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# ps2 - Problem Set#2 1 Basics For the rst ve utility...

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Problem Set #2 1 Basics For the first five utility functions below, find the demand functions. 1. u ( x, y ) = x 2 y 3 2. u ( x, y ) = ( x - 2)( y - 3) 3. u ( x, y ) = 2 ln x + 3 ln y 4. u ( x, y ) = x 2 3 y 5. u ( x, y ) = x 1 2 y 1 2 6. Find the indirect utility function associated with 1 above. 7. Find the indirect utility function associated with 5 above. 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. 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, minimize E = p x x + p y y subject to the constraint that u = u ( x, y )). 2 Word Problems 1. Suppose that an individual has utility function u ( x, l ) = ( x - x ) 1 - α l α , where x denotes consumption of goods while l denotes leisure time; x and α are parameters of the utility function. The individual’s total income is I = we + A , where A is asset income, e denotes working time, and w is the wage rate. All income is spent on consumption of

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