Spring 1994

14.01 Midterm Exam #2

Professor Jeffrey Harris

Instructions

1. This is a closed book exam. In addition, no calculators are to be used. On the cover of each exam booklet, please write: (1) The number of the question you are answering, (2) your name, (3) the time your class meets and (4) the name of your TA. (Those of you who take lecture with Prof. Harris, please write the name of your Friday recitation instructor instead.)

2. Place each question in a separate booklet.

3. In case you have forgotten your TA’s name or the correct spelling of his or her name, here is a list of TA’s followed their class times:

Amy Ando (MWF 9:00 am) Paul Schulstad (MWF 9:00 am) Darren Timothy (MWF 11:00 am, 12:00 noon) Stefanie Schmidt (MWF 12:00 noon) Aaron Yelowitz (MWF 11:00 am, 1:00 pm) Guillermo Llorente-Alvarez (F 10:00 am) Alia Karaouni (F 10:00 am) Xiaoming Zhang (F 11:00 am, 12:00 noon)

4. There are 3 questions on the exam. Answer all questions. You have 2 hours to complete the exam. Read all questions carefully. Make sure to show your work; otherwise, it is difficult to award partial credit.

5. The exam will be graded out of a total of 90 points. The point value of each question is recorded on the exam.

6. Please do not start working on the exam until the proctors announce you may begin. Please hand in your exams promptly when the proctors announce you must cease work.

Place your answer to this question in booklet #1

Question #1 (20 points)

True/False/Uncertain

Please evaluate \underline{each} of the 4 statements as either true, false or uncertain. Each statement is worth five points. Credit is determined by the quality of your explanation. \underline{No} credit will be given for answers lacking an adequate explanation.

(a) (5 points) If a firm has market power in the output market, it will be able to price discriminate.

(b) (5 points) Suppose the government places a price ceiling P̄ on the price of some good X. (Assume that the price ceiling is less than the equilibrium price without the price ceiling.) This action will always increase deadweight loss in the market for that good.

(c) (5 points) A monopsonist faces the following supply curve for materials, which are used in her production process: P_{M} = 5 + M, where P_{M} is the price of materials and M is the quantity of materials supplied. The marginal revenue product of materials is: MRP_{M} = 10 − M. In this case, a profit maximizing monopsonist will purchase 1 unit of material at a price of 9.

(d) (5 points) Suppose we are in an economy with only two goods: food and leisure. For an individual worker for whom leisure is a normal good, an increase in the wage will result in an increase in labor supplied if the substitution effect between food and leisure due to the change in wage is larger than the income effect.

Question #2 (35 points)

The mineral Kryptonite is found in only two countries. Country 1 can produce it with costs C_{1}(Q_{1}) = 10Q_{1}. Country 2 can produce it with costs C_{2}(Q_{2}) = 5Q_{2} + \frac{1}{2}Q_{2}^{2}. The market demand curve for Kryptonite is P = 40 − (Q_{1} + Q_{2}).

1) Assume that the two countries do not attempt to collude, and that they deliver their chosen outputs on the market simultaneously.

a) (3 points) Write down a separate expression for the profit made by each country as a function of its own output and the output of the other country.

b) (3 points) Find the Cournot equilibrium values for Q_{1} and Q_{2}. What are total output and the corresponding market price?

c) (4 points) How much profit does each country make in equilibrium? Are those profits equal to each other? Explain.

2) Now suppose the countries are thinking about forming a cartel in order to increase their combined profits.

a) (7 points) Find the joint-profit-maximizing levels of Q_{1} and Q_{2}. Give MC_{1} and MC_{2} evaluated at those quantities, and explain why the results make sense. What are total output and the corresponding market price?

b) (3 points) If each country pays the cost of its own production and gets the revenue only from what it produces, how much profit does each firm get?

3) Now compare your answers in parts 1) and 2) as follows:

a) (5 points) How does total output change by moving from the Cournot equilibrium to the collusive regime? Is the change in total output divided equally between the two countries? Explain why the result you get makes sense.

b) (5 points) Compare the countries’ profits under joint-profit maximization to their profits under the Cournot regime. What happens to total profit? Is each country made better off by forming the cartel? Why or why not?

c) (5 points) Suppose both countries can agree for one to pay the other a fixed fee as part of the cartel agreement. Will that make it easier for the countries to achieve the collusive outcome? What is the minimum AND maximum fee that will be paid, and to whom?

Question #3 (35 points)

Conan has the following utility function:

U(X, L) = min(X, L)

where X is his consumption of compact disks (CD’s) and L is the amount of Conan’s leisure time.

Conan has 25 hours in the day. His time is allocated between three potential activities. He can divide his hours between work (H), leisure (L), and travelling to discount stores that sell CD’s at low prices. Conan earns w dollars per hour worked. He can choose to buy his CD’s at one of two places. If he buys at a local store, he spends no time travelling, but the CD’s sell for $2 per unit. If instead he goes to a discount store located in another state, he spends 5 hours traveling, but the price of CD’s at this store is $1 per unit. (For parts (a) and (b) below, w is left free to be any number; later it will take on specific values. In addition, assume that CD’s are divisible goods, i.e. that they can be consumed in non-integer quantities.)

(a) (6 points) Suppose Conan does \underline{not} travel to the outlet store. What are Conan’s time and income constraints? What is his opportunity cost of consuming an hour of leisure? Calculate Conan’s utility maximizing amount of time spent consuming leisure. How many CD’s does he buy? What is Conan’s maximum level of utility? (Your answers should be a function of w.)

(b) (6 points) Suppose now instead that Conan does travel to the discount store to purchase his CD’s. What are Conan’s new time and income constraints? What is his new opportunity cost of consuming an hour of leisure? Calculate Conan’s utility maximizing amount of time spent consuming leisure. How many CD’s does he buy? What is Conan’s maximum level of utility? (Your answers should again be a function of w.)

(c) (2 points) If Conan’s wage was $1 per hour would Conan choose to travel to the discount store? Why or why not?

(d) (2 points) If Conan’s wage was $4 per hour would Conan choose to travel to the discount store? Why or why not?

(e) (3 points) Does Conan’s decision change between parts (c) and (d)? Give intuition for your answer.

(f) (3 points) Calculate the wage at which Conan would be indifferent between shopping at the discount store and shopping at the store nearby.

(g) (4 points) Does Conan’s labor supply function slope upward or downward? What property of the utility function is responsible for your answer?

(h) (3 points) Does this model explain who in reality tends to shop at discount stores?

(i) (6 points) Now suppose that you are the retailer of the consumption good. You have two choices: (1) Build one store where the majority of the customers live or (2) build two stores with the second store located far away from the majority of the customers and where customers can get great deals relative to the other store. Discuss whether the second option can potentially yield higher profits than the first, despite the cost of building an additional store.