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Derived demand, MRP, MFC, wage determination, monopsony, and labor unions
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Factor markets โ for labor, capital, and land โ 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 โ derived from the demand for the goods that input produces.
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:
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?
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For a perfectly competitive output market, , so . For a monopolist seller, โ MRP is lower than for a perfect competitor with the same physical productivity.
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.
Most labor supply curves slope upward โ 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.
In a competitive labor market, and are set where supply. Two important imperfections:
Each worker's wage in a competitive market reflects their MRP โ productivity and the value of what they produce. Differences in wages across occupations reflect differences in productivity, education, risk, and demand for the output.
MRP_L = MP_L \times P = 8 \times \5 = \boxed{$40}$ per day.
Compare to wage: MRP_L = \40 > w = $30 โ **hire the third worker** (adds \10 to profit).
Why is the demand for labor called a "derived" demand?
Firms don't hire workers for their own sake โ 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.
A coffee shop's hiring schedule:
| Workers | Total cups/hr | Cup price | ||
|---|---|---|---|---|
| 1 | 20 | $3 | โ | โ |
| 2 | 36 | $3 | ||
| 3 | 48 | $3 | ||
| 4 | 56 | $3 | ||
| 5 | 60 | $3 |
Fill in and . If the wage is $30/hr, how many workers should the shop hire?
| Workers | (3$) |
|---|
In a small town, the only large employer is a meat-packing plant โ 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.
(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 โ there are mutually beneficial hires the firm refuses to make. Deadweight loss is positive.
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.
MRP-based (demand-side) explanations:
Supply-based explanation: 4. Restricted supply into A โ 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.
| 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.