# A production function is a mathematical relation between a firm or country's inputs (capital and...

## Question:

A production function is a mathematical relation between a firm or country's inputs (capital and labor) and outputs. Use the Cobb-Douglas Production Function

{eq}Y = K^ \alpha L ^{1 - \alpha}{/eq}

where Y is output (GDP or national income), K is capital, and L is labor (number of workers).

a) Show the production function can be written as {eq}ln(Y) = \alpha ln(K) + (1 - \alpha)ln(L){/eq}.

b) Find the marginal product of capital and labor by taking the derivative of Y with respect to K and L.

## Cobb-Douglas Function:

It is a type of production function where input factors labor and capital are implicit variables of the function. The elasticities of labor and capital are also part of the functional parameters. It represents the technological relationship between two-factor inputs.

## Answer and Explanation: 1

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View this answerThe production function is given as:

{eq}{\rm{Y = }}{{\rm{K}}^{\rm{\alpha }}}{{\rm{L}}^{{\rm{1 - \alpha }}}} {/eq}

a) Assuming logarithm on both...

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Chapter 1 / Lesson 7Learn the definition of a production function in economics, understand the definition of a Cobb-Douglas production function and its formula, and explore some examples of Cobb-Douglas production function.

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