by postponing the more costly extraction process as long as possible.

Chapter 16

Externalities, Property Rights, and the Coase Theorem

Answers to Review Questions 1. The parties involved will contract so that the person with the lowest cost will eliminate the externality. The cost will be borne by whoever is liable.

2. Library space, space in the dining halls, and parking are free to all and hence very overcrowded.

3. The general rule implies that other parties would also eliminate their externalities, which you would prefer.

4. Many people who live near airports moved to the nuisance  that is, the airport was already there, and they located near the airport because property was cheaper (to compensate them for the externality) or proximity to the airport is convenient. The transactions costs for airports would be too high to negotiate with every property owner. By contrast, a real estate developer should negotiate for an easement because transactions costs would be lower.

5. The water is considered public property and various safety and flooding issues might make that consideration very legitimate.

6. Yes, the liable party in effect incurs a loss of wealth.

Answers to Chapter 16 Problems 1. a. The payoffs in the table confront Ushi and Kabir with a prisoner's dilemma. The

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dominant strategy for each person is to burn, even though each would do better if both bagged. b. They will commit to bag their leaves, thereby increasing their payoffs to 6 each. c. This time burn is the dominant strategy for each individual. It is also collectively optimal. With or without an agreement, each will burn his leaves.

2. a. The most efficient outcome is for Ushi to produce with a filter. If Ushi is not liable for damages, Kabir will pay 45 < P < 50 to induce Ushi to install a filter. b. If the cost of the filter rises by $10/wk, the most efficient outcome is now for Ushi to produce without one. Ushi will produce without a filter and pay $85/wk to cover Kabir's damages.

3. a. The efficient outcome is for Ushi to produce with soundproofing (because the net gain is 28 with as opposed to 25 without). Kabir will pay Ushi 116 < P < 119 to induce Ushi to do so. b. With $4/wk transactions costs, it is no longer efficient to conduct the transaction in part (a). The total gain from installing soundproofing is only 28 – 25 = 3, which is $1/wk less than the cost of maintaining the agreement. c. Now the best option is for Kabir to move. That way he loses only $120/wk. The minimum payment to get Ushi to install soundproofing is $116/wk, which, when added to the $6/wk noise damage Kabir suffers with soundproofing, results in a total loss of $122/wk.

4. a. The total savings in rent is 600 – 450 = $150/mo. The least costly accommodation to the stereo problem is to have Gian listen (cost = $80/mo). The least costly solution to the singing problem is to have Nimit tolerate it (cost = $75/mo). The total cost of the least costly accommodation to the two externalities is thus $155/mo, so they should not live together. b. With the headphone option, the least costly solution to the stereo noise problem falls to $40/mo, making the total cost of accommodation only $115/mo. Now it pays them to live together, so that they can share the 150 – 115= $35/mo surplus. Since all of the costs of adjustment fall on Nimit, his share of the rent must be at least $115/mo less than he would have paid living alone. That is, Nimit will pay at most $185/mo if they live together. If they split the $35/mo surplus equally, Nimit's share will be 185 – 17.50 = $167.50/mo. Gian will pay the remaining $282.50.

5. The rent savings from living together is 800 – 600 = $200/mo. The costs of accommodation are as follows: 112 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

loss of privacy 60 smoke damage to Ava 60 noise damage to Sophia 90 ___________ total $210/mo It follows that they should live separately.

If Sophia didn't mind giving up her privacy, the total cost of accommodation would fall to $180/mo, and it would pay them to live together. The costs of accommodation are now $90/mo for each person. If they share the $20/mo surplus equally, each will pay $300/mo in rent.

6. a. If there are no transactions costs, Dionne will keep bees and Kenya will grow apples. Dionne will have to pay Kenya at least $50 to induce him to give up pig farming, which pays $50 more than apple growing when Dionne keeps bees. b. With transactions costs of $150, it is impractical to negotiate an agreement. Kenya will raise pigs, and Dionne will keep bees. c. The most Kenya can earn in (a) is $550. If Dionne paid Kenya any more than $150, Dionne would be worse off than with no agreement at all, as in (b). Kenya will earn exactly $450 in (b).

7. The gain in the total value of the herd as a function of the number of steers is given below in the table: Number of steers

Price per Total gain in 2-year-old value of herd steer

Avg. gain in value of herd

Marginal gain in value of herd

200 1 $1,200 200 200 ______________ ___________________________________________________ 150 2 1,175 350 175 ______________ ___________________________________________________ 100 3 1,150 450 150 ______________ ___________________________________________________ 50 4 1,125 500 125 _______________ ___________________________________________________ 0 5 1,100 500 100 _______________ ___________________________________________________ -50 6 1,075 450 75 _______________ ____________________________________________________

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a. If residents make decisions as individuals, they will buy steers until the average gain in value is no lower than the alternative gain they could obtain from bonds. Since the gain on bonds is 110 per year, this means that 4 will buy steers and 2 will buy bonds. This is the point where all village residents are choosing their best response with respect to all of the other residents and therefore is the Nash equilibrium. b. The socially optimal number of steers is the one for which the marginal gain in the value of the herd is no lower than the gain on bonds. This means buying 2 steers and 4 bonds. c. Any grazing fee between 41 and 64 per steer will result in 2 steers being sent onto the commons. The average gain, net of the grazing fee, will be between 134 and 111 when there are 2 steers.

8. The relationship between total, average, and marginal catch is given for each shore in the table: East Shore Total Avg. Marginal

West Shore Total Avg. Marginal

Number of boats per side 100 1 100 100 _________ _____________________________ 80 2 180 90 _________ _____________________________ 75 3 255 85 _________ _____________________________ 65 4 320 80 _________ _____________________________ 30 5 350 70 _________ ____________________________

85 85 85 _________ _________________ 65 150 75 _________ _________________ 60 210 70 _________ _________________ 50 260 65 _________ _________________ 40 300 60 _________ _______________

a. When each decides independently, boat owners will fish wherever the average catch is highest, provided it exceeds 70. The result is four boats on the east shore, only one on the west shore. The net catch is 320 + 85 – 5(70) = 55. b. This distribution is not optimal, for two reasons: First, the marginal product on each shore is not the same; and second, the marginal product on the east shore is lower than the marginal cost of the fourth boat there. The optimal allocation is to send three boats to the east shore, one to the west shore, and leave one boat idle. The net catch will be 255 + 85 – 4(70) = 60.

9. a. Each firm will use process A. Total emissions will be 8 tons/day. b. When 4 permits for 1 ton/day each are auctioned, they will sell for $50 each per day. At that price, Firm Y will buy 3, Firm X only 1. The total cost of smoke reduction will be 70 (the cost to X of switching from process A to process D) + 40 (the cost to Y of switching from A to B) = $110/day.

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c. When each firm cuts emissions by half, the total cost is 40 + 90 = $130/day.

10. Optimal pollution reduction requires that the marginal cost of reduction be the same for all firms. Marginal cost schedules are likely to differ across firms. Regulators would thus need detailed knowledge of these marginal cost schedules in order to calculate the optimal distribution of cutbacks. But regulators are unlikely to have reliable information about these schedules.

11. a. The average product in fishing is F/L = 8 – 2L. People choosing independently will fish until 8 – 2L = w = 4, which solves for L = 2. Total earnings will be 8(2) – 2(2)2 = 16 from fishing and 4(4) from factory work, making the total earnings = $24/day. b. The socially optimal number is the one for which the marginal product in fishing is equal to the factory wage. MP = dF/dL = 8 – 4L = 4, which solves for L = 1. Earnings from fishing will be 6, while earnings from factory work will be 5(4) = 20, making total earnings equal to $26/day. c. The disparity between individual and social optimality results from the fact that individual decision makers fail to take into account the fact that an extra person fishing reduces the catch of those who were already fishing.

12. At Latrell‘s house, the Coke is, in effect, a common property resource. Each child consumes Coke rapidly to prevent the other from encroaching on his share. Jabari, by contrast, has established property rights in Coke, which permits his children to consume at the best pace.

13. a. For the café, MRopen = 30 – 0.4 Q = MC = 10.

So Q = 50, P = 20, and π = 50 (20 –10) = 500.

MRclosed = 25 – 0.4 Q = 10.

So Q = 37.5, P = 17.5, and π = 281.25 The payoff matrix is: The café Krisha

Closed 281.25 0

Open 500 -5

Without a contract, Krisha will close her windows and the café will make a profit of only 281.25. With a contract, Amoli pays Krisha (5 < P < 218.75) to keep her windows open. b. If Amoli does not make the investment first, the amount she will have to pay Krisha to leave the windows open will be (5 < P < 168.75). Krisha will accept the offer, and both will be better off. But if Amoli makes the investment before signing a contract, her 115 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

expenditure becomes a sunk cost. At that point, if Krisha keeps the windows shut, it costs Amoli 218.75. So to ensure that the windows open, Amoli will have to pay (5 < P < 218.75). Amoli should sign a contract before making the investment. c. The payoff matrix is now: Closed The café 281.25 Krisha 0

Open 500 -50

Again the efficient outcome is for the windows to be open. Since Amoli's power as mayor enables her to ensure this outcome, the efficient outcome will be reached, provided Krisha gets at least 50 in benefits from keeping the bakery open. If she does not, she will shut the bakery down unless Amoli compensates her for her net loss.

14. a. Early is a dominant strategy for both players, so (Rashida Early, Maya Early) will be the outcome. b. They will commit to either (Rashida Early, Maya Late) with Rashida paying Maya 10 < P < 20 or (Rashida Late, Maya Early) with Maya paying Rashida10 < P < 20.

15. a. Early is a dominant strategy for both players, so (Rashida Early, Maya Early) will be the outcome. b. They will commit to (Rashida Early, Maya Late) with Rashida paying Maya 10 < P < 30. c. The players commit to the action pair with the highest total payoff. Now Rashida has the larger benefit from going to work early so (Rashida Early, Maya Late) is superior to (Rashida Late, Maya Early).

16. a. Bexley is a dominant strategy for Nora. Given that Nora will choose Bexley, Ivy will choose Arlington, so (Nora Bexley, Ivy Arlington) will be the outcome. b. They will commit to (Nora Arlington, Ivy Bexley). Ivy pays Nora 100 < P < 300.

17. a. As before, Bexley is a dominant strategy for Nora. Given that Nora will choose Bexley, Ivy will choose Arlington, so (Nora Bexley, Ivy Arlington) will be the outcome. b. They will not sign any agreement—selfish behavior leads to maximum total benefit now. c. Bexley has become more attractive to Nora and less attractive to Ivy, so Ivy can no longer compensate Nora sufficiently to change the equilibrium.

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Chapter 17 General Equilibrium and Market Efficiency Answers to Review Questions 1. If the MRS were different, then the two parties could gain from trade since one party values one product more than the other does. One would trade the good of relatively less value for the one of higher relative value. When the relative values are equal there are no more gains from trade possible.

2. An allocation is Pareto optimal if no reallocation can make one party better off without making another worse off. A Pareto preferred or Pareto superior position makes both parties better off than they were before.

3. It may not be easy to create an exchange which would move to a Pareto optimal situation. In particular, if transactions costs are significant, then reallocation is often difficult. Also, some people may be malevolent—willing to incur cost to injure others.

4. If both parties are egoistic, then one will end up somewhere on the portion of the contract curve which is between the two indifference curves which intersect the initial allocation.

5. No. By Walrus‘ Law, if there is a surplus of one good, there is a shortage of some other good.

6. First, she might point to the existence of monopoly, public goods, and externalities. Second, she might argue for a redistribution of income. Third, she might argue that transactions costs or other problems render the invisible hand theorem false. Finally, without property rights and contract enforcement (both public goods) markets cannot exist.

7. The slope of the production possibilities frontier reflects the tradeoff in the costs of producing one good vs. another, which is given by the ratios of the marginal production costs.

8. If a government sets taxes to correct market failure caused by public goods or externalities, then taxes can increase efficiency. Taxes do, however, change incentives and can lead to inefficiency if levied on goods with no external costs. Taxes do allow redistribution from the rich to the poor, but this is an equity rather than efficiency argument.

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Answers to Chapter 17 Problems 1. The Edgeworth box has width of size 30 and height of size 20. With Bert in the bottom-left corner, the initial endowment point is the point located at distance (10,10) from the bottomleft corner of the box. See graph included in problem 2 below.

2.

Ernie's clothing 20 15 10

30

O

E

Contract Curve Bert's food Ernie's 10 food

10 ParetoSuperior Set

initial allocation

O

B

10

20 15 Bert's clothing

30

b. Pareto efficiency requires Ernie to have clothing and food in a 3 to 2 ratio. c.

Equilibrium price ratio = 1. (Any other price ratio would result in a corner solution for Bert.)

3. This time the initial allocation lies on the contract curve, so there are no other allocations Pareto superior to it. The equilibrium price ratio must again be 1. See graph on the following page.

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Ernie's clothing 20 15 10

30

O

E

Bert's food Ernie's 10 food

10 initial allocation

O

B

10

30

20 15 Bert's clothing

4. To buy 6 units of clothing at the observed price ratio, A must give up 2 units of food. But B also wants to sell 2 units of food. There is thus excess supply of food, excess demand for clothing, and price ratio PF/PC will have to fall.

5. Now A wants to buy 1 unit of food while B still wants to sell 2 units of food. So there is again excess supply of food, which again means that PF/PC will have to fall.

6.

Brian's Y 6 6 Sarah's X 4

O

2

IB

B

Pareto Superior Set 2 Brian's X

2

O

S

initial allocation

4 IS 6

4 Sarah's Y

7. Efficiency in production requires that the MRTS between capital and labor be the same for all goods produced. An MRTS of 4 in food production means that if we reduce capital by 1 unit in food production, we need add only 1/4 unit of labor to maintain the original level of output. An MRTS of 2 in clothing production means that if we take 1/4 unit of labor from food production, we need add only 1/2 unit of capital to restore the original level of clothing output. Transferring 1/4 unit of labor from clothing to food production thus leaves 1/2 unit 119 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

of extra capital free to distribute between the two processes, which will give us a higher level of output of both goods than we had to start with.

8. Efficiency in product mix requires that the MRT equal the MRS for each consumer. If the MRT between food and clothing is 2, we can reduce clothing output by 1 unit and obtain an additional 2 units of food. But consumers require only 1.5 units of food to compensate them for losing 1 unit of clothing. So everyone can be made better off if we produce less clothing and more food.

9, 10, and 11.

Optimal production bundle with trade

Food 25 20

Opportunity set with international trade

15 10 5

Original optimal bundle (production & consumption)

Optimal consumption bundle with trade

Original PP curve

0 5

10

15

20

25

30

60 Clothing

12. See the graphs here and on the following page.

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Opportunity set withinternational trade

Chun and Friday are both best employed producing food: Chun's 5 units can be sold for 20 units of clothing and Friday‘s 20 units can be sold for 80 units of clothing.

13. If the competitive firms form an effective cartel, they will be able to charge the monopoly price. And since marginal cost and elasticity of demand are the same as in the monopoly industry, the cartel price will be the same as the monopoly price, which means that the equilibrium MRS will be 1. The equilibrium MRT will also be 1 because the marginal costs are the same in the two industries. So the cartel proposal will indeed result in an efficient product mix. We already know that there is efficiency in production and consumption, even in the presence of monopoly. So the resultant allocation will be Pareto optimal.

14. The capital allocated to clothing and food must add to the total capital endowment KC + KF = K (height of box is 100). Similarly, the labor allocated to cloth and food should add to the total labor endowment LC + LF = L (width of box is 200). The isoquants for food production are L-shaped, with the bend at KF = LF. The contract curve is the line segment AB in the diagram. The contract curve has a slope of positive one: every unit of labor allocated to food production requires a unit of capital be allocated as well and thus when a unit of labor is freed from food production for clothing production, a unit of capital is freed as well.

Labor in Food 100 Capital in Clothing 50

Capital in Food

B 0 50

100 Labor in Clothing

150

200

15. Let yF denote the output of food; thus yF units of both capital and labor will be needed to produce food. The corresponding capital allocation to clothing production will be KC = 100 – 121 © 2021 by McGraw-Hill. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

yF, while the labor constraint implies labor allocation to clothing production LC = 200 – yF. The output of clothing will then be the sum of the capital and labor allocated to clothing production, divided by 2 yC = (KC + LC)/2 = (100 – yF + 200 – yF)/2 = 150 – yF. The production possibilities frontier is a straight line with slope negative one, so the opportunity cost of food in terms of clothing is one.

This graph is for problems 16-15 and 16-16 Clothing 200

150

0

150

200

Food

16. The new capital allocation to clothing production is K'C = 200 – yF. The output of clothing is then yC = (K'C + LC)/2 = (200 – yF + 200 – yF)/2 = 200 – yF. The production possibilities frontier is still a straight line, but it has shifted out in a parallel fashion. The greater capital endowment expanded production possibilities for both goods.

Chapter 18 Government Answers to Review Questions 1. The vertical axis expresses the amount that each individual is willing to pay for each unit of the public good. Given nondiminishability, the more people there are, the greater the total willingness to pay since the sum of the individual values of each person is the total social value.

2. With jointly produced private goods, if one produces one item, one must also produce the other. With public goods, if one consumer is provided with the good, the other must be provided with the good also since public goods are the ultimate joint product.

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3. In a society with unequal incomes, an equal tax levied on every citizen will generally result in under-provision of public goods. To the extent that willingness to pay for public goods increases with income, high-income citizens therefore have selfish reasons to support a progressive tax structure. The progressive tax, by this argument, enables the rich to pay for the public goods that everyone needs but that only the rich can afford.

4. With a public good the cost of providing the good to another individual is zero; with increasing returns to scale, the cost falls as production increases. There are advantages to having many consumers of the good—but this means less flexibility in terms of meeting each individual‘s needs.

5. If three groups (A,B, and C) vote for three policies (X,Y, and Z), where policy rankings are transitive, no group is a majority, and each policy is ranked first, second, and third by one of the groups, then whatever policy is adopted will be inferior to some other policy.

6. Groups lobbying for monopoly power distort market efficiency. Domestic producers lobbying for tariffs and quotas prevent gains from trade.

7. A negative income tax requires a break-even level considerably below the average income level if there is to be an effective work incentive.

Answers to Chapter 18 Problems 1. a. The optimal quantity of the public good is 6, the quantity for which the aggregate willingness-to-pay curve intersects the marginal cost curve. Total willingness to pay is (27), which is the area under the aggregate w.t.p. curve up to Q = 6. This exceeds the public good's total cost of 19, which is 10 plus the area under the marginal cost curve up to Q = 6.

$ 6

aggregate w.t.p. curve MC B‘s w.t.p. curve

4 3 2

A‘s w.t.p. curve

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0

3

5

6

12 Quantity

b. The most A is willing to pay for the public good is the area under his w.t.p. curve up to Q = 6, which is 9. If B can be taxed no more than A is willing to pay, then 18 is the most that can be raised in taxes, and that is not enough to finance the optimal quantity of this public good.

2. By definition, the marginal cost of an additional person using a public good is zero (the nondiminishability criterion). Accordingly, there should be no charge for the use of the public good.

3. The maximum each individual is willing to pay is the area under his W.T.P. curve up to Q = 50. At Q = 50, w.t.p. = 2.5 so maximum willingness to pay for all 50 units equals 2.5(50) + ½(5-2.5)50 = 125 + 62.5 = 187.5. For all ten consumers this sums to $1,875.

This graph is for problems 18-3 and 18-4.

Willingness to pay ($100s) 50

MC 25

5 0

50 Local park land (acres)

100

4. To find the optimal size of local parks, equate the aggregate willingness to pay P = 50 – 1/2 Q and the marginal cost MC = 1/2Q to find Q = 50 acres.

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5. This practice might be interpreted as an attempt to exploit the silver-lining effect.

6. To achieve added respect in the community, donors like their gifts to generate name recognition. Having a building (or better, a school) named after the donor regularly remind the community of the donor's generosity. Donating money for maintenance (like bringing the elevator up to code) does not carry such value.

7. False. Although national issues may be more important, the odds of casting the decisive vote in a presidential election are essentially nil. The probability of being decisive in a small village election, by contrast, is significantly greater than zero, and so a purely self-interested voter has stronger reasons to vote at the local level. Probability of decisiveness and the consequences of the election must both be considered in the final decision however. If an incidental local vote was compared with a national vote of huge consequence, the answer could be different.

8. False. Even in close presidential elections, the odds of casting the decisive vote are negligible. It is no more rational to vote in a close election than in a landslide.

9. To see Kai elected, sophomores should first pit Cressida against Destiny, which will result in a win for Cressida. In the subsequent pairing of Cressida against Kai, Kai will win by 40 to 20. Seniors should pair Kai and Destiny in the preliminary round. Destiny wins and then loses to Cressida.

10. a.

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b. They would have to work more than 20 hours/day before Shen ends up with more aftertax income.

11. Social contagion refers to the tendency for people to mimic the behavior of others who are either nearby or whom they have been exposed to. It suggests that behaviors are catchy. Whether you smoke very largely depends on whether your parents or friends smoke.

This is an example of negative social contagion. Propose some behaviors that might cause positive social contagion—actions that might do more good than their direct economic impact because they may inspire others to do the same.

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