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ProblemSet2_2009

# ProblemSet2_2009 - Econ 6202 Fall 2009 Dmitry Shapiro...

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Econ 6202, Fall 2009 Dmitry Shapiro Problem Set 2 Due Tuesday September 15 1. Bob consumes ice creams ( x 1 ) and hamburgers ( x 2 ). His utility function is u ( x 1 , x 2 ) = ( x 1 ) 1 2 ( x 2 ) 1 2 . Bob’s income is \$100. The price of each hamburger is \$2. The price of an ice cream depends on the quantity that Bob consumes. Specifically, he can buy the first ten ice-creams at the price of \$2 each. For each additional ice cream there is a discount, and Bob has to pay only \$1. Derive Bob’s budget constraint and compute his optimal consumption plan. 2. (JR 1.53) The n -good Cobb-Douglas utility function is: u ( x 1 , . . . , x n ) = A n Y i =1 x α i i , where A > 0 , α 1 > 0 , . . . , α n > 0 and n i =1 α i = 1. (a) Derive the Marshallian demand functions [Hint: your life will become much easier if you use a monotone transformation of the utility function. You may want to look at PS1 to get an idea of what transformation to use.] (b) Derive the indirect utility function. (c) Compute the expenditure function.

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ProblemSet2_2009 - Econ 6202 Fall 2009 Dmitry Shapiro...

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