A consumer's utility function is -a u = x1x², where ₁ and 2 are the quantities consumed of goods one and two, respectively, and a is a parameter. Let p₁ and p2 denote the prices of goods one and two, respectively, so that the total expenditure in goods one and two is p₁1 + P2x2. The minimum expenditure that can be achieved subject to the constraint that the consumer achieves the level of utility ū is given by e = P₁P₂ 1-ªμа (this expression can be obtained by solving the corresponding constrained optimization problem). Calculate an approximation to the change in e due to increasing the level of utility by a small quantity d.

A consumer's utility function is -a u = x1x², where ₁ and 2 are the quantities consumed of goods one and two, respectively, and a is a parameter. Let p₁ and p2 denote the prices of goods one and two, respectively, so that the total expenditure in goods one and two is p₁1 + P2x2. The minimum expenditure that can be achieved subject to the constraint that the consumer achieves the level of utility ū is given by e = P₁P₂ 1-ªμа (this expression can be obtained by solving the corresponding constrained optimization problem). Calculate an approximation to the change in e due to increasing the level of utility by a small quantity d.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter5: Income And Substitution Effects

Section: Chapter Questions

Problem 5.5P

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