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Krugman_SolMan_CH18

# Krugman_SolMan_CH18 - Krugman_SolMan_CH18 4:40 PM Page 143...

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chapter Uncertainty, Risk, and Private Information 1. a. The expected value of the share price is (0.5 × \$100) + (0.5 × \$70) = \$50 + \$35 = \$85. b. The expected value of Sharon’s winnings is (0.7 × \$0) + (0.2 × \$10) + (0.1 × \$50) = \$0 + \$2 + \$5 = \$7. c. The expected value of Aaron’s profit is (0.9 × \$100) + (0.1 ×− \$20) = \$90 + ( \$2) = \$88. 2. a. Vicky’s marginal utility of income is given in the accompanying table. Since her marginal utility declines, she is risk-averse. 143 18 Income Total utility (utils) Marginal utility (utils) \$0 0 50 1,000 50 35 2,000 85 30 3,000 115 25 4,000 140 23 5,000 163 20 6,000 183 17 7,000 200 15 8,000 215 14 9,000 229 12 10,000 241 b. If the company succeeds, Vicky will have income of \$10,000 (the \$2,000 she did not invest plus the \$8,000 the company pays out to her). If the company fails, Vicky will have income of \$2,000 (the \$2,000 she has not invested). The expected value of Vicky’s income is (0.5 × \$10,000) + (0.5 × \$2,000) = \$1,000 + \$5,000 = \$6,000. c. Vicky’s expected utility from making the investment is (0.5 × 85) + (0.5 × 241) = 42.5 + 120.5 = 163. d. If she does not make the investment, Vicky’s utility is the utility of having \$4,000 income, that is, 140. Since the expected utility from making the investment is greater than her utility from not making the investment, she will invest in the company. 3. If the company succeeds, Vicky will have income of \$10,000. If the company fails, Vicky will have income of \$0 (she loses her entire investment). Vicky’s expected utili- ty from making the investment is (0.5 × 241) + (0.5 × 0) = 120.5 + 0 = 120.5. Since this is less than her utility from not investing 140 utils, she will not invest in the company. 4. a. The expected value of your earnings from investing in Ford stock is (0.2 × \$1,500) + (0.4 × \$1,100) + (0.4 × \$900) = \$300 + \$440 + \$360 = \$1,100. Krugman_SolMan_CH18 11/11/04 4:40 PM Page 143

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b. You have a choice between getting \$1,100 for certain by putting your money into the bank or getting \$1,100 on average by investing in Ford stock. Both investments pay the same on average, but investing in Ford stock is risky. Since you are risk- averse, you would prefer to get \$1,100 for certain. So you will definitely put your money in the bank. 5. a. The expected value of your earnings from investing in General Motors stock is (0.4 × \$1,600) + (0.4 × \$1,100) + (0.2 × \$800) = \$640 + \$440 + \$160 = \$1,240. b. Since getting \$1,100 for certain is better for you than getting an average (but risky) \$1,240, you must be risk-averse: you are willing to take a lower (but cer- tain) payoff instead of a higher (but risky) one. 6. a. The expected value of Wilbur’s income is (0.6 × \$60,000) + (0.4 × \$10,000) = \$36,000 + \$4,000 = \$40,000. b.
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