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penn101_09s_hw5sol

# penn101_09s_hw5sol - Intermediate Microeconomics(Econ 101...

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Intermediate Microeconomics (Econ 101) Spring, 2009 Solutions to Additional Problems in Assignment 5 Solution to Question 1. (1) True. Note that for Brad, the two goods are perfect substitutes. In equilibrium, for Brad to consume both goods, it must be that the price ratio equals his MRS. Let p x = p and p y = 1. Then we must have | MRS B | = 1 7 = p . On the other hand, Ann has quasilinear preferences, and hence her consumption of good y is independent of her endowment. Ann’s demand for y is obtained by solving: | MRS A | = p 1 154 2 y - 1 2 = 1 7 y = 121. (In this problem, we see that sometimes it is possible to determine equilibrium price and consumption without using the aggregate resource constraints. ) (2) True. Using the notation in your textbook (p. 233), here we have σ m = s and x = 1 / 2, so σ 1 / 2 = s/ 2. (3) False. Ann’s utility function is concave. This means she is risk-averse. Since betting \$10 on a fair coin toss has an expected winning of 0, Ann would prefer to get 0 for sure, that is, not to take this gamble, than to gamble. (4) False. The battle of sex game would be a counterexample. Solution to Question 2. (1) Let p 2 = p . (a) Step 1: Find out the demand function for one of the goods. Carl’s demand function for good 1 is x 1 C = 1 3 m C ; David’s demand function for good 1 is x 1 D = 1 3 m D ; (b) Step 2: Find out their endowments’ worth: For Carl: m C = 9 + 6 p x 1 C = 1 3 (9 + 6 p ); For David: m

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