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# ps2fall200 - 14.03 Fall 2000 Problem Set 2 Due in Class#7...

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14.03 Fall 2000 Problem Set 2 Due in Class #7 Theory: 1) Nicholson 3.2 (Note that: log base a x 1 x = ( x ln a ) , 3.4, 3.7 (Hint: observe how these three functions are related), 4.2, 4.5 (Note: use low-tech math and common sense here), 5.2 and 5.9. 2) Let U ( x , y ) = − 1 x 1 y . Suppose that prices are P x and P y , and income is I . (A) Calculate the utility-maximizing choices of x and y, that is, the Marshallian demand functions d x ( P x , P y , I ) and d y ( P x , P y , I ) . (B) Calculate “indirect utility,” i.e., the utility at the optimal choices, V ( P x , P y , I ). (C) For a given utility level U 0 , solve the dual expenditure-minimization problem, and compute the optimal choices of X and Y , i.e., the “compensated demand functions” h x ( P x , P y , U o ) and h y ( P x , P y , U o ) . (D) Calculate the minimum expenditure function E ( P x , P y , U 0 ) . Show that the expenditure and indirect utility functions you have calculated are inverses of one another, i.e., show that

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ps2fall200 - 14.03 Fall 2000 Problem Set 2 Due in Class#7...

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