Chapter 18: The Markets for the Factors of Production

Where wages, rents, and interest come from — and why each factor earns its marginal product

Section 1

Flipping the Diagram: Input Markets

Every chapter so far has been about output markets — firms selling goods. Chapter 18 flips the picture to input markets: where firms buy labor, rent land, and rent capital. These inputs are the factors of production, and their prices determine how income gets divided among workers, landowners, and capital owners.

Labor

Workers

Human effort firms hire. Price: the wage.

Land

Natural resources

Farmland, oil, natural resources. Price: the rental rate of land.

Capital

Machines, tools, buildings, trucks

Equipment workers use to produce output. Price: the rental price (per-period cost of using the machine, comparable to an hourly wage).

Derived demand. Firms hire labor because it produces something they can sell. Labor demand is derived from the demand for the output it produces. Same for land and capital.

Section 2

The Production Function and MPL

Start with Mankiw's apple orchard: fixed trees, variable workers. The production function maps workers to output: add workers, get more apples. But each new worker adds less than the last because they share the same trees and ladders. That's diminishing marginal product of labor.

Delta (Δ) just means "change in." So ΔQ / ΔL means: how much output changes when labor changes by one worker.

MPL = ΔQ / ΔL = the extra output from one more worker
Workers (L) Output (Q) MPL
00—
177
2136
3196
4256
5283
6291
7290

MPL falls as L rises — diminishing marginal product.

Concave shape = falling slope = falling MPL.

Section 3

Value of the Marginal Product → Labor Demand

MPL is measured in apples, bushels, or widgets. A firm needs dollars. The value of the marginal product of labor converts the extra output from one more worker into extra revenue.

VMPL = P × MPL

A competitive firm keeps hiring as long as the next worker adds more revenue than she costs:

Hire as long as VMPL > W
Stop hiring when VMPL = W
Equivalently P × MPL = W every worker earns her marginal value

Because MPL diminishes, VMPL slopes downward. At any wage, the firm hires the L where VMPL = W. This is the payoff: once the market settles, the wage is tied to the marginal worker's VMP. So the VMPL curve IS the labor-demand curve — the single most important insight of the chapter.

The firm reads the wage off the market and hires L* workers — the point where its VMPL curve crosses W.

Section 4

The Labor Supply Curve

Workers choose between work and leisure. The wage is the opportunity cost of leisure. Higher wages draw more workers (or more hours), so the labor supply curve slopes upward.

Things that shift the labor supply curve:

Tastes

Changes in preferences

More people preferring leisure → supply shifts left.

Alt. options

Changes in alternative opportunities

Workers leave for a booming rival industry → supply shifts left.

Immigration

Immigration

Immigrants enter → supply shifts right, wage falls, employment rises. The most-tested supply shift on exams.

Section 5

Labor Market Equilibrium: Wage = VMPL

Demand (VMPL) slopes down; supply slopes up. Where they cross: equilibrium wage W* and employment L*.

The equilibrium wage is set where labor demand = labor supply. Because demand is the VMPL curve, at equilibrium the wage equals the value of the marginal product of labor.

The central result: in equilibrium, W = VMPL = P × MPL. Each worker earns the market value of her marginal contribution.

Section 6

What Shifts Labor Demand and Labor Supply?

Changes to VMPL = P × MPL shift demand. Changes to workers' willingness to work shift supply.

Shock Shifts Direction
Output price P rises Labor demand Right (↑ VMPL)
New productive tech raises MPL Labor demand Right (↑ VMPL)
More capital / better tools per worker Labor demand Right (↑ MPL)
Immigration Labor supply Right (↓ W, ↑ L)
Workers leave for a booming rival industry Labor supply (this market) Left (↑ W, ↓ L)
Preference shift toward more leisure Labor supply Left (↑ W, ↓ L)

A productivity boost or a higher output price pushes the labor-demand curve right. Both the equilibrium wage and employment rise.

Productivity → wages. From 1960 to 2017, U.S. productivity and real wages rose roughly in step. As MPL grows, VMPL grows, and the wage follows.

Section 7

Land and Capital: Same Story, Different Factor

Same logic, different factor. Replace "one more worker" with "one more acre of land" or "one more machine." Find the extra output, turn it into dollars, and rent the factor up to the point where its VMP equals its rental price.

Land equilibrium Rentland = P × MPLand
Capital equilibrium Rentcap = P × MPK
The general rule Every factor earns its VMP in a competitive equilibrium

Each factor earns its marginal contribution. In the competitive model, wages, rents, and capital returns together account for the value of what is produced.

Factor markets are linked

A shock to one factor spills into the others, because factors are used together.

Hurricane example: a storm destroys half the ladders. Surviving ladders' rental price rises. But fewer ladders per worker → MPL falls → labor demand shifts left → wages fall.
Black Death, 1348. A third of Europe's workers die. Labor supply collapses → wages double. But fewer workers per acre → MP of land falls → rents drop 50%+. Workers got rich; landowners got poor.

Section 8

Key Takeaways

  • Factor demand is derived demand. Firms hire labor/rent capital because it produces sellable output.
  • Diminishing MPL → downward-sloping VMPL. Each extra worker adds less output. VMPL = P × MPL is the labor-demand curve.
  • W = VMPL in equilibrium. Every worker earns her marginal contribution. Productivity drives wages.
  • Shifts: immigration → supply right (↓W, ↑L). Productivity/output price → demand right (↑W, ↑L).
  • Same VMP logic for land and capital. Factor markets are linked — a shock to one ripples through the others.