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Monopsony and the marginal cost of hiring
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Analyze monopsony and the marginal cost of hiring using explicit assumptions, calculated results and a stated limit of the model.
A competitive employer hires where the relevant marginal revenue product meets the wage, with discrete increments checked individually. That rule uses the assumption that another hire does not change the wage paid to existing workers. We now relax that assumption.
| Term | What it means |
|---|---|
| Monopsony | A buyer-side market-power model with one employer or purchaser in the defined input market. |
| Upward-sloping firm labor supply | A relationship requiring the employer to offer a higher wage to attract more labor. |
| Uniform wage | The same wage paid to all workers covered by the specified hiring rule. |
| Marginal factor cost | The change in the entire input bill caused by one additional input unit. |
| Competitive benchmark | The allocation where labor demand meets labor supply when employers take the wage as given. |
| Binding wage floor | A legal or stipulated minimum wage above the wage the unregulated model would otherwise choose. |
Monopsony is the input-side counterpart to monopoly. Instead of a seller facing downward product demand, an employer faces an upward supply of labor to the firm and can influence the wage needed to attract workers. The simplest model has a single employer in a defined labor market. Broader applications can involve hiring frictions or limited alternatives that give several employers some wage-setting power, but those require additional assumptions beyond the single-buyer benchmark.
The labor-market boundary matters. A firm may be the only employer in a small location yet face competition from nearby jobs, remote work or other occupations. Whether it has monopsony power depends on workers' relevant alternatives and their ability to switch, not merely the employer's size. The classroom model stipulates the labor supply it faces so the choice is mathematically determinate.
Assume the employer must pay every worker the same wage. Hiring more workers requires raising that common wage according to the supplied labor-supply schedule. The additional cost of a hire then includes both the new worker's wage and the increase paid to existing workers. Marginal factor cost therefore exceeds the wage over the increasing portion of a smooth supply schedule. Ignoring the pay increase to earlier workers incorrectly treats the employer as a competitive wage taker.
This is a model of the employer's incentives under a uniform-wage rule. If it could pay each worker a separate reservation wage, the marginal-cost relationship would change. If wages were fixed by a collective agreement or regulation, it would change again. Naming the wage-setting institution is therefore essential before solving the hiring problem. The same labor supply cannot be combined with an unstated payment rule and expected to produce a unique answer.
Another way: Build the whole wage bill before taking a difference
Suppose attracting zero, one, two, three and four workers requires common daily wages of zero, three, five, seven and nine dollars respectively. The total wage bills are zero, three, ten, twenty-one and thirty-six. Multiplying employment by the wage at that employment level is the first step. The third worker does not merely cost seven dollars: moving from two to three workers raises the whole bill from ten to twenty-one, an eleven-dollar increase.
The marginal labor costs are therefore three, seven, eleven and fifteen. The second hire costs seven because the new worker receives five and the first worker's wage rises by two. The third costs eleven because the new worker receives seven and each of the two existing workers receives two more. The table's differences make the common-wage assumption concrete.
Suppose each worker adds eleven dollars to revenue over these four feasible choices. The first hire raises profit by eight, the second by four, the third by zero and the fourth lowers it by four. Two and three workers tie for the largest contribution. A question requesting one quantity must specify a convention; our activity asks for the larger maximizing quantity, so the answer is three. A learner should not be penalized for noticing a genuine tie that the model itself creates.
At three workers, the common wage is seven dollars, read from labor supply. Marginal factor cost is eleven, matching the stipulated MRP at the boundary. Reporting eleven as the wage would confuse the total hiring increment with each worker's payment. Total revenue is thirty-three and the wage bill is twenty-one, giving a contribution of twelve. At two workers, revenue twenty-two minus a ten-dollar bill also gives twelve, confirming the tie independently.
Another way: Compare with the competitive allocation
In a smooth single-employer model, the profit-maximizing hiring condition equates marginal revenue product with marginal factor cost on the relevant range. Employment is chosen at that intersection. The wage is then read from the labor-supply curve at the chosen employment. The two-step procedure resembles monopoly's choice of quantity from MR and MC followed by price from demand, but the curves represent different economic roles.
The competitive benchmark instead equates labor demand, represented by MRP under the stated conditions, with labor supply. Because monopsony marginal factor cost lies above supply, the unregulated monopsonist generally hires fewer workers and pays a lower wage than that benchmark in the standard model. There are potential hires whose revenue contribution exceeds their opportunity cost but who are not employed under the uniform-wage monopsony incentive.
The lost gains can be represented between labor demand and labor supply over the employment gap, when those curves capture the relevant social benefits and costs. A lower wage on workers still employed also transfers surplus from workers to the employer. As with monopoly, transfers and unrealized gains should be distinguished. The entire reduction in worker earnings is not automatically the deadweight loss.
A numerical benchmark must use a sufficiently complete domain. The finite four-worker table in the earlier example is explicitly the complete set of feasible choices; it should not be extrapolated to predict a fifth worker without data. A smooth diagram may allow a wider employment range, but that is a different supplied model. Before comparing allocations, confirm that both are defined over compatible feasible choices and use the same revenue and opportunity-cost assumptions.
Another way: A wage floor can alter both wages and employment
In a competitive labor-market model, a sufficiently high binding wage floor can reduce labor demanded relative to the otherwise clearing quantity. In a monopsony model, a moderate wage floor can instead raise employment by changing the employer's marginal hiring cost over a range. These statements are not contradictory: they begin with different wage-setting institutions and therefore different marginal-cost relationships.
If a floor establishes a common wage above the unregulated monopsony wage, workers may be willing to supply more labor at that wage. For hires within the available quantity at the floor, the employer need not raise the wage on earlier workers to attract one more. Marginal factor cost can equal the fixed floor over that segment rather than follow the original upward-sloping MFC curve. The employer's optimal hiring can therefore increase, depending on the floor's level and the MRP schedule.
A floor set too high can reduce employment even in the monopsony model. Once the imposed wage exceeds the revenue contribution of relevant workers, hiring them becomes unprofitable. Thus 'a minimum wage always raises employment under monopsony' is false, just as importing the competitive result without checking market structure is incomplete. The exact effect requires the supplied floor, labor supply, MRP and feasible choices.
For a finite example, reconstruct the wage bill at every feasible employment under the new rule and compare revenue minus cost again. This direct method avoids ambiguities near kinks and jumps in a diagram. It also makes clear whether the firm can attract the desired number of workers at the floor and whether any old wage schedule resumes beyond that quantity. A correct answer identifies the relevant segment instead of treating the floor as an unlimited supply guarantee.
Real wage-setting involves additional institutions, heterogeneity, enforcement and dynamic adjustment. A classroom model with exact labor supply does not estimate those features or settle an actual wage policy. It demonstrates why evidence about employer power and workers' alternatives matters. A policy audit should distinguish an assumed monopsony mechanism from evidence that the mechanism is quantitatively important in the market being studied.
The reusable method is therefore to identify the payment rule, construct total labor expenditure, calculate marginal expenditure or compare total contributions, choose employment, and read the actual wage from the appropriate schedule. Then compare the allocation with a clearly defined benchmark. Keeping these steps separate prevents the wage, MFC and MRP from being treated as interchangeable numbers merely because they all have dollar units.
Another way: Tie rules report rather than create incentives
Choosing the larger of two equal-profit quantities is a reporting convention, not an extra profit incentive. Both remain maximizers under the underlying table. If the model added a small unlisted hiring cost, the lower quantity could become uniquely preferable; if it added a small participation benefit to the objective, the higher might. Exact ties therefore deserve explicit acknowledgment rather than being hidden by rounding or a memorized equality rule.
A fictional employer can hire at most four workers. The common wage required at one through four workers is three, five, seven and nine dollars per day. Every worker adds eleven dollars to revenue. Total wage bills are three, ten, twenty-one and thirty-six, while revenues are eleven, twenty-two, thirty-three and forty-four. Contributions are eight, twelve, twelve and eight. Two and three workers tie; under a declared larger-quantity tie rule, the model chooses three at a wage of seven dollars.
An analyst who multiplies the third worker's seven-dollar wage by one and calls it marginal cost misses the wage increases for the first two workers. The correct third-hire increment is twenty-one minus ten, or eleven. Another analyst who reports eleven as the wage confuses that marginal bill with the seven dollars each worker receives. The total-expenditure table catches both errors.
Now impose an eight-dollar wage floor. The first three workers can be attracted at eight dollars, but the fourth still requires nine under the original supply schedule. Wage bills become eight, sixteen, twenty-four and thirty-six. Contributions become three, six, nine and eight. Three workers now uniquely maximize the contribution, and their wage rises to eight. In this finite example employment is unchanged relative to the chosen unregulated tie outcome; a generic claim that every wage floor raises or lowers employment would be wrong.
The conclusion follows from the exact table, the four-worker limit, the uniform-wage rule and the eleven-dollar revenue increment. It is not a prediction for an actual employer. The exercise shows why a policy comparison should recompute feasible outcomes rather than attach a universal employment effect to a label such as monopsony or wage regulation.
For a uniform-wage monopsonist, the new hire changes existing workers' pay too. MFC is the change in the entire bill; the wage is read from labor supply after choosing employment. A wage floor's employment effect depends on its level and the supplied market structure.
Construct total labor bills.
[0, 3, 10, 21, 36]
Hiring more workers raises the wage paid to existing workers as well.
Take the third-worker increment.
21 - 10 = 11
Marginal labor cost is the change in the entire wage bill.
Compare marginal costs with revenue.
MFCs 3,7,11,15; MRP 11
The first two units increase profit, the third leaves it unchanged, and the fourth lowers it.
Apply the declared tie rule.
Choose 3 workers
Two and three workers tie; the question explicitly selects the larger maximizer.
Read the wage from labor supply.
W(3) = 7
The wage paid is below the marginal cost of expanding employment.
Construct total labor bills.
[0, 4, 12, 24, 40]
Hiring more workers raises the wage paid to existing workers as well.
Take the third-worker increment.
24 - 12 = 12
Marginal labor cost is the change in the entire wage bill.
Compare marginal costs with revenue.
MFCs 4,8,12,16; MRP 12
The first two units increase profit, the third leaves it unchanged, and the fourth lowers it.
Apply the declared tie rule.
Choose 3 workers
Two and three workers tie; the question explicitly selects the larger maximizer.
Read the wage from labor supply.
W(3) = 8
The wage paid is below the marginal cost of expanding employment.
Construct total labor bills.
[0, 5, 14, 27, 44]
Hiring more workers raises the wage paid to existing workers as well.
Take the third-worker increment.
27 - 14 = 13
Marginal labor cost is the change in the entire wage bill.
Compare marginal costs with revenue.
MFCs 5,9,13,17; MRP 13
The first two units increase profit, the third leaves it unchanged, and the fourth lowers it.
Apply the declared tie rule.
Choose 3 workers
Two and three workers tie; the question explicitly selects the larger maximizer.
Read the wage from labor supply.
W(3) = 9
The wage paid is below the marginal cost of expanding employment.
Check revenue less the wage bill.
At 2: 12; at 3: 12; at 4: 8
Total net contributions confirm the tie and the loss from the fourth hire.
Construct total labor bills.
[0, 6, 16, 30, 48]
Hiring more workers raises the wage paid to existing workers as well.
Take the third-worker increment.
30 - 16 = 14
Marginal labor cost is the change in the entire wage bill.
Compare marginal costs with revenue.
MFCs 6,10,14,18; MRP 14
The first two units increase profit, the third leaves it unchanged, and the fourth lowers it.
Apply the declared tie rule.
Read the wage from labor supply.
In the fictional Elm model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 7, 9, 11, 13] dollars per worker per day. Every worker adds 15 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity.
| Calculated value | |
|---|---|
| Marginal cost of third worker | |
| Workers at largest-profit tie | |
| Common wage |
In the fictional Dune model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 6, 8, 10, 12] dollars per worker per day. Every worker adds 14 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity.
Calculate marginal cost of third worker.
g0
Marginal labor cost is the change in the entire wage bill.
Calculate workers at largest-profit tie.
g1
Two and three workers tie; the question explicitly selects the larger maximizer.
Calculate common wage.
g2
The wage paid is below the marginal cost of expanding employment.
In the fictional Fern model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 8, 10, 12, 14] dollars per worker per day. Every worker adds 16 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity.
Marginal cost of third worker: b0
Workers at largest-profit tie: b1
Common wage: b2
In the fictional Grove model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 9, 11, 13, 15] dollars per worker per day. Every worker adds 17 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity.
Marginal cost of third worker: b0
Workers at largest-profit tie: b1
Common wage: b2
In the fictional Harbor model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 10, 12, 14, 16] dollars per worker per day. Every worker adds 18 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity.
| Calculated value | |
|---|---|
| Marginal cost of third worker | |
| Workers at largest-profit tie | |
| Common wage |
A sole employer must raise the common daily wage to recruit additional staff. Payroll requests the whole-bill effect of a third hire and the maximizing employment under an explicit tie convention. The new employee's own payment is only one part of the hiring increment. In the fictional Island model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 11, 13, 15, 17] dollars per worker per day. Every worker adds 19 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity.
| Calculated value | |
|---|---|
| Marginal cost of third worker | |
| Workers at largest-profit tie | |
| Common wage |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
In the fictional Juniper model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 12, 14, 16, 18] dollars per worker per day. Every worker adds 20 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity.
| Calculated value | |
|---|---|
| Marginal cost of third worker | |
| Workers at largest-profit tie | |
| Common wage |
Reconstruct the model without the worked example. Explain each requested measure's units and identify an assumption that the conclusion depends on.
10. In the fictional Dune model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 6, 8, 10, 12] dollars per worker per day. Every worker adds 14 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity., step 4
Choose 3 workers
Two and three workers tie; the question explicitly selects the larger maximizer.
10. In the fictional Dune model, a single employer must pay every worker the same wage. To employ 0,1,2,3,4 workers it must offer respectively [0, 6, 8, 10, 12] dollars per worker per day. Every worker adds 14 dollars to revenue over this range. These are the complete feasible hiring choices. Calculate the marginal labor cost of moving from two workers to three, the profit-maximizing number of workers, and their common wage. No worker may receive a different wage. If adjacent quantities tie for maximum profit, report the larger quantity., step 5
W(3) = 10
The wage paid is below the marginal cost of expanding employment.