Given two inputs X1 and X2 with prices W1 and W2 respectively and a production function Y=f(X1,X2), show that cost minimisation implies that the marginal rate of substitution between the inputs X1 and X2 is equal to the ratio of the two inputs prices

Given two inputs X1 and X2 with prices W1 and W2 respectively and a production function Y=f(X1,X2), show that cost minimisation implies that the marginal rate of substitution between the inputs X1 and X2 is equal to the ratio of the two inputs prices

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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Question

Given two inputs X₁and X₂ with prices W₁and W₂respectively and a production function Y=f(X₁,X₂), show that cost minimisation implies that the marginal rate of substitution between the inputs X₁and X₂is equal to the ratio of the two inputs prices

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