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### Course: AP®︎/College Microeconomics>Unit 5

Lesson 3: Profit-maximizing behavior in perfectly competitive factor markets

# Profit-maximizing behavior in perfectly competitive factor markets

## Problem

Slytherthings, Inc. is a perfectly competitive firm producing lockets. It pays $\mathrm{}60$ per unit for the $10$ units of capital it uses, and the marginal product of the ${10}^{\text{th}}$ unit of capital is $420$ lockets. The firm can’t change its use of capital in the short run, but it can change its use of labor, and it can hire as much labor as it wants at a wage of $\mathrm{}30$. The firm’s production function is given in the table shown here:
Units of laborTotal output
$0$$0$
$1$$750$
$2$$1420$
$3$$1920$
$4$$2270$
$5$$2480$
$6$$2580$
$7$$2540$
How many units of labor should the firm hire to minimize costs and maximize profits?