Firms buy labor the way they make output: one more unit at a time (Profit-Maximizing Output: MR = MC). What a worker is worth to the firm depends on how much the worker adds to output, marginal product from Short-Run Production, and what that output sells for.
Key idea
The marginal revenue product of labor is the extra revenue from one more worker: $$MRP = MP \times MR,$$ which is $MP \times P$ when the firm sells its output in a competitive market. A firm hires workers as long as $MRP \ge$ the wage, and stops where $MRP = W$. The MRP curve is the firm's demand curve for labor.
Why it works
A new worker adds MP units of output, and each sells for P (or brings in MR), so the worker adds $MP \times P$ to revenue. The worker costs the wage. If the worker brings in more than the wage, hiring adds to profit; if less, it subtracts. Because marginal product eventually falls, MRP falls too, so the firm hires up to the point where the last worker's MRP just covers the wage. That's why labor demand is a derived demand: it comes from the demand for what the workers make.
| Workers | TP | MP | MRP at \$5 |
|---|---|---|---|
| 1 | 10 | 10 | \$50 |
| 2 | 24 | 14 | \$70 |
| 3 | 36 | 12 | \$60 |
| 4 | 44 | 8 | \$40 |
| 5 | 48 | 4 | \$20 |
| 6 | 50 | 2 | \$10 |
Worked example: How many to hire
Using the table, how many workers should the bakery hire at a wage of \$30 a day?
- MRP is MP times \$5: \$50, \$70, \$60, \$40, \$20, \$10.
- Workers 1 to 4 each bring in at least \$30; worker 5 brings in only \$20.
- Hire 4 workers.
Answer: 4 workers.
Worked example: The wage changes
The wage falls to \$15. Now how many? What kind of change is this on the labor demand curve?
- Worker 5's MRP (\$20) now covers the wage; worker 6's (\$10) doesn't.
- Hire 5. A wage change moves the firm along its labor demand (MRP) curve.
Answer: 5 workers; a movement along the curve.
Common mistake
Comparing the wage with marginal product in units of output ("the 5th worker makes 4 loaves, and the wage is \$15, so…"). Loaves and dollars can't be compared. Multiply MP by the price (or MR) first. Check: both sides of the comparison should be in dollars.
If the firm has market power where it sells, it must cut its price to sell more, so it uses $MRP = MP \times MR$, which is smaller than $MP \times P$.