Factor Markets
Profit-Maximizing Behavior

Learn how firms decide how many workers to hire by comparing marginal revenue product to the wage rate in perfectly competitive factor markets.

AP Microeconomics

What Is a Factor Market?

In a factor market (also called a resource or input market), firms are the buyers and households are the sellers. Firms purchase the factors of production they need: labor, land, and capital.

Labor

Workers sell their time and skills to firms in exchange for wages.

Capital

Physical tools, machines, and equipment rented or purchased by firms.

Land

Natural resources and real estate leased by firms for production.

The Concept of Derived Demand

A firm's demand for a factor of production is derived from the demand for the product that the factor helps create. If consumers demand more pizza, the pizzeria demands more workers.

Key Terms You Must Know

Marginal Product (MP)

The additional output produced by hiring one more unit of a factor. $ MP_L = \frac{\Delta Q}{\Delta L} $

MRP

Marginal Revenue Product: the extra revenue from one more input unit. $ MRP = MP \times MR $

MFC (or MRC)

Marginal Factor Cost: the extra cost of hiring one more input unit. In perfect competition: $ MFC = W $

Wage Rate (W)

The market-determined price of labor. A price-taking firm pays this rate for every worker hired.

The Profit-Maximizing Hiring Rule

A perfectly competitive firm maximizes profit in the factor market by hiring inputs until the marginal revenue product equals the marginal factor cost:

1

If $ MRP > W $: each additional worker adds more revenue than cost. Hire more.

2

If $ MRP < W $: each additional worker adds more cost than revenue. Hire fewer.

3

If $ MRP = W $: profit is maximized. The firm is at its optimal hiring level.

MRP Is the Factor Demand Curve

Why Does MRP Slope Downward?

The downward slope of the MRP curve comes from the law of diminishing marginal returns. As you add more labor to a fixed amount of capital, each additional worker produces less additional output.

1

Diminishing $ MP_L $: As more workers are hired, each worker's marginal product falls.

2

Constant $ MR $: For a perfectly competitive firm, product price (and thus $ MR $) is constant.

3

Falling $ MRP $: Since $ MRP = MP_L \times P $, a declining $ MP_L $ means MRP must also decline.

MRP vs. VMP: What's the Difference?

	MRP	VMP
Formula	$ MP \times MR $	$ MP \times P $
Applies to	Any firm (competitive or not)	Perfectly competitive firms only
Key relationship	Uses marginal revenue	Uses product price
In perfect competition	$ MRP = VMP $ because $ MR = P $

Step-by-Step: Find Optimal Hiring

1

Calculate $ MP_L $: Find the change in total product for each additional worker: $ MP_L = \Delta TP / \Delta L $.

2

Calculate $ MRP $: Multiply each worker's $ MP_L $ by the product price: $ MRP = MP_L \times P $.

3

Identify the wage $ W $: In perfect competition, the wage is given by the market. Every worker costs the same $ W $.

4

Hire where $ MRP = W $: Find the last worker whose $ MRP \geq W $. That is the profit-maximizing quantity of labor.

5

Check: Never hire a worker whose $ MRP < W $, even if $ MRP > 0 $. The worker adds output, but not enough revenue to cover their wage.

Worked Example: The Pizza Shop

A pizza shop sells each pizza for $ P = \$10 $ in a perfectly competitive product market. The market wage is $ W = \$40 $. How many workers should the shop hire?

Workers (L)	Total Product (TP)	$ MP_L $	$ MRP = MP_L \times P $
0	0	---	---
1	10	10	$100
2	18	8	$80
3	24	6	$60
4	28	4	$40
5	30	2	$20

Graphing the Pizza Shop Decision

What If the Wage Changes?

Using the same pizza shop, suppose the market wage falls from $ \$40 $ to $ \$20 $. What happens to the optimal number of workers?

Hiring Multiple Factors

When a firm uses more than one input (e.g., labor and capital), it should allocate its budget so that the last dollar spent on each factor yields the same marginal product:

The least-cost rule minimizes cost for a given output. Adding the condition that the ratio equals 1 also ensures the firm is producing the profit-maximizing quantity.

The Competitive Labor Market

Common Mistakes to Avoid

✕ Confusing MRP with MP

$ MP $ is the additional output. $ MRP $ is the additional revenue. Always multiply: $ MRP = MP \times P $.

✕ Hiring Where MRP > 0

A worker who adds positive output but has $ MRP < W $ still costs more than they earn. Stop at $ MRP = W $, not $ MRP = 0 $.

✕ Forgetting Derived Demand

A change in product price shifts the entire MRP curve (and thus the labor demand curve), not just a movement along it.

Summary: Factor Market Essentials

Concept	Key Formula / Rule
Marginal Product	$ MP_L = \Delta TP / \Delta L $
Marginal Revenue Product	$ MRP = MP_L \times P $ (perf. comp.)
Profit-max hiring rule	$ MRP = W $ (or $ MRP = MFC $)
Factor demand curve	The MRP curve itself
Least-cost rule	$ MP_L / P_L = MP_K / P_K $
Profit-max (multi-factor)	$ MP_L / P_L = MP_K / P_K = 1 $

Question 1 of 5

A firm in a perfectly competitive product and labor market sells its output at $ P = \$5 $. The 6th worker has a marginal product of 8 units. What is the MRP of the 6th worker?

$ MRP = MP \times P = 8 \times \$5 = \$40 $. The MRP is the additional revenue from hiring one more worker, not the MP alone.

Question 2 of 5

In a perfectly competitive labor market, a firm should hire additional workers as long as:

The firm hires workers as long as the additional revenue they generate (MRP) is at least as large as their cost (W). Hiring where $ MP > 0 $ or $ MRP > 0 $ ignores whether the worker covers their wage.

Question 3 of 5

If the price of the final product increases, what happens to the firm's demand for labor?

Because $ MRP = MP \times P $, a higher product price raises the MRP at every level of employment. This shifts the entire MRP (labor demand) curve to the right. Only a change in the wage causes movement along the curve.

Question 4 of 5

A firm uses labor and capital. Currently, $ MP_L / P_L = 5 $ and $ MP_K / P_K = 3 $. To minimize cost for a given output, the firm should:

Since $ MP_L / P_L = 5 > MP_K / P_K = 3 $, the last dollar spent on labor produces more output than the last dollar on capital. The firm should shift spending toward labor (and away from capital) until the ratios equalize.

Question 5 of 5

A perfectly competitive firm pays a wage of $ W = \$30 $. The table below shows the firm's data. How many workers should the firm hire?

L	MRP
1	$60
2	$45
3	$30
4	$18
5	$10

The firm hires where $ MRP = W $. Worker 3 has $ MRP = \$30 = W $. Worker 4 has $ MRP = \$18 < W $, so the 4th worker should not be hired. The answer is 3 workers.

	MRP	VMP
Formula	\( MP \times MR \)	\( MP \times P \)
Applies to	Any firm (competitive or not)	Perfectly competitive firms only
Key relationship	Uses marginal revenue	Uses product price
In perfect competition	\( MRP = VMP \) because \( MR = P \)

Concept	Key Formula / Rule
Marginal Product	\( MP_L = \Delta TP / \Delta L \)
Marginal Revenue Product	\( MRP = MP_L \times P \) (perf. comp.)
Profit-max hiring rule	\( MRP = W \) (or \( MRP = MFC \))
Factor demand curve	The MRP curve itself
Least-cost rule	\( MP_L / P_L = MP_K / P_K \)
Profit-max (multi-factor)	\( MP_L / P_L = MP_K / P_K = 1 \)

Factor MarketsProfit-Maximizing Behavior

What Is a Factor Market?

The Concept of Derived Demand

Key Terms You Must Know

The Profit-Maximizing Hiring Rule

MRP Is the Factor Demand Curve

Why Does MRP Slope Downward?

MRP vs. VMP: What's the Difference?

Step-by-Step: Find Optimal Hiring

Worked Example: The Pizza Shop

Graphing the Pizza Shop Decision

What If the Wage Changes?

Hiring Multiple Factors

The Competitive Labor Market

Common Mistakes to Avoid

Summary: Factor Market Essentials

Question 1 of 5

Question 2 of 5

Question 3 of 5

Question 4 of 5

Question 5 of 5

Factor Markets
Profit-Maximizing Behavior