ps2_09 - Cornell University Economics 3130 Problem Set 2...

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Cornell University Economics 3130 Problem Set 2 Due 2/6/09 1. True/False/Explain. State whether each of the following is true or false, and explain why. Please limit your answers to no more than two sentences. All credit is based on the explanation. (a) Suppose a consumer is fully apathetic in that he is indifferent between all possible consumption bundles. His preferences are not rational. (b) If a utility function satisfies monotonicity, then its indifference curves have a negative slope. (c) If two consumers are willing to engage in trade, their preferences must be different because otherwise they would have the same marginal rates of substitution and would not be willing to trade. 2. For each of the following two sets of utility functions, show which represent the same preferences. (a) i. u ( x ) = - 7 x 1 3 1 x 2 3 2 ii. u ( x ) = - 1 2 ln ( 7 x 1 ) - ln (7 x - 1 2 ) iii. u ( x ) = 1 2 ln ( x 2 1 ) + ln ( x 2 2 ) (b) i. u ( x ) = - 1 x 1 - 1 x 2 ii. u ( x ) = 1 x 2 1 + 2 x 1 x 2 + 1 x 2 2 iii. u ( x ) = 1 x 1 + 1 x 2 Note that “ln” means natural log.
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