6. Assume that utility is given by U(x, y) = 10.30.7 and Income. I, price of good x = p, and price of good y = Py Show your work for each of the following parts (a) Use the uncompensated demand functions to compute the indirect utility function and the expenditure function (E) for this case. (b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good z. (c) Use the results from part (b) together with the uncompensated demand function for good z to show that the Slutsky equation holds for this case.

6. Assume that utility is given by U(x, y) = 10.30.7 and Income. I, price of good x = p, and price of good y = Py Show your work for each of the following parts (a) Use the uncompensated demand functions to compute the indirect utility function and the expenditure function (E) for this case. (b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good z. (c) Use the results from part (b) together with the uncompensated demand function for good z to show that the Slutsky equation holds for this case.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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6. Assume that utility is given by U(x,y) = x03J07 and Income I, price of good x = P and price of good y = Py 1 Show your work for each of the following parts (a) Use the uncompensated demand functions to compute the indirect utility function and the expenditure function (E) for this case. (b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good x. (c) Use the results from part (b) together with the uncompensated demand function for good x to show that the Slutsky equation holds for this case.
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