3. Prove the following proposition, that an increase in w₁, the price of input i, all else constant, weakly decreases x,, the unconditional input demand for input i. Proposition. Suppose w' and w differ only in the i-th component, where w > W₁. The market price of output is fixed at p. Suppose x solves the profit maximization problem at (p, w), and x' solves the profit maximization problem at (p, w'). Then x₁ = x₁.

3. Prove the following proposition, that an increase in w₁, the price of input i, all else constant, weakly decreases x,, the unconditional input demand for input i. Proposition. Suppose w' and w differ only in the i-th component, where w > W₁. The market price of output is fixed at p. Suppose x solves the profit maximization problem at (p, w), and x' solves the profit maximization problem at (p, w'). Then x₁ = x₁.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.12P

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