Microeconomics II Exam HS 2022 PDF

Microeconomics II (HS 2022) Exam PART 1 (50 Points) In this section of the exam, for each of the following statements there are three possible an- swers: true, false, or abstention. The number of attainable points is indic...

Microeconomics II (HS 2022) Exam PART 1 (50 Points) In this section of the exam, for each of the following statements there are three possible an- swers: true, false, or abstention. The number of attainable points is indicated in brackets. For a correct answer, you receive the number of attainable points. For an incorrect answer, the number of attainable points is subtracted from the total number of points obtained for a given problem. For an abstention, you receive 0 points. If the total number of points for a given problem is negative it will automatically be set to zero. Please enter all your answers in the answer sheet enclosed (only the answer sheet will count for the evaluation). Problem 1. Consumer Behavior (6 Points) Suppose there are two goods, X and Y , and two consumption bundles, A and B. The preferences of an individual are characterized by the utility function U (X, Y ) = 12 XY. (a) If A % B, then the individual is indifferent regarding the two consumption bundles A and B. (1.5 Points) (b) If A ∼ 21 B, then it must also be that U (A) = 21 U (B). (1.5 Points) (c) The indifference curves of the individual are strictly convex. (1.5 Points) (d) The preferences of the individual can also be represented by the utility function 1 U (X, Y ) = 2X 2 Y. (1.5 Points) Problem 2. Individual and Market Demand (6 Points) A utility maximizing individual with the utility function U (X, Y ) = max{2X, Y } spends all of his/her income I = 15 on the two goods X and Y. The prices of the goods X and Y are given by PX = 3 and PY = 5. (a) Good X and good Y are perfect complements. (1.5 Points) (b) The income expansion path is a straight line. (1.5 Points) (c) In the utility maximum the individual obtains the utility U ∗ = 5. (1.5 Points) (d) If the price of good X doubles, then the total effect of the price change is equal to the income effect of the price change. (1.5 Points) Problem 3. Production and Cost (8 Points) Suppose that a profit maximizing firm produces with the production function Q(K, L) = 16K 2 L2 , where Q denotes the output, K capital, and L labor. The price of one unit of capital is R = 4, and the price of one unit of labor is W = 1. 1 of 6  (a) The production function has increasing returns to scale. (2 Points) 1 (b) The conditional factor demand for labor is L(Q) = Q 4. (2 Points) (c) The marginal costs of the firm are increasing in Q. (2 Points) (d) Suppose the firm has to produce Q = 81. Then the total costs of the firm are TC = 6. (2 Points) Problem 4. Perfect Competition and Monopoly (8 Points) Consider the following cost curves of a profit maximizing firm. The firm operates in a market with free market entry and exit. The market price is P ∗ , and the profit maximizing quantity is Q∗. (a) At a price P ∗ the profit maximizing firm should leave the market immediately. (2 Points) (b) The producer surplus of the firm corresponds to the area ABE. (2 Points) (c) The average fixed costs of producing Q∗ correspond to the area ABCD. (2 Points) (d) The long-run supply curve of the firm is equal to the marginal cost curve from point F onward. (2 Points) Problem 5. Imperfect Competition (8 Points) Consider a market with inverse demand P (Q) = 50 − 25 Q, where Q denotes the quantity and P the price. The market is served by two firms, so that Q = q1 + q2. Both firms produce the good at constant marginal and average total costs of c1 = c2 = 5. (a) The fixed costs of the two firms are equal to zero. (2 Points) (b) If the two firms form a collusive monopoly, then the industry profit is π1 + π2 = 202.50. (2 Points) (c) If the two firms compete in quantity, then the market price in the Cournot-Nash equilibrium is P = 35. (2 Points) 2 of 6  (d) If the two firms compete in prices, then the produced industry quantity in the Bertrand-Nash equilibrium is Q = q1 + q2 = 18. (2 Points) Problem 6. Investment, Time, and Insurance (8 Points) An individual can participate in a lottery and receive a payoff of x. With probability p the individual wins the amount x = 10. With probability (1 − p) the individual wins the amount x = 0. The utility function of the individual is given by U (x) = x2 − 10. (a) The individual is risk-loving. (2 Points) (b) The expected utility of the lottery is 90p. (2 Points) (c) If p = 45 , then the utility of the expected payoff is 54. (2 Points) √ (d) If p = 54 , then the certainty equivalent of the lottery is 4 5. (2 Points) Problem 7. Monopoly and Climate Protection (6 Points) The conditional indirect utility of a consumer is u(κ, p; λ) = v − p − z(κ; λ) − E with consumption and u(κ, p; λ) = −E without consumption, where v ∈ [0, ∞) denotes the utility, p ≥ 0 the price, κ ∈ (0, 1) the product carbon footprint, λ ≥ 0 the intensity of climate concerns, z(κ; λ) ≥ 0 the “loss” from the consumption of a product with the carbon footprint κ and E ≥ 0 the “loss” from the climate externality caused by other consumers. (a) If v < p + z(κ; λ), then the consumer always refrains from consuming the product. (1.5 Points) (b) For z(κ; λ) = κλ, the conditional indirect utility u(κ, p; λ) with consumption de- creases with an increase in the intensity of climate concerns λ, all other things being equal. (1.5 Points) (c) The greater the “loss” E from the climate externality caused by other consumers, the more consumers refrain from consuming the product. (1.5 Points) (d) Stronger climate concerns λ always lead to a higher profit maximizing price p of the product if the supplier’s marginal cost c(κ) decrease with an increasing product carbon footprint κ. (1.5 Points) 3 of 6  Part 2 (40 Points) In this section of the exam, you are given a list of five possible answers for each part of each problem. Only one of these five answers is correct. Your task is to identify the correct answer. The number of attainable points is indicated in brackets. For a correct answer the points are added. For a wrong answer you receive 0 points. For an abstention you receive 0 points. Please enter all your answers in the answer sheet enclosed (only the answer sheet will count for the evaluation). Problem 1. Game Theory (20 Points) Consider the following sequential game: 1 L M R 2 ` r ` r ` r (1, 4) (1, 0) (0, 0) (3, 5) (x, x) (0, 3) (a) Determine the number of subgames. (5 Points) A. 1 B. 2 C. 3 D. 4 E. None of the above. (b) How many pure-strategy combinations survive the iterated elimination of strictly dominated strategies (IESDS) for x = 5? (5 Points) A. 1 B. 4 C. 6 D. 12 E. None of the above. (c) For which values of x does the game have exactly one Nash equilibrium in pure strategies? (5 Points) A. x < 4 B. 1 < x < 3 C. 0 < x < 4 D. x > 3 E. None of the above. 4 of 6  (d) For x = 0 determine the probability p with which player 1 plays the pure strategy L in the unique Nash equilibrium in mixed strategies. (5 Points) 1 A. p = 4 5 B. p = 9 2 C. p = 3 4 D. p = 5 E. None of the above. Problem 2. General Equilibrium (20 Points) There are two utility maximizing individuals i = A, B in a country, and there exist two goods ` = 1, 2. The utility functions of the individuals A and B are given by UA (xA A 1 , x2 ) = 1 3 1 (xA A 4 B B B B 2 1 ) (x2 ) and UB (x1 , x2 ) = (x1 )(x2 ). The initial endowments of the two individuals 4 are given by ωA = (2, 0) and ωB = (0, 1). The prices of the goods ` = 1, 2 are denoted by p1 and p2. (a) Calculate the offer curve of individual A. (5 Points) p2 3p1
A. OCA (p) = 2p , 1 2p2 B. OCA (p) = 3p p1 1
, 2p2 3p2 p2 3
C. OCA (p) = 2p , 1 2 D. OCA (p) = 12 , 3p 1
2p2 E. None of the above. (b) Indicate the price ratio in the Walrasian equilibrium. (5 Points) p1 1 A. p2 = 3 p1 4 B. p2 = 9 p1 2 C. p2 = 3 p1 D. p2 =1 E. None of the above. (c) What are the quantities that are consumed by individual B in the Walrasian equi- librium? (5 Points) A. xB = 21 , 31
B. xB = 12 , 32
C. xB = 32 , 21
D. xB = 32 , 31
E. None of the above. (d) Suppose that the country signs a free-trade agreement with the utility maximizing individual C that also consumes the goods ` = 1, 2 only. The utility function C 12 of individual C is given by UC (xC C C 1 , x2 ) = (x1 ) (x2 ). The initial endowment of individual C is given by ωC = (0, 1). The price ratio in the Walrasian equilibrium with free trade is pp12 = 32. Which of the following statements is correct? (5 Points) 5 of 6 A. In equilibrium, individual A consumes the same amount of good x1 under free trade as under autarky. B. In equilibrium, the introduction of free trade leads to a Pareto-improvement compared to the situation without free trade. C. In equilibrium, individual B is better off under free trade than under autarky. D. In equilibrium, individual C is indifferent between free trade and autarky. E. None of the above. 6 of 6