Chapter 72, Problem 1CYU

To determine

Whether the firm is employing the cost-minimizing combination of inputs when it produces its output using only capital that costs $200 per unit per day and labor that costs $100 per worker per day, the marginal product of the last worker employed is 500 and the last unit of capital is 1,000.

Explanation of Solution

Yes, the firm is employing the cost-minimizing combination of inputs when it produces its output using only capital that costs $200 per unit per day and labor that costs $100 per worker per day with the marginal product of the last worker employed being 500 and the last unit of capital is 1,000 because the marginal product per dollar is equal for capital and labor as:

  $\begin{array}{l}\begin{array}{l}\text{Marginal product per dollar of labor: }\\ \text{= }\frac{\text{ The Marginal product of the last worker employed }}{\text{labor cost per worker per day}}\end{array}\hfill \\ \text{= }\frac{\text{500}}{\text{\$100}}\hfill \\ \text{= 5 units}\hfill \\ \begin{array}{l}\\ \text{Marginal product per dollar of capital: }\\ \text{= }\frac{\text{ The Marginal product of the last unit of capital employed }}{\text{capital cost per unit per day}}\end{array}\hfill \\ \text{= }\frac{\text{1000}}{\text{\$200}}\hfill \\ \text{= 5 units of output per dollar}\text{.}\hfill \end{array}$

Here, the marginal product per dollar is equal for both capital and labor, therefore, the firm is employed the cost-minimizing combination of inputs.

Economics Concept Introduction

Introduction: Cost minimization refers to the control of cost by which a firm maximizes its productivity by investing the lowest cost amount in inputs to produce a particular product.