Econ100a_PSET2 - Econ 100A Problem Set 2 Utility...

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Econ 100A - Problem Set 2 Utility Maximization and Demand 1. George’s utility is given by U(x 1 , x 2 ) = 6x 1 *x 2 2 . Use calculus to work through the utility maximization problem and derive his demand functions x 1 (p 1 , p 2 , I) and x 2 (p 1 , p 2 , I). 2. Ted’s demand function for goods 1 and 2 is given by U(x 1 , x 2 ) = 3lnx 1 + 2x 2 . Derive his demand function for good 1. 3. When Lisa cooks a chicken she only eats the chicken wings. Her utility function over whole chickens and chicken-wings is U(X C , X W )= 2X C + X W , where X C and X W are chickens and chicken-wings, respectively. What is her demand function X C * (p c , p w , I) for chickens? 4. If x 1 (p 1 , p 2 , I), x 2 (p 1 , p 2 , I) are my demand functions for commodities 1 and 2, and MRS(x 1 , x 2 ) denotes my marginal rate of substitution at the commodity bundle (x 1 , x 2 ), what is the numerical value of the expression MRS(x 1 (1,3,12), x 2 (1,3,12))? (Assume x 1 and x 2 are positive.) 5. My utility function is U(x 1, x 2 ) = 2x 1 2 x 2 and my utility-maximizing bundle (at existing
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