Problem Set 2 Solutions

# Problem Set 2 Solutions - Economics 11 Microeconomic Theory...

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Economics 11: Microeconomic Theory 1 Professor Christian Hellwig Homework 1, to be handed in Thursday May 1, at noon Instructions: You are encouraged to discuss and work in groups, but you must write up your own solutions. Please write your name, student ID number, and the name of your TA on the front page of the assignment that you hand in. Also, please put boxes around your final answer to each part. 1. Joe spends all his income on books (x) and cigarettes (y). His utility function is given by U(x,y) = y 2 x. a) Find the uncompensated demand functions for x and y, using the Lagrangian Method. The Lagrangian is [ ] y p x p M x y L y x + = λ 2 . The resulting first order conditions are y p yx = 2 and x p y = 2 . Combining the two, one finds x y p p y x / 2 / = or y p x p y x = 2 . Substitute this into the budget constraint to find x=M/(3p x ) and y=2M/(3p y ). b) What is Joe’s indirect utility function? () x y x y y x p p M p M p M M p p V 2 3 2 2 27 4 3 9 4 , , = = c) Confirm that Roy’s identity holds for the demand functions for x and y. y x y x y y x x y x y x x y x y y x y x p M p p M p p M M V p V p M p p M p p M M V p V p p M M V p p M p V p p M p V 3 2 27 12 27 8 and 3 27 12 27 4 :

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## This note was uploaded on 05/15/2008 for the course ECON 11 taught by Professor Cunningham during the Spring '08 term at UCLA.

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Problem Set 2 Solutions - Economics 11 Microeconomic Theory...

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