RelativeResourceManager-2 - Second Midterm Examination,...

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Unformatted text preview: Second Midterm Examination, Fall 2009 Fin 580 FEl / FE2 Financial Economics Instructions: You have 80 minutes to complete the following examination. The exam consists of 10 multiple choice questions and 4 additional questions. The multiple choice questions are contained in a separate packet. The answers to the multiple choice questions must be recorded on the scantron answer sheet using a pencil. For the other four questions, write your answers in the spaces provided in this packet. You may use the back pages if you need extra space for calculations or explanations. Answer all parts of all questions. If you believe that the question is ambiguous, explain why and state what assumption you are making to resolve the ambiguity, and then answer the question given that assumption. When explanations are required, the explanation will count for most of the answer. Numerical answers are not necessarily whole numbers. The exam has 80 points. As a guide, you should spend no more than 1 minute on a question for every point that it is worth: 10 points 9 10 minutes. Numbers in square brackets at the start of each question tell how many points that question (or part of a question) is worth. You may use a calculator. However, it should be used for simple arithmetic only. No other materials are allowed. Please write your name and your University ID # in the space below. NAME: University ID: Do not open this packet until the exam begins. NAME: University ID: Question Multiple Choice Questions 1 — 10 are multiple choice questions. Each question is worth 3 points. The questions are in a separate packet. Please write your responses on the scantron answer sheet using a pencil. You will receive credit only for responses on the scantron sheet. Computational/Short Answer Questions: Please write your answers in the space provided. Partial credit will be awarded for partially correct work. So, write legibly and show your work. Full credit will not be given for a correct answer without showing supporting work. 11. Consider a consumer who lives for two periods, 0 and 1, with utility function: 111(01) UC,C =lnC (01) (mm; where 8 > 0. The consumer receives income 100 in each period and can borrow or save as much as desired at real interest rate r = O. a. What is the consumer’s intertemporal budget constraint? [6 points] C0 +C| é b. Suppose 8 =0.1. If the consumer maximizes utility, what are the optimal values of C0 and C1? [9 points] NV 2 J— MU : _._I,_. 0 C0 1' U‘HDC; Po=Pt1 i 12. Consider a decision maker with utility function u(x) = -l/x, and assume that this decision maker maximizes expected utility. This decision maker is given the opportunity to draw a ball out of an urn containing 100 balls. Some of the balls are red, and some are black. If the decision maker draws a red ball, he wins $50,000. If the decision maker draws a black ball, he loses $50,000. Let R be the number of red balls he believes are in the urn. If the decision maker’s initial wealth is $500,000, and he is willing to accept this opportunity, what must be true about how many red balls (R) he believes are in the urn? Be as accurate as possible. [15 points] Vitae oi RED 3 E- P [00 H 8.5.0 000 P r > xv 8 001000 + __ S—@ 000 ‘1 (Salem) $10,000 P + 0—?) é __L [I @' ‘é‘? lo [0 [lo- LOE’ .4. Cl“? «1013.4: "Ll P 2 “/w 4.27/23 2 5‘? Write your answer in this space KS: 55’ 13. A Decision Maker has utility function U(w) = ln(w) and initial wealth 100. The decision maker faces the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset returns $1 with certainty. With probability 1/2, the state is “good,” and $1 invested in the risky asset returns $1.25. Otherwise, (i.e., with probability 1/2), the state isnbadfland $1 invested in the risky asset returns $0.80. Let y denote the amount of money DM invests in the risky asset. a. In terms of y, what is the decision maker’s final wealth in each (i.e., good and bad) state. [7 paints] Scuff % [00 — «j Rani 3 Ed 34m 6mm; 6mm [00 It) +, £5 000—334-[13’3 = /00’ ,23 Z / 00 + , zg‘ E) Final Wealth in Good State Final Wealth in Bad State: Mo — ,a b. What is the optimal investment in the risky asset? [8 points] 1 ELF ill/1000 +1833 + {£14 (100"be PD *7 \ 0:95 __ I (,1) _ O . ZS‘ _ (2.. (00+.‘LS‘3 [coo—.13 25‘- 151.233: 20 +15- (.233 5:.13 we 14. Suppose the government implements a policy where they pay people to get vaccinated against the H1N1 flu virus. Using ideas from the course, in two or three sentences explain why such a program might be justified as improving efficiency. [5 points] Shine e/‘H'a U Mei/tka lecM/fi-l 0 ~ S. axle/maxi} / AA, 0 ’H‘Q “ film/(€71 " (w: H lea/we Jr) (kgdggg {QQ m U4 Cdflgé‘wta a ? (Q 01:) a 'n #11 (Meat MM - (Q J0 (/4 00,4 219 “fig: Qayflmi cam/X mlgqflflzsL/w ~C3~ Va ' W END OF EXAM First Midterm Examination, Fall 2009 FIN 580 FEl / FE2 Financial Economics Multiple Choice. [3 points each] Select the best answer to each question. Write the letter corresponding to your answer on the scantron answer sheet using a #2 pencil. If you do not write your answer on the scantron answer sheet using a #2 pencil, if you select more than one answer, or if it is ambiguous which answer you have selected, you will not receive credit. 1. A utility-maximizing consumer has initial wealth w and no additional income, and lives for two periods, 0 and 1. If the real interest rate increases this consumer will: a. Increase his savings in period 0. b. Decrease his savings in period 0. c. Not change his savings in period 0. The effect on savings cannot be determined without more information. 2. According to the Fisher Separation Theorem: a. All consumers should choose the same consumption bundle, regardless of their income stream. All consumers should choose the same income stream, regardless of their preferences. c. All consumers should choose to save the same amount, regardless of the interest rate. d. All consumers should borrow the same amount, regardless of their utility functions. 3. According to the Lifecycle Model of consumption over time: @ consumer’s current consumption should depend more on permanent income than on current income. b. A consumer should consume the same amount (in real terms) each period. c. A consumer should choose the income stream that maximizes the present value of lifetime consumption. (1. A consumer’s current consumption should only depend on current income. 4. Which of the following is true of a risk averse decision maker: a. The expected utility of any lottery is equal to its expected value. b. The expected utility of any lottery is less than its certainty equivalent. 0. The certainty equivalent of any lottery is greater than its expected value. The expected utility of any lottery is less than the utility of the lottery’s expected value. 5. Consider a decision maker with utility function u(w) = w“2 and initial wealth w = 100. This consumer’s coefficient of relative risk aversion is: a. 1/200 c. 2 d. 50 6. Prospect theory incorporates all of the following except: Aversion to ambiguity about probabilities. .b. Different risk attitudes toward gains and losses. c. Reference Points. (1. Non-linear weighting of probabilities. 7. The stochastic discount factor is: a. The expected value of the rate of time preference. he intertemporal marginal rate of substitution. c. The slope of the capital markets line. d. The ratio of state prices. 8. According to the Consumption CAPM model, an asset should have a high expected rate of return when: a. Its returns are positively correlated with market’s returns. b. Its returns are more variable than the market’s returns. @Its returns are negatively correlated with the stochastic discount factor. (1. Its return is near zero in absolute value. 9. Consider a model with two consumers, C1 and C2. C1 undertakes an activity x which also affects C2. The level of X is chosen by C1. Let Cl ’s utility be given by U1(x,m1) = 50X — x2 + m1, where m is the amount of money C1 has, and C2’s utility be given by U2(x,m2) = 500 — x + m2. Suppose that activity x is free. If the government wants to induce the Pareto Optimal choice of x, it should: @mpose a tax on C1 of $1 per unit of x consumed. b. Impose a tax on C1 of $2x per unit of x consumed. c. Impose a subsidy on C1 of $1 per unit of x consumed. d. Impose a tax on C1 equal to U2(x,m2). 10. Suppose that there are three states of the world, a, b, and c. The probabilities of the three states are 1:1 = 0.25, it; = 0.5, and M = 0.25. Let A, B, and C denote the Arrow- Debreu securities that pay $1 in states a, b, and c, respectively. That is, A = (1,0,0), B = (0,1,0) and C = (0,0,1). Let pA = 0.4, p3 = 0.5 and pc = 0.2 denote the prices ofA, B, and C. Consider a security X which is worth $2 in state a, $3 in state b, and $1 in state c. If there are liquid markets for A, B, C and X, what is the price of X? ...
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RelativeResourceManager-2 - Second Midterm Examination,...

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