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# ps3 - Problem Set#3 1 Basics 1 Demand functions 2...

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Problem Set #3 1 Basics Consider the utility function u = x α y 1 - α . For this utility function, find: 1. Demand functions. 2. Compensated Demand functions. 3. The Expenditure function. 4. The Indirect Utility function. 5. Using your expressions above and the Slutsky equation, develop math- ematical expressions for the size of the income effect and the size of the substitution effect as functions of prices and income. 2 Applications Consider a situation in which p x = \$5, p y - \$10, I = \$100, and α = 1 2 . (Note that if you couldn’t get answers in the previous section, you might be able to for the case α = 1 2 .) 1. Using the indirect utility function, find the consumer’s utility at the given prices and income level. Using the demand functions, find the consumer’s consumption level of each good. 2. Suppose that p x rises to \$10. How much of each good is the con- sumer now consuming? Using the indirect utility function, find the consumer’s utility at the new price.

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