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micro-ex-4 - Ani Guerdjikova Department of Economics...

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Ani Guerdjikova Fall 2006 Department of Economics Intermediate Microeconomics Cornell University ECON 313 Problem Set 4 Problem 15 (Utility maximization, Cob-Douglas utility function) A household consumes only apples and bananas. We denote a consumption bundle consisting of x a bags of apples and x b bags of bananas is denoted by ( x a ; x b ) . The preferences of the household are given by the utility function U ( x a ; x b ) = x 1 / 2 a · x 1 / 2 b a) Suppose that prices for apples and bananas are p a = 4 and p b = 2 and let the income of the household be $20 . Derive the optimization problem of the household and represent it in a graph.. b) Determine the marginal rate of substitution ( MRS ) for any consumption bundle ( x a ; x b ) . Does the optimization problem of the household have a corner solution? Determine the household’s optimum graphically and analytically. c) Now assume that the income of the household is y dollars and the prices p a and p b are positive.
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