Monopsony Graph: Marginal Factor Cost, Wages and the Minimum Wage

On a small island, one fish cannery does nearly all the hiring. It wants more workers, yet it keeps its wages low. Why? Stranger still: on that island, a minimum wage could mean more jobs, not fewer. This is Module 5.4, monopsony.

A monopsonist is the single buyer of a factor of production. A market with one is a monopsony. Our cannery is the island's only buyer of labor. Monopsony is imperfect competition, like monopoly, but in a factor market, and the power sits with the buyer.

Quick refresher from Module 5.1, part two: a firm in a competitive labor market is a wage taker. At a $20 market wage, each extra worker costs $20, so its MFC is flat at the wage.

The cannery is different. As the only buyer, it faces the market's upward-sloping labor supply curve: to hire one more worker, it must offer a higher wage. And it must pay that higher wage to every worker, not just the new one.

Here's its wage schedule. One worker will come for $16 an hour, and each extra worker needs $2 more, so five workers need $24.

Quick refresher: the total wage bill is the wage times the number of workers. Four workers at $22 is $88; five at $24 is $120.

Marginal factor cost, MFC, is what one more worker adds to the total wage bill. For the fifth worker: $120 minus $88 is $32. Why $32, when her wage is only $24? Her own $24, plus a $2 raise for each of the 4 workers already there: $8. $24 plus $8 is $32. Fill the column: $16, $20, $24, $28, $32. The wage climbs $2 per worker, but MFC climbs $4. After the first worker, MFC is always above the wage.

So what just happened? One: each extra worker needs a $2 higher wage. Two: everyone gets the raise, so the fifth worker costs $24 plus $8: $32. Three: MFC sits above the wage, climbing twice as fast.

Sound familiar? It's the monopoly story, flipped.

Quick refresher from Module 4.2: to sell one more, a monopolist cuts its price on every unit. Four at $10 is $40; five at $9 is $45. The fifth adds just $5, so MR lies below demand.

To hire one more, a monopsonist raises everyone's wage, so MFC lies above supply. Both start at the first worker, $16, and MFC rises twice as steeply. That gap is the sign of market power.

So how many workers does it hire? Add the cannery's marginal revenue product curve, MRP, sloping down.

Quick refresher from Module 5.1, part one: MRP is marginal product times marginal revenue. The cannery sells cans at a market price of $2, so MR is $2. The fourth worker adds 17 cans an hour: 17 times $2 is $34.

It keeps hiring while MRP is above MFC, right up to where they meet. Fourth worker: MRP $34, MFC $28, so hire. Sixth: MRP $30, MFC $36, so stop. They meet at 5 workers and $32: QM is 5. Now the wage. Don't read it at that crossing. Drop straight down to the supply curve: 5 workers will work for $24. So WM, the wage, is $24. So the fifth worker adds $32 to revenue but is paid $24: less than both her MFC and her MRP. Exam trap: QM is where MRP meets MFC, not where MRP meets supply. On a recent AP exam, the supply crossing was the mistake that cost this point.

Exam trap two: the wage comes from the supply curve at QM, never from MRP or the crossing's height. On a recent AP exam, only about half of students earned that point. In a competitive labor market, the wage and quantity would sit where supply meets MRP: 7 workers at $28, called QC and WC. So the monopsonist hires 2 fewer workers, and pays $4 less an hour. That answers our first question: each new hire means a raise for everyone, so the cannery stops early and keeps wages low.

So what just happened? One: MRP meets MFC at 5 workers. Two: straight down to supply, the wage is $24. Three: a competitive market would hire 7 at $28: monopsony means fewer workers, lower pay.

Now add a minimum wage, a price floor on wages.

Quick refresher from Module 2.8B: in a competitive labor market, a minimum wage above equilibrium is a binding floor. Say 60 people want jobs but firms fill only 40: 20 are unemployed.

A floor's effect depends on the market structure. In a monopsony, it changes MFC. Case one, the case a recent AP exam used: a minimum above the competitive wage, say $34. Up to the 10 workers who'll come at $34, each new worker costs exactly $34, with no raises. MFC is flat at $34. So it hires where MRP equals $34: 4 workers. Since $34 is above even the fifth worker's $32 MRP, hiring falls from 5 to 4, and the wage rises from $24 to $34. The total wage bill is the minimum wage times the new number of workers: $34 times 4 is $136.

So what just happened? One: a $34 minimum makes MFC flat at $34. Two: MRP equals $34 at 4 workers, so the cannery hires 4. Three: the wage bill is $34 times 4: $136.

Case two, from your textbook: a minimum between the monopsony and competitive wages, say $26. Six workers will come for $26, so each of the first 6 costs just $26. MFC is flat out to supply, then jumps back up to the old MFC. The sixth worker's MRP, $30, beats her $26 cost, so she's hired. A seventh means raising everyone's pay again: a $40 MFC for a $28 MRP. So: 6 workers, not 5, at $26, not $24. That answers our second question: more jobs and higher pay. A recent AP exam scored case one; case two comes from your textbook.

So what just happened? One: a $26 minimum lets the cannery hire 6 without raising anyone else's pay. Two: the sixth worker's $30 MRP beats $26. Three: hiring rises from 5 to 6.

One more change, with no minimum wage. Say demand for canned fish rises. Its price and MR rise, so every worker's MRP rises, and labor demand, the MRP curve, shifts right. Now MRP meets MFC at 6 workers, where MFC is $36. The last worker's MFC rose from $32 to $36, because hiring more means climbing the MFC curve.

So what just happened? One: higher fish demand raised MRP. Two: the cannery now hires 6. Three: the last worker's MFC rose from $32 to $36.

Exam trap: when MRP rises, the last worker's MFC is higher. MFC is a production cost, so don't say cost stays the same. And answer with MRP and MFC, not MR and MC.

Exam moment: two questions the way the AP exam asks them, then one free-response part.

Question 1. An orchard, the only employer of fruit pickers in a valley, pays all its pickers the same wage. To hire 3 pickers it must pay $18 an hour; to hire 4, $21 an hour. What is the marginal factor cost of the 4th picker? A) $3 B) $9 C) $21 D) $30 E) $84

The answer is D. The wage bill goes from 3 times $18, $54, to 4 times $21, $84: $30 more. That's her own $21 plus a $3 raise for each of the 3 others. A is the raise alone. B is the raises without her wage. C is her wage alone, a competitive firm's MFC. E is the whole wage bill, not the change.

Question 2. A profit-maximizing shipyard is the only employer of welders in a coastal town. Its labor market is on the graph. How many welders does it hire, and what hourly wage does it pay? A) 12 welders at $48 B) 8 welders at $36 C) 6 welders at $48 D) 6 welders at $36 E) 6 welders at $30

The answer is E. MRP meets MFC at 6 welders, so the shipyard hires 6. Then straight down to supply: 6 welders will work for $30. A goes across to supply, not down. B is the competitive outcome, where supply meets MRP. C reads the wage at the MFC crossing. D pairs the right number with the competitive wage.

Free response, 1 point. Use the shipyard's graph. The government sets a minimum wage of $54 an hour for welders. Calculate the shipyard's total wage bill at its new profit-maximizing number of welders. Show your work.

What earns the point: the work and the answer. MRP equals $54 at 5 welders, so the shipyard hires 5. Wage bill: $54 times 5 equals $270. The costly mistake: keeping the old 6 welders or the old $30 wage, like $54 times 6. On a recent AP exam, only about four students in ten earned this point.

So what earned the point? One: MRP equals the $54 minimum at 5 welders. Two: the wage bill is $54 times 5. Three: $270.

Recap: each hire means a raise for everyone, so MFC lies above supply. A monopsonist hires where MRP equals MFC and pays the wage on supply: fewer workers, lower pay. A minimum wage changes MFC: above the MRP at QM, it cuts hiring; between WM and WC, it raises hiring. Next: the Unit 5 review, worked.