AP® Microeconomics review sheet from Aim for Five (aimforfive.com/micro/units/5/5-1)
Unit 5 · Topic 5.1
5.1 Introduction to Factor Markets
In factor markets, firms are the buyers and households are the sellers of labor, land and capital. A firm wants workers only because people want what those workers produce, so the demand for labor is derived demand. A worker's value to the firm is their marginal revenue product, and the MRP curve is the firm's demand curve for labor.
Key terms
- factors of production
- factor market
- derived demand
- marginal product
- marginal revenue product (MRP)
- marginal factor cost (MFC)
Who buys and who sells
The factors of production are the inputs used to make goods and services: land (natural resources), labor (people's work), capital (tools, machines and buildings) and entrepreneurship (organizing production and taking risks).
In the product market, households buy and firms sell. In the factor market (also called the resource market), the roles flip: households sell or rent out their factors, and firms buy them. The payments for factors are household income.
| Factor | What it is | Payment to its owner |
|---|---|---|
| Land | Natural resources, including the ground itself | Rent |
| Labor | Human work and skill | Wages |
| Capital | Tools, machines, buildings | Interest |
| Entrepreneurship | Organizing production and taking risks | Profit |
Derived demand
A bakery doesn't hire bakers because it enjoys having them around. It hires them because customers want bread. The demand for a factor is derived demand: it comes from (is derived from) the demand for the product the factor helps make.
So anything that changes demand for the product changes demand for the workers who make it. If people start buying more bread, the bakery's demand for bakers goes up (5.2).
Marginal product and marginal revenue product
Marginal product (MP) of labor is the extra output from hiring one more worker. Because of diminishing marginal returns (3.1), MP eventually falls as you add workers to a fixed amount of capital.
What the firm really cares about is revenue. Marginal revenue product (MRP) is the extra revenue from hiring one more worker: MRP = MP × MR. You can also find it from a table as the change in total revenue divided by the change in the number of workers.
If the firm sells its product in a perfectly competitive market, MR equals the product's price, so MRP = MP × P. If the firm has market power where it sells, MR is below price and falls as output grows, so MRP falls even faster.
The MRP curve is the demand for labor
Graph it with the wage (and MRP) on the vertical axis and the quantity of labor on the horizontal axis. Because MP falls as more workers are hired, the MRP curve slopes down. At any wage, the firm hires up to the worker whose MRP equals that wage. So the MRP curve is the firm's demand curve for labor.
Marginal factor cost (MFC) is the extra cost of hiring one more unit of a factor. When a firm can hire all the workers it wants at the going wage, MFC is just the wage. The firm compares the two: hire one more worker if that worker adds at least as much revenue as cost (MRP ≥ MFC). The full hiring rule is in 5.3, and the case where MFC is above the wage is in 5.4.
Notice the parallel with the product market. There, firms compare MR with MC. Here, they compare MRP with MFC. Same logic, different market.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Calculating MP and MRP for a competitive seller
A strawberry farm sells in a perfectly competitive market at $5 per box. With 1 worker it picks 12 boxes per hour; with 2 workers, 22; with 3, 30; with 4, 36; with 5, 40; with 6, 42. Find the marginal product and the marginal revenue product of each worker.
Show the solutionHide the solution
- Step 1: MP = change in total output. Worker 1: 12 − 0 = 12. Worker 2: 22 − 12 = 10. Worker 3: 30 − 22 = 8. Worker 4: 36 − 30 = 6. Worker 5: 40 − 36 = 4. Worker 6: 42 − 40 = 2.
- Step 2: The farm is a price taker in the strawberry market, so MR = P = $5 and MRP = MP × $5.
- Step 3: MRP: worker 1, 12 × 5 = $60; worker 2, $50; worker 3, $40; worker 4, $30; worker 5, $20; worker 6, $10.
- Step 4: MP falls with each worker (diminishing marginal returns), so MRP falls too. These MRP values trace out the farm's downward-sloping demand curve for labor.
Answer: MP: 12, 10, 8, 6, 4, 2 boxes. MRP: $60, $50, $40, $30, $20, $10 per hour.
- Example 2Calculator allowed
MRP for a firm with market power (classic trap)
A firm is the only seller of a specialty sauce. With 1 worker it makes 10 jars a day and can sell them for $10 each. With 2 workers it makes 18 jars, but to sell them all it must charge $9 each. With 3 workers it makes 24 jars at $8 each. A student calculates the 2nd worker's MRP as MP × price = 8 × $9 = $72. Find the correct MRP of the 2nd and 3rd workers.
Show the solutionHide the solution
- Step 1: Total revenue = price × output. With 1 worker: 10 × $10 = $100. With 2: 18 × $9 = $162. With 3: 24 × $8 = $192.
- Step 2: MRP = change in total revenue. Worker 2: 162 − 100 = $62. Worker 3: 192 − 162 = $30.
- Step 3: Why the student's $72 is wrong: to sell the extra 8 jars, the firm had to cut the price on the first 10 jars too, from $10 to $9. That loses $10 of revenue, so 72 − 10 = $62.
- Step 4: MP × P works only when the firm sells in a perfectly competitive market, where MR = P. With market power, use MP × MR, or just the change in total revenue.
Answer: The 2nd worker's MRP is $62 (not $72), and the 3rd worker's is $30.
Common mistakes
- Saying households demand labor. In the factor market, firms are the buyers (demand) and households are the sellers (supply).
- Using MRP = MP × P for a firm with market power in its product market. Use MRP = MP × MR, or the change in total revenue.
- Mixing up marginal product (extra output, in units) with marginal revenue product (extra revenue, in dollars).
- Explaining the downward-sloping labor demand curve with the law of demand alone. The reason is diminishing marginal product (and, with market power, falling MR).
On the exam
- Expect a table of workers and output and a question asking for MP or MRP of a specific worker. Show the subtraction and the multiplication.
- If asked why labor demand is 'derived', name the product the workers make and say the firm's demand for workers comes from consumers' demand for that product.
Connected topics
Videos
Check yourself
4 questions on 5.1 Introduction to Factor Markets. Pick an answer to see if you got it, and why.
| Number of workers | Total product (units) | Price of product |
|---|---|---|
| 1 | 10 | $20 |
| 2 | 18 | $18 |
| 3 | 24 | $16 |
| 4 | 28 | $15 |
| 5 | 30 | $14 |
Hypothetical data for a firm that is the only seller of its product and hires workers in a perfectly competitive labor market. The price is the highest price at which the firm can sell that total product.
What is the marginal revenue product of the second worker?
If the wage is $50 per worker, how many workers will the firm hire to maximize profit?
This firm's MRP falls faster than it would for a firm that could sell all its output at $20. Why?
The demand for carpenters rises whenever more new homes are built. This is an example of
0 of 4 answered