A consumer has preferences over 3 goods represented by the utility function u(x₁, x2, x3) = √√x1x₂-2-23. As usual, goods 1 and 2 are perfectly divisible, meaning that ₁ and ₂ can take on any nonnegative real values and need not be integers. Good 3 is indivisible and unique, meaning that ä3 must be either 0 or 1 (for example, good 3 could be an original painting). (a) Show that this consumer's preferences are monotone. (b) Find this consumer's Marshallian demand. (c) Find this consumer's expenditure function.

A consumer has preferences over 3 goods represented by the utility function u(x₁, x2, x3) = √√x1x₂-2-23. As usual, goods 1 and 2 are perfectly divisible, meaning that ₁ and ₂ can take on any nonnegative real values and need not be integers. Good 3 is indivisible and unique, meaning that ä3 must be either 0 or 1 (for example, good 3 could be an original painting). (a) Show that this consumer's preferences are monotone. (b) Find this consumer's Marshallian demand. (c) Find this consumer's expenditure function.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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