MPL/PL = MPK/PKA bubble-tea shop pays $16/hour. Should it hire a fourth worker? The owner doesn't care about the worker's feelings about tapioca — she asks one question: will this worker bring in more than $16/hour of extra revenue? If the fourth worker adds 12 drinks an hour at $2 each, that's $24 > $16: hire. A fifth adds 7 drinks = $14 < $16: stop. You already know this logic — it's MR = MC wearing a hard hat. Factor markets (10–13% of the exam) reuse everything from Units 2–4 with inputs instead of outputs.
Demand for a factor (labor, land, capital) is derived demand — it exists only because the factor produces sellable output. Demand for baristas is derived from demand for lattes. If latte demand booms, barista demand follows.
MRP = MP × MR — the extra revenue from hiring one more unit. For a firm selling output in a perfectly competitive product market, MR = P, so MRP = MP × P.Hiring rule: employ factor units up to where MRP = MFC (for a competitive-labor-market firm: MRP = W).
| Workers | Output | MP | MRP (P = $2) | Hire at W = $16? |
|---|---|---|---|---|
| 1 | 20 | 20 | $40 | ✓ |
| 2 | 38 | 18 | $36 | ✓ |
| 3 | 52 | 14 | $28 | ✓ |
| 4 | 64 | 12 | $24 | ✓ |
| 5 | 71 | 7 | $14 | ✗ stop at 4 |
The firm's demand curve for labor IS its MRP curve — downward-sloping because of diminishing marginal product (and, for imperfectly competitive sellers, also because MR falls).
[GRAPH: Two panels. LEFT (Labor market): downward market labor demand D_L (ΣMRP), upward market labor supply S_L, equilibrium wage W = $16, employment L. RIGHT (Firm): horizontal line at W labeled "S_L = MFC = W" (perfectly elastic supply of labor to the firm); downward MRP curve labeled "D_L = MRP"; hiring at l where MRP = MFC.]
Mirror image of Lesson 9: the market sets the wage; the individual firm is a wage taker facing horizontal labor supply at W*.
Shifters: - Labor demand (MRP) shifts when: product price/demand changes, worker productivity changes (training, technology, more capital per worker), or the number of employers changes. - Labor supply shifts when: population/immigration, worker preferences, alternative opportunities in other markets change. - A wage change alone = movement along the curves (same grammar as Lesson 3).
A monopsony is a market with a single (or dominant) employer — the coal-town mine, the only hospital for 100 miles. It faces the whole upward-sloping market labor supply: to hire one more worker it must raise the wage — for everyone already employed. So the marginal cost of an extra worker exceeds the new worker's wage:
MFC lies above the labor supply curve (exactly parallel to monopoly's "MR below demand," flipped to the buying side).
[GRAPH: Monopsony. X-axis "Labor", Y-axis "Wage". Upward S_L; steeper MFC above it; downward MRP. Hiring Lm where MRP = MFC; wage Wm read DOWN from Lm to the SUPPLY curve — below the competitive wage Wc at Lc (where MRP crosses S_L). Gap between MRP(Lm) and Wm visible.]
Monopsony two-step: (1) hire where MRP = MFC → Lm; (2) pay the wage from the supply curve at Lm → Wm.
Results vs. a competitive labor market: fewer workers hired (Lm < Lc), lower wage (Wm < Wc), and W < MRP (workers paid less than the revenue their marginal colleague generates). Deadweight loss appears just like monopoly's.
Minimum wage twist: in a competitive labor market a binding minimum wage causes unemployment (Lesson 5). In a monopsony, a minimum wage set between Wm and Wc flattens the MFC (the firm can hire additional workers at the set wage without raising everyone's pay) and can raise both wages and employment — a favorite AP curveball.
When a firm chooses between labor and capital, cost is minimized where the last dollar spent on each input yields equal marginal product:
MP_L / P_L = MP_K / P_K
Same logic as the consumer's utility-max rule with MP replacing MU. If MP_L/P_L > MP_K/P_K, shift dollars toward labor. (Least-cost gets you the cheapest way to make any output; the profit-maximizing level of each input is still MRP = MFC for each.)
Product price $5 (competitive). Wage $60/day. MP of workers 1–5: 20, 16, 12, 8, 6. How many workers?
Solution: MRP: 100, 80, 60, 40, 30. Hire while MRP ≥ W ($60) → 3 workers (3rd worker's MRP = 60 = W; 4th's 40 < 60).
Interpretation: Exactly the taco-truck logic; the table is the answer if you build the MRP column.
Wages in the strawberry-picker market. The retail price of strawberries doubles. Trace the effects.
Solution: Pickers' MRP = MP × P doubles at every quantity → labor demand shifts right → equilibrium wage ↑ and employment ↑.
Interpretation: Derived demand in action: the product price moved the factor market. (A wage change never shifts labor demand — that's the movement-along trap again.)
The only hospital in Milltown hires nurses. Labor supply: (W, L) = ($20, 2), ($25, 3), ($30, 4), ($35, 5). MRP: 3rd nurse = $45, 4th = $40, 5th = $30. Compute MFC and find employment and wage.
Solution: Total labor cost: 2 nurses × $20 = $40; 3 × $25 = $75; 4 × $30 = $120; 5 × $35 = $175. MFC: 3rd nurse = 75 − 40 = $35; 4th = 120 − 75 = $45; 5th = 175 − 120 = $55. Compare MRP: 3rd (45 ≥ 35 ✓), 4th (40 < 45 ✗). Hire 3 nurses, pay the supply-curve wage: $25. Note MFC(3) = $35 > W = $25, and MRP(3) = $45 > wage paid — the monopsony wedge.
Interpretation: MFC from totals, always — the jump in the whole wage bill, not just the new hire's wage.
MP_L = 40, wage = $8; MP_K = 90, rental rate = $15. Cost-minimizing?
Solution: Labor: 40/8 = 5 output per $. Capital: 90/15 = 6 per $. Not minimized → use more capital, less labor until ratios equalize (diminishing returns lowers MP_K, raises MP_L).
Interpretation: Identical mechanics to MU/P — compare per-dollar, shift toward the bigger number.
1. (E) Factors are wanted only for what they produce — demand passes through from the product market.
2. (C) MRP = MP × MR (with MR = P under competitive selling).
3. (A) MRP = MFC; with competitive hiring, MFC = W → MRP = wage.
4. (B) MRP: 80, 60, 48, 40, 24. Hire through worker 3 (MRP = 48 = W); worker 4's 40 < 48.
5. (C) Productivity ↑ → MP ↑ → MRP ↑ at every level → demand right. (A) shifts it left; (B) is along-the-curve; (D) shifts supply.
6. (D) The wage raise for incumbents piggybacks on each new hire — total cost jumps by more than the new wage.
7. (D) Restrict hiring where MRP = MFC (< competitive L), pay off the lower supply curve.
8. (C) Equal marginal product per dollar = least-cost condition satisfied.
9. (B) The minimum wage flattens MFC up to the set wage, removing the raise-everyone penalty — the firm hires more while paying more, up toward the competitive outcome.
10. (FRQ rubric, 9 points) - (a) 2 pts: MP: 15, 13, 10, 7, 5 (1). MRP (× $10): 150, 130, 100, 70, 50 (1). - (b) 2 pts: 4 workers (1) — hire while MRP ≥ W: the 4th worker's MRP ($70) just equals the $70 wage; the 5th ($50 < 70) is unprofitable (1). - (c) 2 pts: 3 workers (1) — at W = 95, MRP(3) = 100 ≥ 95 but MRP(4) = 70 < 95; same MRP = W rule at the higher wage (1). - (d) 3 pts: Market panel: downward D_L, upward S_L, W = 70, L (1). Firm panel: horizontal S_L = MFC = W at $70 (1); downward MRP with l* = 4 at the intersection (1).
10. (FRQ-style) GadgetCo sells widgets in a perfectly competitive product market at $10 each and hires workers in a perfectly competitive labor market at $70 per day.
| Workers | Total output |
|---|---|
| 1 | 15 |
| 2 | 28 |
| 3 | 38 |
| 4 | 45 |
| 5 | 50 |
(a) Calculate the marginal product and marginal revenue product of each worker. (b) How many workers does GadgetCo hire? Explain using the hiring rule. (c) The market wage rises to $95. How many workers now? What rule did you apply? (d) Draw side-by-side graphs of the labor market and GadgetCo's hiring decision at the original $70 wage, labeling the market wage W, market employment L, the firm's labor supply curve, its MRP curve, and its employment level l*.
1. (E) Factors are wanted only for what they produce — demand passes through from the product market.
2. (C) MRP = MP × MR (with MR = P under competitive selling).
3. (A) MRP = MFC; with competitive hiring, MFC = W → MRP = wage.
4. (B) MRP: 80, 60, 48, 40, 24. Hire through worker 3 (MRP = 48 = W); worker 4's 40 < 48.
5. (C) Productivity ↑ → MP ↑ → MRP ↑ at every level → demand right. (A) shifts it left; (B) is along-the-curve; (D) shifts supply.
6. (D) The wage raise for incumbents piggybacks on each new hire — total cost jumps by more than the new wage.
7. (D) Restrict hiring where MRP = MFC (< competitive L), pay off the lower supply curve.
8. (C) Equal marginal product per dollar = least-cost condition satisfied.
9. (B) The minimum wage flattens MFC up to the set wage, removing the raise-everyone penalty — the firm hires more while paying more, up toward the competitive outcome.
10. (FRQ rubric, 9 points) - (a) 2 pts: MP: 15, 13, 10, 7, 5 (1). MRP (× $10): 150, 130, 100, 70, 50 (1). - (b) 2 pts: 4 workers (1) — hire while MRP ≥ W: the 4th worker's MRP ($70) just equals the $70 wage; the 5th ($50 < 70) is unprofitable (1). - (c) 2 pts: 3 workers (1) — at W = 95, MRP(3) = 100 ≥ 95 but MRP(4) = 70 < 95; same MRP = W rule at the higher wage (1). - (d) 3 pts: Market panel: downward D_L, upward S_L, W = 70, L (1). Firm panel: horizontal S_L = MFC = W at $70 (1); downward MRP with l* = 4 at the intersection (1).
Exam tip: Factor-market questions are Units 2–4 with the labels swapped: MRP plays demand, MFC plays supply/marginal cost, and monopsony is monopoly in a mirror (quantity at the intersection, then jump down to the supply curve for the wage, just as monopoly jumps up to demand for the price). If you can do Lessons 9–10, you can do this — translate, don't relearn.