ps2sol_09 - Cornell University Economics 3130 Problem Set 2...

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Economics 3130 Problem Set 2 Solutions 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. Rational preferences are those that are complete and transitive. It is implied that all bundles can be compared because the consumer is indifferent between any pair; this indifference also satisfies the requirement for transitivity. (b) If a utility function satisfies monotonicity, then its indifference curves have a negative slope. Since one bundle must be preferred to another when it has more of every good, the indifference curves cannot have positive slope. As we wrote the definition, though, indifference curves that are horizontal or vertical (as when there are two goods) also satisfy it. (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. Even consumers with the same preferences may trade if they have different en- dowments of goods. For any given bundle their MRS is the same, but at different bundles, their MRS’s may differ. 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 ) Notice that you can use the property of the natural log to rewrite (ii) as 1 2
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ps2sol_09 - Cornell University Economics 3130 Problem Set 2...

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