Name: I pledge to obey the Duke University Honor Code during this exam. ECON201 - Final Exam - Spring 2018 Professor Chelsea Garber

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1 Professor Chelsea Garber Name: Please answer all questions in the space provided. You do NOT need to provide explanations for your answers unless the question specifically asks for an explanation. If it does, a brief explanation is all that is needed. Feel free to use the back of each sheet if you need to. There are 100 points on the exam, and you have 3 hours to complete the exam. The total number of points for each part is indicated in each question. No calculators, books, notes, or other electronic devices are permitted. Good luck! Before starting the exam, you must sign the following statement: I pledge to obey the Duke University Honor Code during this exam. Signed:

2 Problem 1-16 points Consider the intertemporal model with consumption this year and consumption next year. Suppose that you have exogenous income I this year but that you do not plan to have income next year. The current interest rate is r. For this problem you can assume that consumption this year and consumption next year are neither perfectly substitutable not perfectly complementary. (a) [1 point] In a graph with Dollars of Consumption This Year on the horizontal and Dollars of Consumption Next Year on the vertical, illustrate your initial budget constraint. Label the slope and the endowment point. (b) [1 point] Congress passes an interest rate tax, which effectively reduces the interest rate from r to (1- t)r. Draw the new budget constraint on your picture above and label the new intercept. (c) [2 points] If you have homothetic tastes, can you predict what will happen to current consumption as a result of this tax? Can you predict what will happen to future consumption? (d) [2 points] Suppose the uncompensated capital supply curve is perfectly inelastic. Does this mean tastes must be homothetic? Would this information change either of your answers from part (c)? Explain. 2

3 (e) [4 points] In a new picture with Dollars of Consumption This Year on the horizontal and Dollars of Consumption Next Year on the vertical, indicate the amount of tax revenue that the government collects from you. Then, using an appropriate indifference curve in your analysis, indicate the deadweight loss from this tax. (f) [6 points] Suppose that I=$1000 and that current consumption was initially $500. Suppose that a corrupt government official comes to you and says he could be bribed not to pass the interest rate tax. You consider the offer and decide to go through with the bribe. You find that in this scenario your current consumption is $400. In a graph with both the uncompensated and the compensated capital supply curve, shade the area that corresponds to the bribe that you paid. Use as many exact values as possible to receive full credit. 3

4 Problem 2-18 points Consider the market for gizmos. The market for gizmos is perfectly competitive and is characterized by many identical firms. Gizmos require both labor (always variable) and capital (fixed in the short run). Each firm produces gizmos with technology that exhibits initially increasing marginal product of labor until l units of labor are hired and has diminishing marginal product of labor after l units of labor are hired. There are no recurring fixed costs in the industry. (a) [1 point] Suppose the market is initially in long run equilibrium with prices p*, w*, and r*. Each gizmo firm is producing at bundle A in the picture above. What two equations must be true at bundle A? (b) [1 point] What one equation is true at bundles N, A, G, and M? (c) [2 points] Suppose the government imposes a wage tax in the gizmo labor market that increases the wage to w*+t. Assuming that firm continues to produce, what labeled production plan(s) could the firm move to in the short run? (d) [2 points] If labor and capital are relatively substitutable in the gizmo production process, what two conditions must be true in the short run? (Hint: One will be an inequality.) 4

5 (e) [2 points] In the new long run equilibrium each gizmo firm ends up producing more than it did in the initial long run equilibrium. Given this information, which labeled production plan(s) could the firm move to in the long run? (f) [2 points] Draw a two- panel graph with the industry demand and short run market supply on the left side. On the right side, illustrate the short run supply curve and the long run average cost curve for the firm in the initial long run equilibrium. Pay close attention to the description of the firm s technology. (g) [3 points] Illustrate the short run effect of this wage tax on your picture above. Indicate the effect on price, industry output, and firm output. (h) [3 points] In a new picture below, illustrate the long run effect of this wage tax. Indicate the effect on price, industry output, and firm output. (i) [2 points] In the new long run equilibrium, each firm notices that it employs the same number of workers as it did initially. If the government provides a lump sum subsidy to gizmo firms on top of the wage tax, what possible bundles could the gizmo firm move to in the long run? 5

6 Problem 3-18 points The figure below shows the market supply curve and demand curve for fire extinguishers. Assume that tastes for fire extinguishers are quasilinear. (a) [1 point] Suppose that fire extinguishers yield a positive social benefit equal to $20 per unit. What is the socially optimal output level? (b) [1 point] Given the social value of $20 per fire extinguisher, what optimal Pigouvian policy should the government employ to correct the market failure? 6

7 (c) [12 points] Suppose the optimal policy from (b) has been implemented. Fill in the chart below with letters corresponding to areas in the figure above. Before Policy After Policy Consumer Surplus Producer Surplus Social Benefit Government Spending Total Surplus Deadweight Loss (d) [2 points] Suppose that instead of the policy from (b) the government announces a price floor of $40. How large is the disequilibrium surplus? (e) [2 points] In coordination with the price floor, the government announces a purchasing program. It will buy the entire surplus of fire extinguishers directly from the producers at the price floor and it will resell those fire extinguishers to consumers at a sufficiently low single price. How much money will the government spend on this purchasing program? How does government spending under this purchasing program compare to government spending under the policy from (b)? 7

8 Problem 4-14 points Consider an insurance market with no fixed costs in the industry. The market demand curve for insurance is given by the equation P=20- X. The insurance companies face two types of consumers, each with a different but constant marginal cost. Type A has a marginal cost of $2 and Type B has a marginal cost of $6. (a) [2 points] If this insurance market is perfectly competitive and the insurance companies have perfect information, what will be the price and quantity offered to each consumer type? (b) [1 point] Suppose that the insurance firms do not have perfect information, but they know that 50% of the population is Type A and 50% of the population is Type B. What is the insurance companies expected marginal cost? (c) [2 points] Under the pooling equilibrium in perfect competition, what is the total deadweight loss? (d) [3 points] Suppose instead that the insurance market is served by a single monopolist. Calculate total consumer surplus, profit, and deadweight loss under first degree price discrimination. 8

9 (e) [2 points] What is deadweight loss under third degree price discrimination for the monopolist? (f) [2 points] What is deadweight loss under the pooling equilibrium for the monopolist? (g) [1 point] Which is more efficient for this monopolist - third degree price discrimination or the pooling equilibrium? Is this always the case? (h) [1 point] Suppose the government wants to impose a subsidy on a third degree price discriminating monopolist to push the output level towards the efficient quantity from part (a). Can the government achieve this with a lump sum subsidy, a per unit subsidy, or both? 9

10 Problem 5-18 points Consider the payoff matrix below, which depicts a simultaneous game between Player 1 and Player 2. Player 2 Left Middle Right Up 12, 9 4, 10 9, 7 Player 1 Middle 4, 4 5, 6 1, 4 Down 10, 1 10, 8 2, 5 (a) [2 points] List all pure strategy Nash equilibria. (b) [2 points] Does Player 1 have a dominant strategy? Does Player 2 have a dominant strategy? If yes, identify the dominant strategy. (c) [4 points] Suppose that the government imposes a fine of 2 on any player who plays Middle. Fill in the payoff matrix below, updating the payoffs to reflect this fine. List all pure strategy Nash equilibria. Up Player 2 Left Middle Right Player 1 Middle Down 10

11 (d) [6 points] Suppose that Player 1 plays Up with probability ρ1, plays Middle with probability ρ2, and plays Down with probability ρ3. Player 2 plays Left with probability λ1, plays Middle with probability λ2, and plays Right with probability λ3. Using the payoff matrix from part (c), find the mixed strategy Nash equilibrium. Fill in the space below with the mixed strategy equilibrium probabilities. Player 1: ρ1= ρ2= ρ3= Player 2: λ1= λ2= λ3= (e) [2 points] Return to the original payoff matrix from part (a). Suppose the benevolent social planner wants to impose a fine of X on any player who plays Middle. What outcome would the social planner prefer? What is the smallest integer value of X that would guarantee the efficient outcome to be the unique Nash equilibrium? (f) [2 points] If this were a sequential game instead of a simultaneous game where Player 1 moved first and Player 2 moved second, how many complete strategies would each player have? 11

12 Problem 6-16 points Consider the following sequential game. In the first stage, Firm 1 decides whether to set a High (H) or a Low (L) price. In the second stage, Firm 2 decides whether to Enter (E) or to Not Enter (N). In the event that Firm 2 enters, Firm 1 has to make a decision in a third stage to launch either a limited advertising campaign (A) or a full- scale marketing campaign (M). (a) [2 points] List all strategies for Firm 1 and Firm 2. (b) [2 points] Find the subgame perfect Nash equilibrium of this game. (c) [2 points] Suppose the government set a price ceiling between the H price and the L price. Would this change the equilibrium path? Explain. 12

13 (d) [2 points] Suppose the government set a price floor between the H price and the L price. Would this change the equilibrium path? Explain. (e) [2 points] Does either the price ceiling or the price floor enhance efficiency in this context? Explain. (f) [6 points] Represent the sequential game above in a payoff matrix. List all Nash equilibria of this game. 13

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