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 until now has been about output markets — firms selling apples, tacos, monopoly smartphones. Chapter 18 flips the picture. Now we stare at the input markets: the markets where firms buy labor, rent land, and rent capital. These inputs are called the factors of production, and together their prices determine how the total value produced in the economy gets divided up among workers, landowners, and capital owners.

Labor

Workers

The hours of human effort firms hire. Its price is the wage. Labor earns roughly two-thirds of U.S. national income.

Land

Natural resources

Acres of farmland, oil in the ground, the space under a city block. Its price is the rental rate of land.

Capital

Machines, tools, buildings, trucks

The stock of equipment that workers use to produce output. Capital has two prices: the purchase price (buying the machine outright) and the rental price (paying per hour of use). Factor-market analysis uses the rental price, because that's what a firm pays to get one more hour of the machine's services — directly comparable to an hourly wage.

Derived demand. Factor demand isn't like consumer demand for pizza. Nobody hires a worker because the worker is fun to have around — firms hire labor because it helps produce something valuable to sell. The demand for labor is derived from the demand for the output it produces. Same story for land and capital.

Section 2

The Production Function and MPL

Mankiw starts with an apple orchard. Suppose the orchard has a fixed number of trees, and the only input the owner varies is the number of workers. The relationship between labor L and output Q is the production function Q = f(L).

As more workers are added, output grows — but not forever. The first few workers each add a lot of apples. The tenth worker has to share ladders and trees with everyone else, so she adds fewer. This is diminishing marginal product of labor: each additional worker contributes a little less than the previous one.

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

Output rises but its growth slows. That's diminishing MPL in a table.

The production function is concave: each additional worker still adds output, but adds less than the one before. The slope = MPL, and it's falling.

Section 3

Value of the Marginal Product → Labor Demand

A firm hires workers because each one adds revenue. How much revenue? That's the value of the marginal product of labor: the extra output a worker produces, times the price of that output.

VMPL = P × MPL

A profit-maximizing competitive firm keeps hiring as long as the next worker adds at least as much revenue (VMPL) as she costs (the wage W). So the profit-max rule for labor is:

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

Here's the clean punchline: because MPL is diminishing, VMPL is also diminishing. Plot VMPL against L and you get a downward-sloping curve. At any given wage, the firm picks the L where VMPL = W. So the firm's VMPL curve IS its labor-demand curve. That's 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.

Heads up on vocabulary: some books write MRPL (marginal revenue product) instead of VMPL. For a firm selling in a competitive output market they're the same, because MR = P. For a monopolist they'd differ because MR < P. Mankiw and this course assume the output market is competitive, so we'll just write VMPL = P × MPL.

Section 4

The Labor Supply Curve

Labor supply comes from individual workers' choices about how to split their time between work and leisure. Going to your shift earns a wage; staying home surfing the web earns you leisure. Every extra hour at work is an hour not enjoying leisure, so the wage is the opportunity cost of leisure.

For most of the chapter we assume that higher wages lead people to supply more hours — the labor supply curve slopes upward. Why? A higher wage makes working relatively more attractive than goofing off, so workers substitute some leisure hours for work hours. Mankiw notes in passing that at very high wages the income effect can dominate and the curve can bend backward, but don't worry about that edge case until Chapter 21.

Things that shift the labor supply curve:

Tastes

Changes in preferences

More parents deciding to stay home raising kids shifts labor supply left. Improvements in childcare availability shift it right.

Alt. options

Changes in alternative opportunities

If the computer industry booms and pencil workers switch careers, the labor supply in the pencil market shifts left.

Immigration

Immigration

When immigrants enter a labor market, the supply of labor in that market shifts right. This pushes the equilibrium wage down and employment up — and it's the single most-tested example of a labor-supply shift on exams.

Section 5

Labor Market Equilibrium: Wage = VMPL

Now put the two curves on one graph. The wage is on the y-axis and the quantity of labor is on the x-axis. Demand (the VMPL curve) slopes down; supply slopes up. Where they cross is the equilibrium wage W* and equilibrium 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 Ch 18 result: in equilibrium, W = VMPL = P × MPL. Each worker earns the market value of her own marginal contribution. This isn't just an accounting identity — it's what "competitive labor market" means. If the wage were lower, firms would bid it up to capture the leftover value. If it were higher, firms would fire workers whose VMPL fell below their wage.

Section 6

What Shifts Labor Demand and Labor Supply?

Anything that changes VMPL = P × MPL shifts labor demand. Anything that changes workers' willingness to work at each wage shifts labor supply. Here's the menu for exams.

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. Mankiw points out that from 1960 to 2017, productivity in the U.S. rose roughly in step with real wages. Periods of rapid productivity growth were also periods of rapid wage growth. That's the labor-demand shift playing out over decades: as MPL grows, VMPL grows, and in a competitive labor market the wage grows with it.

Section 7

Land and Capital: Same Story, Different Factor

Everything we just said about labor applies, with one word swapped, to land and capital. Firms rent land and rent machines up to the point where each factor's marginal contribution to revenue 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

So: workers are paid their marginal contribution, landowners are paid their land's marginal contribution, and capital owners are paid their machines' marginal contribution. Whatever output is left over is exactly zero — there's nothing unclaimed. That's a mathematical identity for constant-returns production functions (the Cobb–Douglas framework Mankiw uses in Problem 9).

Factor markets are linked

Here's the subtle part of Ch 18 that shows up on exams. A shock in one factor market spills over into all the others, because the factors are used together in production.

Mankiw's hurricane example: a storm destroys half the ladders in the apple-picking industry. The rental price of surviving ladders rises (supply of ladders fell, demand didn't). But with fewer ladders to work with, each worker's MPL falls — there are only so many trees she can reach bare-handed. So labor demand shifts left and the wage falls. Owners of undamaged ladders win; workers lose.
Black Death, 1348–1350. A plague wipes out a third of Europe's population, mostly workers. Labor supply collapses → wages approximately double. But with fewer workers per acre, the marginal product of land falls → demand for land drops and rents fall by more than 50%. The peasant classes got rich; landowners got poor. Mankiw uses this as the historical test case for the Ch 18 framework.

Section 8

Key Takeaways

  • Factor markets = markets for inputs. Labor, land, and capital are the three factors of production. Their prices (wages, land rent, capital rental) determine who gets the income produced.
  • Factor demand is derived demand. Firms don't want workers or machines for their own sake — they want them because they produce output that the firm can sell.
  • Diminishing MPL. As more workers are added to fixed capital, each one adds less output than the last. The production function is concave.
  • VMPL = P × MPL is the firm's labor-demand curve. The firm hires workers up to the point where VMPL = W. Because MPL is falling, VMPL is a downward-sloping curve.
  • W = P × MPL in equilibrium. In a competitive labor market, the wage equals the value of the marginal product of labor. Every worker earns exactly her marginal contribution.
  • Immigration shifts labor supply right → wages fall and employment rises. Productivity gains and output-price increases shift labor demand right → wages rise and employment rises.
  • Same logic for land and capital. Every factor earns its VMP in equilibrium. Factor markets are linked — a shock to one (a hurricane destroying ladders, a plague killing workers) ripples through the others.