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Unformatted text preview: HOMEWORK ECONOMICS 200A III. DEMAND THEORY AND DUALITY R. R. RUSSELL FALL 2008 1. Consider the following three utility functions: U ( x 1 ,x 2 ) = ( x 1 ) 1 / 2 + x 2 , U ( x 1 ,x 2 ) = x 1 + ln x 2 U ( x 1 ,x 2 ) = ( x 1- ) x 2 , > . (a) Restricting prices to those that yield interior solutions, find the first-order conditions for maximizing these utility functions subject to a budget constraint, p x = y , and check to see that second-order conditions are satisfied. (b) Without restricting prices to those that yield interior solutions, find the first-order conditions for maximizing these utility functions subject to the budget constraint. (Be careful here to consider different signs of and to restrict choices to those where the utility function is well defined.) (c) Derive the demand functions for each utility function and verify the requisite ho- mogeneity condition. (d). Derive the indirect utility function dual to each utility function and verify Roys Identity....
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This note was uploaded on 07/06/2009 for the course ECON 200a taught by Professor Russell during the Fall '08 term at UC Riverside.
- Fall '08