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Unformatted text preview: Problem Set #2Answer Key 1 Basics For the first five utility functions below, find the demand functions. 1. u ( x,y ) = x 2 y 3 . Answers: x * = 2 5 I p x , y * = 3 5 I p y . 2. u ( x,y ) = ( x 2)( y 3) Answers: x * = 1 2 2 p x + I 3 p y p x , y * = 1 2 3 p y + I 2 p x p y . 3. u ( x,y ) = 2ln x + 3ln y Answers: same as question 1 above. 4. u ( x,y ) = x 2 3 y Answers: same as question 1 above. 5. u ( x,y ) = x 1 2 y 1 2 Answers: x * = 1 2 I p x , y * = 1 2 I p y 6. Find the indirect utility function associated with 1 above. Answer: plug the demand functions back into the utility function to get: V = . 3456 I 5 p 2 x p 3 y 7. Find the indirect utility function associated with 5 above. Answer: V = 0 . 5 Ip 1 2 x p 1 2 y 8. If you have done the problems correctly, your answers to 1, 3, and 4 should be identical. Explain in words why this is the case. Answer: This is because these functions are all monotone transformations of each other. The utility function in question 3 is the result of taking the natural logarithm of the function in 1, while the utility function in question 4 is the result of raising the utility function in 1 to the 1 3 power. 9. For the utility function in 4, find the expenditure function  an expres sion for the amount of income necessary to give the consumer a level of utility u given prices. (That is, minimizegiven prices....
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This note was uploaded on 11/12/2009 for the course ECONOMICS 701 taught by Professor Baker during the Spring '09 term at CUNY Hunter.
 Spring '09
 Baker
 Utility

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