# Kaplan University Economics 326-First Midterm

Mar 31st, 2015
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Does the utility function U (X; Y ) = X 3 y 5 satisfy rationality of underlying preferences?

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Economics 326:First Midterm (October 8, 2014)1Short Answers (6 points each)1710(a.) Does the utility function U (X; Y ) = X 3y 5 satisfy rationality ofunderlying preferences?Answer: Yes. By the fact that a utility function can be written, it satis?es transitivity, anti-re?exivity and completeness.(b.) What are second order conditions? What happens if they are not satis?ed? You do not have to compute second order conditions to answer this question - just explain what they are and give an intuitive explanation about why they are important.Answer: Second order conditions are the second derivative of the Lagrangian (or alternatively the utility function). The utility function needs to be concave in order to ensure that the utility maximization problem can be solved using calculus. In the absence of satisfying the second order conditions, taking ?rst order conditions may lead to a consumption bundle which locally maximizes utility or even minimizes utility.(c.) Why do indierence curves usually slope downwards? What do we need to assume in order to assure that they slope downwards?Answer: As long as marginal utility is positive for all goods, indierence curves will slope downwards. If marginal utility is positive, then by losing some of one good, you need more of another in order to retain the same utility level. So, more of one good will be on the same utility curve as less of another good. (d.) Let U (X; Y; Z) = X 3 Y 3 Z 5 be a utility function. Write thre

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