3.C.6" Suppose that in a two-commodity world, the consumer's utility function takes the form u(x) = [a,x + a2x]". This utility function is known as the constant elasticity of substitution (or CES) utility function. %3D (a) Show that when p = 1, indifference curves become linear. (b) Show that as p 0, this utility function comes to represent the same preferences as the (generalized) Cobb-Douglas utility function u(x) = x'x. (c) Show that as p→ -0, indifference curves become "right angles"; that is, this utility function has in the limit the indifference map of the Leontief utility function u(x, x2): Min {x,, x2}.

3.C.6" Suppose that in a two-commodity world, the consumer's utility function takes the form u(x) = [a,x + a2x]". This utility function is known as the constant elasticity of substitution (or CES) utility function. %3D (a) Show that when p = 1, indifference curves become linear. (b) Show that as p 0, this utility function comes to represent the same preferences as the (generalized) Cobb-Douglas utility function u(x) = x'x. (c) Show that as p→ -0, indifference curves become "right angles"; that is, this utility function has in the limit the indifference map of the Leontief utility function u(x, x2): Min {x,, x2}.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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