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Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

Chapter 1 Analyzing Economic Problems Solutions to Review Questions 1.

What is the difference between microeconomics and macroeconomics?

Microeconomics studies the economic behavior of individual economic decision makers, such as a consumer, a worker, a firm, or a manager. Macroeconomics studies how an entire national economy performs, examining such topics as the aggregate levels of income and employment, the levels of interest rates and prices, the rate of inflation, and the nature of business cycles. 2.

Why is economics often described as the science of constrained choice?

While our wants for goods and services are unlimited, the resources necessary to produce those goods and services, such as labor, managerial talent, capital, and raw materials, are “scarce” because their supply is limited. This scarcity implies that we are constrained in the choices we can make about which goods and services to produce. Thus, economics is often described as the science of constrained choice. 3. How does the tool of constrained optimization help decision makers make choices? What roles do the objective function and constraints play in a model of constrained optimization? Constrained optimization allows the decision maker to select the best (optimal) alternative while accounting for any possible limitations or restrictions on the choices. The objective function represents the relationship to be maximized or minimized. For example, a firm’s profit might be the objective function and all choices will be evaluated in the profit function to determine which yields the highest profit. The constraints place limitations on the choice the decision maker can select and defines the set of alternatives from which the best will be chosen. 4. Suppose the market for wheat is competitive, with an upward-sloping supply curve, a downward-sloping demand curve, and an equilibrium price of $4.00 per bushel. Why would a higher price (e.g., $5.00 per bushel) not be an equilibrium price? Why would a lower price (e.g., $2.50 per bushel) not be an equilibrium price? If the price in the market was above the equilibrium price, consumers would be willing to purchase fewer units than suppliers would be willing to sell, creating an excess supply. As suppliers realize they are not selling the units they have made available, sellers will bid down the price to entice more consumers to purchase their goods or services. By definition, equilibrium is a state that will remain unchanged as long as exogenous factors remain unchanged. Since in this case suppliers will lower their price, this high price cannot be an equilibrium.

Chapter 1-1

Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

When the price is below the equilibrium price, consumers will demand more units than suppliers have made available. This excess demand will entice consumers to bid up the prices to purchase the limited units available. Since the price will change, it cannot be an equilibrium. 5. What is the difference between an exogenous variable and an endogenous variable in an economic model? Would it ever be useful to construct a model that contained only exogenous variables (and no endogenous variables)? Exogenous variables are taken as given in an economic model, i.e., they are determined by some process outside the model, while endogenous variables are determined within the economic model being studied. An economic model that contained no endogenous variables would not be very interesting. With no endogenous variables, nothing would be determined by the model so it would not serve much purpose. 6. Why do economists do comparative statics analysis? What role do endogenous variables and exogenous variables play in comparative statics analysis? Comparative statics analyses are performed to determine how the levels of endogenous variables change as some exogenous variable is changed. This type of analysis is very important since in the real world the exogenous variables, such as weather, policy tools, etc. are always changing and it is useful to know how changes in these variables affect the levels of other, endogenous, variables. An example of comparative statics analysis would be asking the question: If extraordinarily low rainfall (an exogenous variable) causes a 30 percent reduction in corn supply, by how much will the market price for corn (an endogenous variable) increase? 7. What is the difference between positive and normative analysis? Which of the following questions would entail positive analysis, and which normative analysis? a) What effect will Internet auction companies have on the profits of local automobile dealerships? b) Should the government impose special taxes on sales of merchandise made over the Internet? Positive analysis attempts to explain how an economic system works or to predict how it will change over time by asking explanatory or predictive questions. Normative analysis focuses on what should be done by asking prescriptive questions. a)

Because this question asks whether dealership profits will go up or down (and by how much) – but refrains from inquiring as to whether this would be a good thing – it is an example of positive analysis. On the other hand, this question asks whether it is desirable to impose taxes on Internet sales, so it is normative analysis. Notably, this question does not ask what the effect of such taxes would be.

Chapter 1-2

Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

Solutions to Problems 1.1 Discuss the following statement: “Since supply and demand curves are always shifting, markets never actually reach an equilibrium. Therefore, the concept of equilibrium is useless.” While the claim that markets never reach an equilibrium is probably debatable, even if markets do not ever reach equilibrium, the concept is still of central importance. The concept of equilibrium is important because it provides a simple way to predict how market prices and quantities will change as exogenous variables change. Thus, while we may never reach a particular equilibrium price, say because a supply or demand schedule shifts as the market moves toward equilibrium, we can predict with relative ease, for example, whether prices will be rising or falling when exogenous market factors change as we move toward equilibrium. As exogenous variables continue to change, we can continue to predict the direction of change for the endogenous variables, and this is not “useless.” 1.2 In an article entitled, “Corn Prices Surge on Export Demand, Crop Data,” the Wall Street Journal identified several exogenous shocks that pushed U.S. corn prices sharply higher. (See the article by Aaron Lucchetti, August 22, 1997, p. C17. on national income.) Suppose the U.S. market for corn is competitive, with an upward-sloping supply curve and a downward-sloping demand curve. For each of the following scenarios, illustrate graphically how the exogenous event described will contribute to a higher price of corn in the U.S. market. a) The U.S. Department of Agriculture announces that exports of corn to Taiwan and Japan were “surprisingly bullish,” around 30 percent higher than had been expected. b) Some analysts project that the size of the U.S. corn crop will hit a six-year low because of dry weather. c) The strengthening of El Niño, the meteorological trend that brings warmer weather to the western coast of South America, reduces corn production outside the United States, thereby increasing foreign countries’ dependence on the U.S. corn crop.

Chapter 1-3

Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

a) Surprisingly high export sales mean that the demand for corn was higher than expected, at D2 rather than D1.

b) Dry weather would reduce the supply of corn, to S2 rather than S1.

c) Assuming the U.S. does not import corn, reduced production outside the U.S. would not impact U.S. corn market supply. El Nino would, however, cause demand for U.S. corn to shift out, the figure being the same as in part (a) above.

Chapter 1-4

Besanko & Braeutigam – Microeconomics, 6th edition

2.3. 4P.

Solutions Manual

The demand and supply curves for coffee are given by Qd = 600 − 2P and Qs = 300 +

a) Plot the supply and demand curves on a graph and show where the equilibrium occurs. b) Using algebra, determine the market equilibrium price and quantity of coffee. a) P 300 S 50

D 300

500

600

600 − 2 P = 300 + 4 P

300 = 6 P 50 = P

Plugging P = 50 back into either the supply or demand equation yields Q=500. 2.4. Suppose that demand for bagels in the local store is given by equation Qd = 300 100P. In this equation, P denotes the price of one bagel in dollars. a) Fill in the following table:

b) At what price is demand inelastic? c) At what price is demand elastic? d) At what price is demand inelastic? e) At what price is demand elastic? P 0.10 0.45 0.50 0.55 2.50 d Q 290 255 250 245 50 εQ,P –0.035 –0.176 –0.2 –0.225 –5 We can find elasticities of demand using the following formula Copyright © 2020 John Wiley & Sons, Inc.

Chapter 2 - 8

Besanko & Braeutigam – Microeconomics, 6th edition

 Q,P =

Solutions Manual

Q d P P P = −100  = . d P Q 300 − 100  P P − 3

This demand curve is linear. The inverse demand function is P = 3 – 1/100 Qd P $3

300 Q d

Observe that for price $1.50 the elasticity of demand is equal to 1.5  Q ,P = = −1 . 1.5 − 3 For all prices below $1.50, the demand is inelastic, while for all prices above $1.50, the demand is elastic. 2.5. The demand curve for ice cream in a small town has been stable for the past few years. In most months, when the equilibrium price is $3 per serving for the most popular ice cream, customers buy 300 servings per month. For one month the price of materials used to make ice cream increased, shifting the supply curve to the left. The equilibrium price in that month increased to $4, and customers bought only 200 portions in the month. With these data draw a graph of a linear demand curve for ice cream in the town. Find price elasticity of demand for prices equal to $3 and $4. At what price would the demand be unitary elastic? Using the data from the problem we can graph the demand curve. The slope of the demand curve is equal to P / Q = −1/100

So the equation of the demand curve is P = A – 0.01Q. We can find the vertical intercept A substituting P = 3 and Q = 300. 3 = A – 0.01(300), so A = 6. The vertical intercept (choke price) is P = $6. The equation of the demand curve is then P = 6 – 0.01Q.

Chapter 2 - 9

Besanko & Braeutigam – Microeconomics, 6th edition

P $6

 = −2

Solutions Manual

 = −1

$4 $3

200

300

600

Elasticity of demand can be computed using formula EQ,P =

Q P P Q

= −100

P Q

= −100

6 − 0.01Q Q

When the elasticity is -1, Q = 300 and P = $3. Thus demand is unitary elastic at a price P = $3. Based on the data from the problem the graph of the demand curve is

P 3− 4 1 = =− = −0.01 Q 300 − 200 100 Find the vertical intercept in the graph or by substituting into P (Q ) = m − 0.01Q one of the two points. The inverse demand function is P(Q) = 6 − 0.01Q . 1 P 1 6 − 0.01Q 600 − Q  =  = The elasticity is  i = . P Q Q −0.01 Q −Q 600 − Q = −1  600 − Q = Q  Q = 300, P = 3 . The function is unit-elastic at −Q 600 − Q 600 − 200 = = −2 At P = 4 and Q = 200 , the elasticity is  i = −Q −200

The slope of the demand curve is equal to

Chapter 2 - 10

Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

2.6. Granny’s Restaurant sells apple pies. Granny knows that the demand curve for her pies does not shift over time, but she wants to learn more about that demand. She has tested the market for her pies by charging different prices. When she charges $4 per pie, she sells 30 pies per week. When she charges $5, she sells 24 pies per week. If she charges $4.50, she sells 27 apple pies per week. a) With this data draw a graph of the linear demand curve for Granny’s apple pies. b) Find the price elasticity of demand at each of the three prices. The demand for apple pies is Qd = 54 – 6P. P

 = −1.25

 = −1

$5 $4.50

 = −0.8

24 27 30

To find the equation of the demand curve, observe that when she drops the price by $0.50, she sells 3 more pies. So, movement along the demand occurs so that Q / P = −3 / 0.5 = −6

The demand curve then has the form Qd = A – 6P, where A is a constant. We can determine the value of A using any one of the three data points on the demand curve. For example, if we use the point P = 5 and Q = 24, we see that 24 = A – 6(5), so that A = 54. So the demand curve can be described by the equation Qd = 54 – 6P. To find elasticity of demand at any point on the demand curve, we use formula EQ,P =

Q P P Q

= −6

P Q

Chapter 2 - 11

Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

2.7. Every year there is a shortage of Super Bowl tickets at the official prices P0. Generally, a black market (known as scalping) develops in which tickets are sold for much more than the official price. Use supply and demand analysis to answer these questions: a) What does the existence of scalping imply about the relationship between the official price P0 and the equilibrium price? b) If stiff penalties were imposed for scalping, how would the average black market price be affected? a) Since the price is being bid up above the official price, quantity demanded must exceed quantity supplied at the official price. This is a situation of excess demand and the official price must be below the equilibrium price. b) Most likely there were be fewer tickets offered for sale in the black market. The effect on the market price of scalped tickets depends on who is at risk of paying the penalty. If sellers are at risk, the price would most likely go up because the supply curve of scalped tickets would shift to the left. If buyers are at risk, the demand for scalped tickets would fall, shifting the demand curve to the left, leading to a lower equilibrium price for scalped tickets. 2.8 You have decided to study the market for fresh picked cherries. You learn that over the last 10 years, cherry prices have risen, while the quantity of cherries purchased has also risen. This seems puzzling because you learned in microeconomics that an increase in price usually decreases the quantity demanded. What might explain this seemingly strange pattern of prices and consumption levels? This could occur as a result of the demand curve shifting to the right, increasing both equilibrium price and quantity. This would not contradict what was learned regarding downward sloping demand curves. 2.9 Suppose that, over a period of six months, the price of corn increased. Yet, the quantity of corn sold by producers decreased. Does this contradict the law of supply? If not, why not? This does not contradict the law of supply. For example, farmers may have experienced something that shifted the supply curve for corn leftward (such as a flooding or a drought). This would have the effect of increasing the equilibrium price of corn, while decreasing the quantity of corn sold by producers. This is shown in the figure below. Another possibility is that, alternatively, the supply curve for corn could have shifted leftward, and the demand curves for could have also shifted, but in such a way that the overall effect is to increase the equilibrium price and decrease the equilibrium quantity. These cases are also shown in the figure below.

Chapter 2 - 12

Besanko & Braeutigam – Microeconomics, 6th edition

Price (dollars per bushel)

Solutions Manual

S2 S1

D1 Quantity (bushels per year) Supply curve shifts leftward, demand curve remains stationary

Price (dollars per bushel)

S2 S1

D1 Quantity (bushels per year)

Supply curve shifts leftward, demand curve also shifts leftward

Chapter 2 - 13

Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

Assume Joe is initially at an interior optimum, point A, and that the price of other goods is $1. Let Joe’s income be M. Point A then consists of GA = 1000 units of gasoline and YA = M – 2000 units of other goods. The effect of the proposal is to rotate the budget line inward (the price change) and then shift it outward (the cash transfer), for a total movement from BL1 to BL2. Notice that BL2 intersects BL1 exactly at point A: after the price increase, (GA, YA) costs Joe 1000*2.50 + M – 2000 = M + 500, which is equal to his income after the cash transfer. Because A was initially optimal, MRSG,Y = 2 at point A. Yet the price ratio along BL2 is 2.5. Hence MRSG,Y < PG / PY, so Joe can increase his utility by purchasing less gas and more of the composite good, at a point such as B depicted in the graph above. Thus, the proposal will make Joe better off. 4.18 Paul consumes only two goods, pizza (P) and hamburgers (H) and considers them to be perfect substitutes, as shown by his utility function: U(P, H) = P + 4H. The price of pizza is $3 and the price of hamburgers is $6, and Paul’s monthly income is $300. Knowing that he likes pizza, Paul’s grandmother gives him a birthday gift certificate of $60 redeemable only at Pizza Hut. Though Paul is happy to get this gift, his grandmother did not realize that she could have made him exactly as happy by spending far less than she did. How much would she have needed to give him in cash to make him just as well off as with the gift certificate? Paul’s initial budget constraint is the line AC, allowing him to purchase at most 50 hamburgers or at most 100 pizzas. The $60 cash certificate shifts out his budget constraint without changing the maximum number of hamburgers that he can buy. The new budget constraint is ABD and he can now buy a maximum of 120 pizzas. Hamburgers

60 55 50

B A

C 100

D 120

Pizza

Initially, Paul’s optimal basket contains all hamburgers and no pizza, at point A where (P, H) = (0, 50), because MUH /PH = 4/6 > MUP / PP = 1/3. His utility level at point A is U(0, 50) = 200. When he gets the gift certificate, Paul’s optimal basket is at point B, spending all of his regular income on hamburgers and the $60 gift certificate on pizza. So point B is where (P, H) = (20, 50) with a utility of U(20, 50) = 220.

Chapter 4-22

Besanko & Braeutigam – Microeconomics, 6th edition

Solutions Manual

However, Paul could also achieve a utility of 220 by consuming 220/4 = 55 hamburgers. To buy the extra 5 hamburgers he would require 5*6 = $30. So, if he had received a cash gift of $30 it would have made Paul exactly as well off as the $60 gift certificate for pizzas. 4.19 Jack makes his consumption and saving decisions two months at a time. His income this month is $1,000, and he knows that he will get a raise next month making his income $1,050. The current interest rate (at which he is free to borrow or lend) is 5 percent. Denoting this month’s consumption by x and next month’s by y, for each of the following utility functions state whether Jack would choose to borrow, lend, or do neither in the first month. (Hint: In each case, start by assuming that Jack would simply spend his income in each month without borrowing or lending money. Would doing so be optimal?) a) U(x, y) = xy2, MUx = y2, MUy = 2xy b) U(x, y) = x2 y, MUx = 2xy, MUy = x2 c) U(x, y) = xy, MUx = y, MUy = x a)

𝑀𝑈

𝑦

In this case, 𝑀𝑅𝑆𝑥,𝑦 = 𝑀𝑈𝑥 = 2𝑥. If Jack neither borrows nor lends, then 𝑦

MRSx,y = 1050/(2*1000) = 0.525. Recall that if the interest rate is r, the slope of the budget line is –(1+r) = –1.05. Thus, if he neither borrows nor lends it will be the case that MRSx,y < 1 + r. That is, the “bang for the buck” for spending this month (good x) is less than that for spending next month (good y). Thus, Jack should lend some of his income this month (so x < 1000) in order to earn interest and have higher spending next month (y > 1050). b) Now MRSx,y = 2y/x. If Jack neither borrows nor lends, MRSx,y = 2.1 > (1 + r). Thus, Jack could increase his utility by borrowing in the first month (so that x > 1000 and y < 1050). c) Now MRSx,y = y/x. If Jack neither borrows nor lends, MRSx,y = 1.05 = (1 + r). Thus, Jack’s utility is maximized when he neither borrows nor lends, simply spending all of his income in each month: (x, y) = (1000, 1050).

Chapter 4-23

Microeconomics , 6th Edition Besanko solution manuals