# A firm has the following production function: Q = 50K + 20L. Each unit of capital costs $4 to...

## Question:

A firm has the following production function: Q = 50K + 20L. Each unit of capital costs $4 to employ and each unit of labor costs $1 to employ. Labor and capital are this firm's only costs of production. The firm is currently producing 250 units of output in a cost-minimizing fashion. Calculate the following:

a. number of units of capital that the firm is currently employing

b. number of units of labor that the firm is currently employing

c. average total cost

## Linear Production Function

The linear production function is the type of production function with perfectly substitutable resources. This means, both the factors of production, labor, and capital can be completely replaced by each other. If producer thinks labor is more productive and less costly than capital, only labor units would be used.

## Answer and Explanation: 1

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**a.** and **b.**

Cost minimizatizing capital and labor units:

{eq}\begin{align*} Q &= 50K + 20L\\ \frac{{MPL}}{w} &= \frac{{20}}{1} =...

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Chapter 11 / Lesson 27Learn about the production function. Read the production function definition in economics, learn the production function formula. Plus, see graphs and examples.

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