# Ps3_09 - Cornell University Economics 3130 Problem Set 3 Due 1 Consider the utility function U(x1 x2 x3 = ln x1 ln x2 ln x3 Assume the consumer has

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Cornell University Economics 3130 Problem Set 3 Due 2/13/09 1. Consider the utility function U ( x 1 ,x 2 ,x 3 ) = α ln x 1 + β ln x 2 + γ ln x 3 . Assume the consumer has income I and faces prices p 1 , p 2 , and p 3 . Find the Marshallian demands. 2. Consider the two-good CES utility function U ( x 1 ,x 2 ) = 1 (1 - α ) ( x 1 - α 1 + x 1 - α 2 ). Suppose that α can take any value from 0 to inﬁnity. As usual, assume that the consumer has income I and faces prices p 1 and p 2 . (a) What is the marginal rate of substitution? (b) What value of α corresponds to perfect substitutes? to Cobb-Douglas? to perfect complements? (c) In class we calculated the elasticity of substitution as follows: σ = MRS r dr dMRS . We deﬁned r = x 2 x 1 . The answer from (a) above is a simple function of r , so you can write the ﬁrst term using r and not x 1 or x 2 . Then, with the MRS written in terms of r , take the derivative dMRS dr . The inverse of that is the second term in the formula for the elasticity of substitution. Verify that the elasticity of substitution

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## This note was uploaded on 08/29/2009 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell University (Engineering School).

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Ps3_09 - Cornell University Economics 3130 Problem Set 3 Due 1 Consider the utility function U(x1 x2 x3 = ln x1 ln x2 ln x3 Assume the consumer has

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