# A production function Q = 100 L 0.4 K ? 0.6 relates to output, Q, to the number of labour units,...

## Question:

A production function{eq}Q = 100L^{0.4}K^{0.6} {/eq} relates to output, Q, to the number of labour units, L, and capital units K.

A) Derive the equation for the marginal and the average products of labour and capital.

B) Prove the identity{eq}Q = L\frac{\partial Q}{\partial L}+K\frac{\partial Q}{\partial k} {/eq}

C) Use partial derivatives to calculate the approximate percentage change in Q when L increases by 6% while K decreases by 4%

## Production Function

Production function refers to the relationship between the output and the inputs for a firm. More specifically, it is a function that shows the amount of output a firm can produce given different combinations of labor and capital.

## Answer and Explanation: 1

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View this answerGiven: {eq}A. Q = 100L^{0.4}K^{0.6} \\MPL = \frac{\partial Q}{\partial L} = 40L^{-0.6}K^{0.6} \\MPK = \frac{\partial Q}{\partial K} =...

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Chapter 4 / Lesson 2In Economics, there are three factors involved in the theory of production: total product, average product, and marginal product. Explore this theory and learn how to maximize the efficiency of these production tools.

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