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Finding Utility-Maximizing Demand for Goods

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Let

U(x,y) = x * (y^2)

1. Derive the indirect utility function as a function of px, py and M, where px and py
are respectively the prices of the two goods x and y, and where M is the consumer's
income.

2. Now calculate the level consumption of both goods and the level of utility achieved
by this consumer if prices and income are as follows: px = 2; py = 3 ;M = 9

3. Now set up the dual of this problem: minimize expenditure subject to the level of
utility that you calculated in part 2 and with prices px and py. Find the expression
for the expenditure function.

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Solution Summary

Solution provides detailed explanation of how to find utility-maximizing demand for goods given a specific utility function. It also shows how to calculate the expenditure function. While a specific functional form for utility function is used , the steps are detailed enough for a student comfortable with basic calculus to repeat the steps for a different utility function.

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Let

1. Derive the indirect utility function as a function of px, py and M, where px and py
are respectively the prices of the two goods x and y, ...

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