Assignment: Microeconomic Theory

This assignment covers welfare analysis, monopoly, monopsony, and price discrimination. Please answer the questions below, which are related to Chapters 9 through 11 of P&R. Beyond reviewing the material from class, the problem sets are intended to develop the ability to apply the concepts from class to new situations. You are encouraged to collaborate with others, to research sources outside of class, and to ask questions during office hours. However, you must write up your responses individually.

You should explain all of your answers in detail. Your score will depend on both the correctness of your solutions and the completeness of your explanations. Please write the question number next to your answer for each question. Your answers to the assignment are due in class on Thursday, December 1. Late assignments may be penalized.

1. Consider a competitive market with supply given by Q_S = P and demand given by Q_D = 10 - P .

(a) Suppose that there is a sales tax of 50% on buyers. That is, buyers must pay the government 50% of the price received by sellers for each unit bought. What is the equilibrium quantity and price received by sellers?

(b) What is the consumer surplus, producer surplus, tax revenue, and deadweight loss of taxation in part (a)?

(c) Suppose that there is an excise tax of $4.00 on sellers. That is, sellers must pay the government $4.00 for each unit sold. What is the equilibrium quantity and price incurred by buyers?

(d) What is the consumer surplus, producer surplus, tax revenue, and deadweight loss of taxation in part (c)?

2. Consider a monopolist with a demand curve given by Q = 12 - 2P and a total cost given by TC = Q².

(a) What is the price and quantity chosen under monopoly?
(b) What would be the price and quantity under competition?
(c) What is the deadweight loss of monopoly?
(d) What would be the quantities produced and demanded if the government imposed a price ceiling at P = 4?

3. Consider a monopolist with the production function F (L) = √L. Assume that the price of L is fixed at one. Let Q = 12 - P be the demand for the output of the monopolist.

(a) What is the total cost of production as a function of quantity Q?
(b) What is the price level selected by the monopolist?
(c) What is the efficient level of output?
(d) If the government provided the monopolist with a subsidy of S = 4 for each unit sold, what quantity of output would the monopolist produce?

4. Consider a monopsonist in the labor market. Let the labor supply be given by L = 4w, where L is the employment level, and w is the wage rate. Suppose that the monopsonist has the production function F (L) = √L. The monopsonist can sell its output at a price of one.

(a) What is the marginal value and marginal expenditure of the monopsonist as a function of the employment level?
(b) What is the wage rate and employment level under monopsony?
(c) What is the deadweight loss of monopsony?
(d) What minimum wage rate would result in an efficient employment level?

5. Suppose that a monopolist faces two markets A and B. The demand in market A is given by Q_A = max(0, 10 - 2P_A). The demand in market B is given by Q_B = max(0, 20 - P_B). The total cost for the monopolist is given by TC = 10 + 4(Q_A + Q_B).

(a) Suppose that the monopolist must charge the same price to consumers in the two markets. What price will the monopolist choose?
(b) What is the consumer surplus and total profits in part (a)?
(c) Suppose that the monopolist can charge a di↵erent price in each of the two markets. What price will the monopolist choose for each market?
(d) What is the consumer surplus and total profits in part (c)?

6. Consider a monopolist with two possible plants 1 and 2 and two possible markets A and B. The total cost of producing output Q₁ in plant 1 is TC₁(Q₁) = Q₂. The total cost of producing output Q₂ in plant 2 is TC₂(Q₂) = Q₂. The demand function for market A is Q_A = 2 - P_A. The demand function for market B is Q_B = 4 - P_B. Assume that the monopolist can charge di↵erent prices in markets A and B.

(a) Suppose that the monopolist can use only plant 1 and can sell only to market A. What is the quantity of output sold in market A?
(b) Suppose that the monopolist can use only plant 1 but can sell to both markets A and B. What is the quantity of output sold in market A?
(c) Suppose that the monopolist can use both plants 1 and 2. How much does it cost the monopolist to produce a total quantity of Q?
(d) Suppose that the monopolist can use both plants 1 and 2 and can sell to both markets A and B. What is the quantity of output sold in market A?

7. This question is for fun. Economics seeks to develop formal models in order to make predictions about a broad range of real world situations. Write down a model to predict what questions will appear on the final exam for this class. What are the explanatory variables in your model? What are the assumptions behind your model? Derive the predictions of your model.