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4808pset4 - Economics 4808 Problem Set 4 1 Consider the...

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Economics 4808 Problem Set 4 1. Consider the utility function U ( x , y ) = 3 x + y . a. Calculate the marginal utility of x ( MU x ) and the marginal utility of y ( MU y ). b. Is the assumption that more is better satisfied for both goods? Relate your answer to the marginal utilities calculated in part a. c. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x ? 2. Suppose a consumer’s preferences for two goods can be represented by the Cobb-Douglas utility function U ( x , y ) = A x α y β , where A , α , and β are positive constants. a. What is MRS x , y ? b. Is MRS x , y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? c. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Indicate on your graph whether the indifference curve will intersect either or both axes. 3. Repeat Problem 2 for the quasi-linear utility function ( 29 y x y x U + = 2 , .
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