Labor Markets & Factor Pricing
Derived demand, MRP, MFC, wage determination, monopsony, and labor unions
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Labor Markets and Factor Markets
Factor markets — for labor, capital, and land — determine the prices of inputs ( for wages, for rent, etc.) and the quantities employed. The same demand-and-supply logic applies, but with one key twist: the demand for an input is a derived demand — derived from the demand for the goods that input produces.
The Marginal Revenue Product (MRP)
A profit-maximizing firm hires another worker only if the worker adds AT LEAST as much to revenue as to cost. The extra revenue is the marginal revenue product of labor:
For a perfectly competitive output market, , so . For a monopolist seller, ⇒ MRP is lower than for a perfect competitor with the same physical productivity.
The Hiring Rule
Hire labor up to the point where equals the marginal resource cost of labor, which equals the wage in a perfectly competitive labor market:
This means the firm's individual labor demand curve IS its curve. Market labor demand sums these across firms.
Shifters of Labor Demand
- A change in the price of the output (output price up ⇒ MRP up ⇒ labor demand right).
- A change in productivity (better technology ⇒ MP up ⇒ MRP up ⇒ labor demand right).
- A change in the price of related inputs (substitutes vs complements in production).
Labor Supply
Most labor supply curves slope upward — higher wages attract more workers (and more hours). At very high wages a backward-bending supply can occur (income effect dominates substitution effect).
Shifters of labor supply: changes in population, immigration, preferences for leisure vs work, opportunities in alternative jobs.
Equilibrium and Imperfections
In a competitive labor market, and are set where supply. Two important imperfections:
- Minimum wage above : causes unemployment (labor surplus).
- Monopsony: a single buyer of labor (e.g., the only large employer in town). Hires LESS labor at LOWER wages than competition, because the firm faces an upward-sloping labor supply curve and so . Both wage and quantity are inefficiently low.
Income Distribution
Each worker's wage in a competitive market reflects their MRP — productivity and the value of what they produce. Differences in wages across occupations reflect differences in productivity, education, risk, and demand for the output.
📚 Practice Problems
1Problem 1easy
❓ Question:
A perfectly competitive firm sells widgets at $5 each. The marginal product of the third worker is 8 widgets per day. Compute that worker's . If the daily wage is $30, should the firm hire the third worker?
💡 Show Solution
MRP_L = MP_L \times P = 8 \times \5 = \boxed{$40}$ per day.
Compare to wage: MRP_L = \40 > w = $30 ⇒ **hire the third worker** (adds \10 to profit).
2Problem 2easy
❓ Question:
Why is the demand for labor called a "derived" demand?
💡 Show Solution
Firms don't hire workers for their own sake — they hire them to produce goods that consumers will buy. Demand for labor therefore DERIVES from (depends on) the demand for the output the labor produces. If demand for the output rises, output price rises, MRP rises, and labor demand shifts right.
3Problem 3medium
❓ Question:
A coffee shop's hiring schedule:
| Workers | Total cups/hr | Cup price | ||
|---|---|---|---|---|
| 1 | 20 | $3 | — | — |
| 2 | 36 | $3 | ||
| 3 | 48 | $3 | ||
| 4 | 56 | $3 | ||
| 5 | 60 | $3 |
Fill in and . If the wage is $30/hr, how many workers should the shop hire?
💡 Show Solution
| Workers | (MP \times \3$) | |
|---|---|---|
| 2 | 16 | $48 |
| 3 | 12 | $36 |
| 4 | 8 | $24 |
| 5 | 4 | $12 |
Hire while MRP_L \ge w = \30. Worker 3 adds \36 (yes); worker 4 adds $24 (no). Hire 3 workers.
4Problem 4medium
❓ Question:
In a small town, the only large employer is a meat-packing plant — a monopsonist in the labor market. Compared to a perfectly competitive labor market with the same labor supply curve and the same MRP curve, predict the differences in (a) the wage paid, (b) the quantity of labor hired, and (c) economic efficiency.
💡 Show Solution
(a) The monopsonist faces an UPWARD-SLOPING labor supply, so hiring one more worker requires raising wages for all workers. Marginal resource cost () lies ABOVE the supply curve. The firm hires where , then pays the wage on the supply curve at that quantity. Wage is LOWER than the competitive wage.
(b) Quantity of labor hired is LOWER than competitive level. Both effects flow from .
(c) Inefficient. At the monopsony quantity, , meaning workers value the wage less than the firm values their output — there are mutually beneficial hires the firm refuses to make. Deadweight loss is positive.
5Problem 5hard
❓ Question:
Two professions have similar education requirements and similar working hours, but profession A pays double profession B in equilibrium. List THREE possible MRP-based explanations and ONE supply-based explanation. State, for each, whether you would expect the wage gap to persist in the long run if the explanation is the dominant one.
💡 Show Solution
MRP-based (demand-side) explanations:
- Output of A is more valuable. Higher product price ⇒ higher MRP. Persistent only if the price difference persists (e.g., A serves a high-WTP market like specialty surgery).
- A workers have higher physical productivity. Better technology, scarce skill, or stronger network effects. Persistent if the productivity advantage is hard to replicate.
- A is a complement to expensive capital (e.g., piloting commercial jets). MRP is high because the capital makes each labor hour more valuable. Persistent as long as the capital structure stays.
Supply-based explanation: 4. Restricted supply into A — long training, licensing barriers, talent constraint, or large compensating differential (risk, unpleasantness). Persistent only if entry barriers persist; if they erode (deregulation, more graduates), the gap shrinks.
In the long run, gaps explained by replicable productivity or removable barriers tend to compress, while gaps grounded in genuine output-market valuation differences persist.
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