Monopsony

A monopsony is a labour market with a single buyer of labour. More generally, a firm has monopsony power whenever it faces an upward-sloping labour supply curve, so that hiring more workers means paying a higher wage. A monopsonist that pays everyone the same wage hires where the value of the marginal product equals the marginal cost of labour, which leaves it with fewer workers, paid less, than a competitive market would have.

Why hiring costs more than the wage

A competitive firm is one of many employers and can hire as many workers as it likes at the going wage: the supply curve it faces is flat. A monopsonist, such as the mine in a one-employer coal town, faces the market’s upward-sloping supply curve. To attract one more worker it must offer a higher wage, and if it pays everyone the same wage, it must raise the pay of everyone it already employs. The marginal cost of labour, $MC_E$, is the new worker’s wage plus the raise for everyone else, so it exceeds the wage.

Workers, E	Wage needed to attract E workers ($ per hour)	Total labour cost, wE	Marginal cost of labour, $MC_E$	Value of marginal product, $VMP_E$
1	10	10	10	30
2	12	24	14	26
3	14	42	18	22
4	16	64	22	18
5	18	90	26	14

Hiring the fourth worker means paying that worker 16 dollars and paying the three existing workers 2 dollars more each: $16 + 3 \times 2 = 22$. The gap between $MC_E$ and the wage grows with each hire, so the marginal cost curve lies above the supply curve and rises more steeply. For a linear supply curve $w = c + dE$, total labour cost is $cE + dE^2$ and

$$MC_E = c + 2dE,$$

twice as steep as supply.

The nondiscriminating monopsonist

A nondiscriminating monopsonist pays all its workers the same wage. It hires until the last worker adds as much to revenue as to cost:

$$VMP_E = MC_E.$$

That fixes employment at $E_M$, point A in Figure 1. The wage is the lowest that attracts $E_M$ workers, read off the supply curve: $w_M$. Three results follow.

1. Too few workers. Competitive firms with the same curves would hire $E^*$, where $VMP_E$ meets supply. The monopsonist stops short because each extra hire raises its whole wage bill.
2. Pay below productivity. At $E_M$ the wage is below the value of the marginal product. The gap, $VMP_E - w_M$, is the markdown. It is larger the less elastic the supply of labour to the firm.
3. A deadweight loss. Workers between $E_M$ and $E^*$ would produce more than their reservation wages but are not hired. The triangle between $VMP_E$ and supply over those workers is lost.

Slope of the labour supply curve

0.25

Elasticity of labour supply at 60 workers

1.3

Employment, monopsony (competitive: 60)

40.0

Wage, monopsony (competitive: $20)

$15.00

Markdown, VMP_E − w_M

$10.00

Deadweight loss (per hour)

$100

Open in Graph Lab

Figure 1. A nondiscriminating monopsonist hires where $MC_E$ meets $VMP_E$ (point A): 40 workers at a wage of $15, although the 40th worker's output is worth $25. A competitive market with the same curves would employ 60 workers at $20. The flatter the supply curve facing the firm, the closer the monopsony outcome comes to the competitive one.

The perfectly discriminating monopsonist

A perfectly discriminating monopsonist pays each worker exactly their reservation wage. Hiring one more worker then costs only that worker’s wage, because nobody else’s pay changes, so the supply curve is the marginal cost curve. The firm hires until $VMP_E$ equals the supply price, which is the competitive employment level $E^*$.

• Employment is efficient, so there is no deadweight loss.
• Every worker earns their reservation wage, so worker surplus is zero and the firm keeps the entire surplus.

Perfect wage discrimination is mainly a benchmark. A firm rarely knows each worker’s reservation wage, and paying equally productive workers different wages is hard to sustain when pay is visible or set by a collective agreement.

Perfect wage discrimination (0 = no, 1 = yes)

0

Workers hired

40

Wage of the last worker hired

$15.00

Producer surplus (per hour)

$600

Worker surplus (per hour)

$200

Deadweight loss (per hour)

$100

Open in Graph Lab

Figure 2. The same market under the two wage policies. The nondiscriminating monopsonist hires 40 workers at $15: producer surplus is $600 an hour, worker surplus $200 and the deadweight loss $100. The perfectly discriminating monopsonist hires the competitive 60 workers, there is no deadweight loss, and the firm keeps all $900 of surplus.

Key idea

A perfectly discriminating monopsonist hires the efficient number of workers and keeps all the surplus. A nondiscriminating monopsonist hires too few, because each hire raises everyone’s wage, so $MC_E$ lies above the supply curve.

A minimum wage can raise employment

A minimum wage $\bar w$ changes the monopsonist’s marginal cost. Up to the number of workers willing to work at $\bar w$, everyone is paid $\bar w$ whatever the firm does, so one more hire costs exactly $\bar w$. The marginal cost curve becomes flat at $\bar w$ until it reaches the supply curve, then jumps up to the old $MC_E$. The firm hires where $VMP_E$ meets this new marginal cost curve.

• Minimum wage at or below $w_M$. The law does not bind and employment stays at $E_M$.
• Minimum wage between $w_M$ and $w^*$. The firm hires everyone willing to work at the minimum wage. Wages and employment both rise, along the supply curve, and at $w^*$ the market reaches the competitive outcome.
• Minimum wage above $w^*$. The firm hires where $VMP_E$ equals the minimum wage, so employment falls as the minimum rises and some people who want jobs cannot get them. Employment stays above $E_M$ until the minimum wage reaches the value of the marginal product at $E_M$; beyond that it falls below the monopsony level.

Minimum wage

$18.00

Workers hired

52.0

Wage

$18.00

Change in employment from 40

12.0

Willing to work but not hired

0.0

Open in Graph Lab

Figure 3. A minimum wage imposed on the monopsonist of Figure 1. At $18 the firm hires 52 workers instead of 40 and pays $18 instead of $15. Employment peaks at the competitive 60 workers when the minimum is $20, falls along $VMP_E$ above $20, and drops below 40 once the minimum exceeds $25.

Minimum wage

$18.00

Employment, competitive market

60.0

Employment, monopsony

52.0

Wage the monopsonist pays

$18.00

Open in Graph Lab

Figure 4. Employment at each minimum wage in a competitive market and under monopsony with the same supply and $VMP_E$ curves. The predictions differ only for minimum wages below the competitive wage of $20, where the competitive market is unaffected and the monopsonist hires more.

This is one explanation for studies that find little or no job loss from moderate minimum wage increases: where employers have monopsony power, a minimum wage moves the market toward the competitive outcome. The broader evidence is in minimum wages.

Worked example

Use the table above: the wage needed to attract each worker, and each worker’s value of marginal product.

1. Nondiscriminating monopsonist. Compare $VMP_E$ with $MC_E$ for each worker: 30 against 10, 26 against 14 and 22 against 18 favour hiring; for the fourth worker 18 is less than 22. The firm hires 3 workers and pays each $14, the wage needed to attract three.

2. Competitive benchmark. Competitive firms hire while $VMP_E$ covers the wage needed: the fourth worker (18 against 16) is hired, the fifth (14 against 18) is not. Employment is 4, at a wage of at least $16.

3. Perfectly discriminating monopsonist. Marginal cost equals each worker’s own wage, so it hires the same 4 workers as the competitive market but pays them $10, $12, $14 and $16.

4. Minimum wage of $16. The first four workers each cost $16, so $MC_E$ is 16 up to four workers; the fourth worker’s $VMP_E$ of 18 covers it. A fifth would need $18 and a $2 raise for four others, a marginal cost of 26. The firm hires 4 at $16: both the wage and employment rise.

5. Minimum wage of $24. Only the first two workers have $VMP_E$ of at least 24, so employment falls to 2, below the monopsony level.

Exercise: the linear case in Figure 1

Supply is $w = 5 + 0.25E$ and $VMP_E = 35 - 0.25E$. Total labour cost is $5E + 0.25E^2$, so $MC_E = 5 + 0.5E$. Setting $35 - 0.25E = 5 + 0.5E$ gives $E_M = 40$, and the wage from the supply curve is $w_M = 5 + 0.25(40) = 15$. At $E_M$, $VMP_E = 25$, so the markdown is 10 dollars. A competitive market sets $35 - 0.25E = 5 + 0.25E$: $E^* = 60$ at $w^* = 20$. The deadweight loss is $\tfrac{1}{2} \times (25 - 15) \times (60 - 40) = 100$ dollars an hour. With a minimum wage of $18, everyone willing to work at $18 is hired: $E = (18 - 5) / 0.25 = 52$.

Evidence

Nurses at veterans’ hospitals. The US Nurse Pay Act of 1990 replaced a national pay scale for nurses at Department of Veterans Affairs hospitals with wages tied to surveys of local pay. About two-thirds of VA hospitals had been paying below the local market and had to raise wages at once. The size of each raise depended on how far the old national scale had left a hospital below local pay, not on any change in that hospital’s own demand for nurses. Staiger, Spetz and Phibbs used these imposed wage changes to measure how a hospital’s nurse employment responds to its own wage. They estimate the short-run elasticity of labour supply to an individual hospital at around 0.1.¹ A competitive employer faces an infinitely elastic supply curve; an elasticity near 0.1 means each hospital faced a steep supply curve and had substantial monopsony power.

The elasticity in a difference-in-differences study is the ratio of two differences. Suppose wages rose 12 percent at hospitals the law affected and 4 percent at comparison hospitals, while nurse employment rose 3 percent and 2 percent. The difference-in-differences change in the wage is 8 percentage points, in employment 1 point, so the elasticity of labour supply to the firm is $1 / 8 = 0.125$. A value near zero signals monopsony power; a very large value signals a nearly competitive employer.

Many employers, still monopsony. Monopsony power does not require a single employer. Anything that stops workers from switching employers freely, such as search costs, moving costs, specialized skills or attachment to a workplace, gives each firm an upward-sloping supply curve. Manning’s review of the evidence concludes that employers have considerable monopsony power.² In online labour markets, Dube, Jacobs, Naidu and Suri estimate labour supply elasticities to individual employers of around 0.1.³ Azar, Marinescu and Steinbaum find that the average local occupational labour market in the United States is highly concentrated by antitrust standards, and that more concentrated markets post lower wages.⁴

Common mistakes

Traps on exams

• Paying $MC_E$ as the wage. The monopsonist chooses employment where $VMP_E = MC_E$, then pays the wage on the supply curve at that employment, which is below both.
• Hiring where supply meets $VMP_E$. That is the competitive outcome, and the perfectly discriminating monopsonist’s, not the nondiscriminating monopsonist’s.
• Giving the perfectly discriminating monopsonist a deadweight loss. It hires the efficient number; it simply keeps all the surplus.
• Claiming any minimum wage raises employment under monopsony. Only one between $w_M$ and the value of the marginal product at $E_M$ leaves employment above $E_M$, and employment peaks at $w^*$.

On the exam

Draw $VMP_E$, the supply curve and $MC_E$ above it. Mark A where $MC_E$ meets $VMP_E$, drop a vertical line to the supply curve to find $w_M$, and mark the competitive point where supply meets $VMP_E$. Label $E_M$, $E^*$, $w_M$, $w^*$ and the deadweight-loss triangle. For a minimum wage, draw the flat segment of marginal cost at $\bar w$ up to the supply curve.

Check yourself

1.

How does a nondiscriminating monopsonist choose employment and the wage?

1It hires where the value of the marginal product equals the marginal cost of labour, and pays the wage on the supply curve at that employment2It hires where the value of the marginal product equals the supply curve, and pays that wage3It hires where the value of the marginal product equals the marginal cost of labour, and pays a wage equal to the marginal cost of labour4It hires where the marginal cost of labour equals the supply curve, and pays the value of the marginal product

Check answer

2.

Compared with a nondiscriminating monopsonist facing the same supply and $VMP_E$ curves, what does a perfectly discriminating monopsonist do?

1It hires the competitive number of workers, causes no deadweight loss, and keeps the entire surplus2It hires fewer workers, because it can pay each one less3It hires the same number of workers but pays all of them the competitive wage4It hires more workers than a competitive market would

Check answer

3.

A labour market has a nondiscriminating monopsonist. Which minimum wage leads to the highest employment?

1The wage at which labour supply meets the value of the marginal product, the competitive wage2The wage the monopsonist pays with no minimum wage3The value of the marginal product at the monopsony employment level4The highest minimum wage the firm can afford

Check answer

Practise more questions on this topic

Sources

1. Staiger, D. O., J. Spetz and C. S. Phibbs (2010). Is there monopsony in the labor market? Evidence from a natural experiment. Journal of Labor Economics, 28(2), 211 to 236. doi:10.1086/652734. ↩

2. Manning, A. (2021). Monopsony in labor markets: A review. ILR Review, 74(1), 3 to 26. doi:10.1177/0019793920922499. ↩

3. Dube, A., J. Jacobs, S. Naidu and S. Suri (2020). Monopsony in online labor markets. American Economic Review: Insights, 2(1), 33 to 46. doi:10.1257/aeri.20180150. ↩

4. Azar, J., I. Marinescu and M. Steinbaum (2022). Labor market concentration. Journal of Human Resources, 57(S), S167 to S199. doi:10.3368/jhr.monopsony.1218-9914R1. ↩