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Unformatted text preview: ECON 256: Intermediate Microeconomics Long Assignment: 4 1 Answer Key Due Date: Thursday, November 11, 2010 1 (a). (Frank p. 194; Question 8) What is the expected value of a random toss of a fair and six-sided die? The expected value of one toss of a six-sided die is: EV = 1 6 (1 + 2 + 3 + 4 + 5 + 6) = 21 6 = 3.5. 1 (b). (Frank p. 195; Question 15) Your current wealth level is M = $49 and you are forced to make the following wager: If a fair coin comes up heads, you get $15; you lose $13 if it comes up tails. Your utility function is = . (i) What is the expected value of this gamble? EV = *15 *13 = 1. (ii) What is its expected utility? EU = * 64 + * 36 = 4 + 3 = 7. (iii) How would the expected value and expected utility change if the payoff for tails fell to a loss of $15? EV = *15 *15 = 0. EU = * 64 + * 34 = 4 + 5.83 2 = 6.91. (iv) What is the most you would pay to get out of the gamble described in (iii)? [ Hint: Let x = the most you would pay to get out of the gamble. Then set the utility from your remaining income to the expected utility from the gamble. ] Let x = the most you would pay to get out of the gamble. Then set, ( ) 49 x = 6.91 49 x = 47.75 x = 1.25 2. (Frank p. 195; Question 14) A farmers hens lay 1000 eggs/day, which he sells for 10 cents each, his sole source of income (so 1000 eggs would earn him $100/day). His utility function is = , where M is his daily income. Each time a farmer carries eggs in from the hen house, there is a 50 percent chance he will fall and break all the eggs. Assuming he assigns no value to his time, is he better off by carrying all the eggs in one trip or by carrying 500 in each of two trips (what should he compare from these two alternatives ECON 256: Intermediate Microeconomics Long Assignment: 4 2 given both scenarios involve probabilities?)? [ Hint: There are three possibilities when he takes two trips: 1000 broken eggs, 500 broken eggs, and no broken eggs. Remember that takes two trips: 1000 broken eggs, 500 broken eggs, and no broken eggs....
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This note was uploaded on 03/27/2011 for the course ECON 256 taught by Professor ?? during the Fall '05 term at Bucknell.
- Fall '05