How to Find the Optimal Quantity of Labor to Hire
Hire labor up to the quantity where marginal revenue product equals marginal factor cost: MRP = MFC, which is the wage in a competitive labor market.
The Optimal Hiring formula
Calculator
Enter each worker's marginal revenue product and the marginal factor cost to find how many workers to hire.
Marginal product times the product's price.
In a competitive labor market this is simply the market wage.
Compared with the optimum to say whether to hire more or fewer.
Hire while each worker's MRP is at least the $60 marginal factor cost. That rule stops at a workforce of 4.
- MRP of the last worker hired
- $60
- MRP of the first worker turned down
- $40
- Wage bill at that quantity
- $240
- Total MRP minus the wage bill
- $120
- Hiring verdict
- Hire fewer
That worker brings in $60 and costs $60, so the hire still pays.
The next hire would add only $40 against $60 of cost, so it would shrink profit.
Marginal factor cost times the number of workers hired.
The workforce brings in $360 and costs $240, leaving $120 toward fixed costs and profit.
Worker 5 brings in $40 against a marginal factor cost of $60.
How to calculate Optimal Hiring, step by step
- 1Build the MRP schedule. For each worker, MRP = marginal product × the product's price, or ΔTotal revenue ÷ ΔLabor if the firm faces a downward-sloping product demand curve.
- 2Find marginal factor cost. In a competitive labor market MFC equals the market wage at every quantity; under monopsony MFC rises faster than the wage and sits above labor supply.
- 3Hire while MRP is at least MFC. Every worker whose MRP exceeds MFC adds more to revenue than to cost, so keep hiring until MRP = MFC.
- 4Set the wage. A wage-taking firm simply pays the market wage. A monopsonist drops from its MRP = MFC quantity down to the labor supply curve and pays the lowest wage that attracts that many workers.
- 5Reject the next worker. Stop before any worker whose MRP is below MFC, since that hire would shrink profit.
Worked example: Optimal Hiring
A firm's MRP schedule is $120, $100, $80, $60, and $40 for workers 1 through 5. In a competitive labor market at a $60 daily wage, MFC = $60, so the firm hires 4 workers: the 4th worker's $60 of MRP exactly covers the wage, and the 5th worker's $40 does not. Now make the same firm a monopsonist facing this supply schedule: 2 workers at $20 each (total factor cost 2 × 20 = $40), 3 at $30 each ($90), 4 at $40 each ($160). MFC of the 3rd worker = 90 − 40 = $50, below its $80 MRP, so hire it. MFC of the 4th = 160 − 90 = $70, above its $60 MRP, so stop. The monopsonist hires 3 workers and pays the $30 wage from the supply schedule, which is below the 3rd worker's $80 MRP.
Optimal Hiring questions
Why hire where MRP equals MFC instead of where profit per worker is highest?
Because every worker whose MRP exceeds MFC adds to total profit, even if earlier workers were more profitable. Stopping sooner leaves profitable hires unmade, and going further adds workers who cost more than they bring in.
Does a monopsonist pay a wage equal to MRP?
No. A monopsonist hires where MRP = MFC and then pays the lower wage shown on the labor supply curve at that quantity, so the wage sits below MRP.
What happens to the optimal quantity if the product's price rises?
It rises. A higher product price lifts MRP at every quantity, since MRP = MP × P, so more workers pass the MRP is at least MFC test.
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