# Sample Short Answer/Problem Questions Question 1: Price Discrimination

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Question 1: Price Discrimination
Part A: The local zoo has hired you to assist them in setting admission prices. The zoo’s managers recognize that there are two distinct demand curves for zoo admission. One demand curve applies to those ages 12 to 64, while the other is for children and senior citizens. The two demand and marginal revenue curves are:
PA = 9.6 – 0.08QA

MRA = 9.6 – 0.16QA

PCS = 4 – 0.05QCS

MRCS = 4 – 0.10QCS

where PA = adult price, PCS = children’s/senior citizen’s price, QA = daily quantity of adults, and QCS = daily quantity of children and senior citizens. Crowding is not a problem at the zoo, so that the managers consider marginal cost to be zero. If the zoo decides to price discriminate, what should the price and quantity be in each market? Calculate the firm’s total revenue in each sub-market.
Optimal price discrimination requires the zoo to set MRA = MRCS = MC.
Thus, MRA = 9.6 – 0.16QA = 0; 9.6 = 0.16QA; QA = 60. PA = 9.6 – 0.08(60) = \$4.80
MRCS = 4 – 0.10QCS = 0; QCS = 40; PCS = 4 – 0.05(40) = \$2
TRA = PA * QA = 4.80 * 60 = \$288

TRCS = PCS * QCS = 2 * 40 = \$80

Part B: Suppose consumers are identical. Will an optimal two-part tariff be less efficient (create more deadweight loss) than perfect competition. Illustrate your answer.
An optimal two-part tariff with only one consumer type consists of P* = MC, and an entry fee, T, equal to all consumer surplus at that price. There is no DWL because Q* is the same as it would be under perfect competition. See Figure 11.9, page 386.

Part C: Numerous restaurants offer discounts to customers who ear dinner between 4 – 6 p.m. (often called “early bird” specials). Can you explain why this is a form of third-degree price discrimination and how the market is being segmented?

The restaurants are choosing their pricing strategy to segment the market primarily on working versus non-working individuals. Although students and children and those who work in the home could take advantage of these “earl birds”, the primary market segment is retired people. They have the flexibility to eat earlier or later, which makes their demand more elastic.

Question 2: Monopolistic Competition/Oligopoly
Part A: Suppose that the market demand for mountain spring water is given as P = 1200 – Q, where MR = 1200 – 2Q. Mountain spring water can be produced at no cost.
a. What is the profit maximizing level of output and price of a monopolist?
The monopoly level of output is found where MR = MC. Thus, MR = 1,200 - 2Q = 0. This gives Q = 600. P = 1,200 - 600 = \$600
b. What level of output would be produced by each firm in a Cournot duopoly in the long run if the firms are identical (symmetric)? What will the price be? Note MR1 = 1200 – 2Q1 – Q2; MR2 = 1200 – 2Q2 – Q1.
The Cournot equilibrium is found by using the reaction curves of the two firms to solve for the equilibrium levels of output. The reaction curve for firm 1 is found by setting MR1 = MC, and similarly for Firm 2. Thus, Firm 1's Reaction Curve: MR1 = 1200 – 2Q1 – Q2. Thus, Q1 = 600 - (1/2)Q2. And Firm 2's Reaction Curve: Q2 = 600 - (1/2)Q1. Solving the reaction curves simultaneously for Q1 and Q2 yields: Q1 = Q2 = 400. Thus the total output is 800 and the price will be \$400.
c. What will be the level of output and price in the long run if this industry were perfectly competitive?
If the industry were perfectly competitive, price will be equated to marginal cost. P = 1,200 - Q = 0 or Q = 1,200 and P = 0

Part B: At its current output level of 10, a monopolistically competitive firm has MR = 4, MC = 4, AC = 6, and P = 8. Is this market in long-run equilibrium? If not, describe the adjustment process necessary to achieve long-run equilibrium?

This means that the firm is making profits of (p-ac)q = (8-6)10 = \$20. Given that economic profits are not zero, the market is not in long-run equilibrium. Given free entry and exit, we would expect new entry into the industry to bid away these excess profits. Each surviving firm would see its individual demand curve shift left so would produce less output at a lower price.
Part C: The two leading U.S. manufacturers of high performance radial tires must set their advertising strategy for the coming year. Each firm has two strategies available: maintain current advertising or increase advertising by 15%. The strategies available to the two firms, G and B, are presented in the payoff matrix below. The entries in the individual cells are profits measured in millions of dollars. Firm G's outcome is listed before the comma, Firm B's after the comma.

Which model is best suited for analyzing this decision? Why? (Remember it is illegal to collude in the United States). Carefully explain the strategy that should be used by each firm.

The prisoner's dilemma model is most appropriate for analyzing this situation because each firm must set its advertising level without knowing its rival's strategy, and we observe a dominant strategy. If the two firms could sit down and write a contract, collusion would be enforceable but of course, that is illegal in the US. Thus, increasing advertising is the dominant strategy, since each firm is better off increasing advertising regardless of its rival's action. For example, if Firm B increases, Firm G earns 27 if it increases, and 12 by not increasing. G is better off to increase. If Firm B doesn't increase, Firm G earns 45 by not increasing, 50 by increasing. Again, Firm G is better off to increase. It is obvious that no matter what B does, G is better off to increase. Firm B faces the same situation.
Question 3: General Equilibrium
Part A: Consider a potential, voluntary exchange between two people. Assume that both people have complete information about each other's preferences and that there are no transaction costs. Consumers A and B have between them 9 units of X and 15 units of Y. Initially, A has 6 of X and 10 of Y, and B has 3 of X and 5 of Y. Consumer A's marginal rate of substitution of X for Y is 2 and B's marginal rate of substitution of X for Y is 1/3. Is there room for a mutually beneficial, voluntary exchange? Draw an Edgeworth box. Determine which consumer would trade for more X and which consumer would trade for more Y. If trade takes place, can you explain the terms of trade? (the range of prices between which trade will take place)
To get one more unit of X, A is willing to give up two units of Y. To give up one unit of X, B needs to get 1/3 of a unit of Y. Thus, a mutually beneficial exchange can be made. A would trade for X and B would trade for Y, and both would be better off. The terms of trade depend upon the bargaining process but will be between 1/3 and 2. How much is traded is determined where the two MRS are made equal.
When you draw the box, put Y on the vertical axis, X on the horizontal axis. Put Consumer A at the bottom left, and Consumer B at the top right. Draw the initial allocation, and then show how they can be made better off.
Part B: What is the necessary condition for cost minimization for a firm that buys inputs in competitive factor markets? Explain why a competitive equilibrium in factor markets is an efficient allocation in the production Edgeworth box. If the amount of productive resources available for use in an economy were to increase, what would happen to the production possibilities frontier?
A cost-minimizing firm operates where MRTS = w/r. If firms take factor prices as given, then MRTS in market 1 = w/r. Also, MRTS in market 2 = w/r. Thus, MRTS1 = MRTS2 which is the condition for efficiency in the Edgeworth box. If the quantity of productive resources were to increase, the production possibilities frontier would shift to the right.

Question 4: Externalities

Part A: The market for paper in a particular region has the following supply and demand curves: QD = 160,000 - 2,000P; QS = 40,000 + 2,000P, where Q is measured in hundred-pound lots, and P is price per hundred-pound lot. There is currently no attempt to regulate the dumping of effluent into streams and rivers by the paper mills. As a result, dumping is widespread. The marginal external cost associated with the paper production is given by the expression: MEC = 0.0002Q.

1. Calculate the competitive price and output, assuming that no attempt is made to monitor or regulate the dumping of effluent.

Solve the demand and supply equations. QD = 160,000 - 2,000P = QS = 40,000 + 2,000P. Obtain the inverse demand equations: P = 80 - 0.0005QD and P = 20 + 0.0005QS. Equate demand and supply, yielding 80 - 0.0005Q = 20 + 0.0005Q. Thus, 60 = 0.001Q, so Q = 60,000. P = 20 + 0.0005(60,000) = 20 + 30 = \$50

1. Determine the socially optimal levels for price and output. If your answers in (a) and (b) are different, explain the source of the difference.

The socially optimal level of output is where demand intersects MSC. MSC = MC + MEC = (20 + 0.0005Q) + 0.0002Q = 20 + 0.0007Q. Equating demand to MSC yields 80 - 0.0005Q = 20 + 0.0007Q. Thus, 60 = 0.0012Q, so Q = 50,000. Finally, P = 20 + 0.0005(50,000) = \$55. The difference between competitive outcome and the socially optimal outcome occurs because the private market is not capturing all of the costs of production.

1. Sketch a diagram showing the costs or benefits to society of allowing the market to operate in an unregulated fashion. Part B: “There is no need for government intervention when positive externalities are present because no one is being harmed”. Discuss the validity of this statement.

When positive externalities are present, the market produces too little relative to the social optimum, and thus, there is a loss in efficiency. Since no one is harmed by consumption of the externality producing good, it may seem that there is no cause for concern. However, society’s welfare (net social benefits) could be increased by having the market produce more (via subsidies, for example). Note that unlike with negative externalities, with positive externalities, agreements might be more easily met, as everyone is better off by moving to the efficient allocation of resources.

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