Enter Values

$
Price per unit of output
$
Wage per worker per period
Workers (L) Total Output (Q)
Productivity parameter in Q = A × Lα
Must be < 1 for diminishing returns
workers
Calculate MRP from L = 1 to this value
MRP Hiring Rule
MRP = P × MPL
Hire where MRP ≥ W | MPL = marginal product of labor | P = output price | W = wage
For competitive firms, MRP = VMP (value of marginal product)
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Hiring Decision

Optimal Workers to Hire --
Total Output --
Total Revenue --
Labor Cost --
Contribution
(Revenue − Labor Cost) --

MRP Schedule

L Q MPL MRP W MRP−W Decision

Formula Breakdown

Model Assumptions
  • Competitive output market (firm is a price taker for output)
  • Competitive labor market (firm is a wage taker, no monopsony power)
  • Labor is the only variable input (capital fixed in the short run)
  • Diminishing marginal product of labor (standard assumption)
  • Homogeneous workers (identical productivity)
  • Output price and wage are constant over the hiring range
  • Firm maximizes profit (hires where MRP ≥ W)
  • Educational textbook model with simplified assumptions. Not professional advice.

Understanding Labor Demand & MRP

What Is the Marginal Product of Labor?

The marginal product of labor (MPL) is the additional output produced by hiring one more worker while holding all other inputs constant. Due to the law of diminishing marginal returns, MPL typically decreases as more workers are added — each additional worker has less equipment and space to work with, contributing progressively less output.

MRP Hiring Rule
MPL = ΔQ / ΔL (additional output per worker)
MRP = P × MPL (dollar value of that output)
Hire where MRP ≥ W (worker earns their wage)

From MPL to Labor Demand

The marginal revenue product (MRP) converts MPL into dollar terms: MRP = P × MPL. For a competitive firm, this equals the value of the marginal product (VMP). The MRP curve is the firm's labor demand curve — it shows how many workers the firm will hire at each possible wage rate. A higher output price shifts MRP (and labor demand) to the right.

The Optimal Hiring Decision

A profit-maximizing firm hires workers as long as the additional revenue they generate (MRP) exceeds or equals their cost (W). The optimal number of workers L* is where hiring one more worker would cost more than they produce. This calculator finds L* by comparing contribution (Revenue − Labor Cost) at each hiring level.

Derived Demand: Labor demand is "derived" from the demand for the goods workers produce. When product demand rises (increasing P), MRP rises at every hiring level, shifting labor demand rightward. This is why wages in high-demand industries tend to be higher.

Frequently Asked Questions

The marginal product of labor (MPL) is the additional output produced by hiring one more worker while holding other inputs constant. MPL diminishes because of the law of diminishing marginal returns — as more workers share fixed resources (equipment, space), each additional worker contributes less output. For example, adding a second cook to a kitchen increases meals served, but the 10th cook in the same kitchen may barely add any output due to overcrowding.

For a competitive firm (the assumption in this calculator), MRP converts the marginal product into dollar terms: MRP = P × MPL, where P is the output price. Since competitive firms are price takers, MR = P, so MRP equals the value of the marginal product (VMP). MRP represents the additional revenue a firm earns from hiring one more worker and forms the firm's labor demand curve.

A competitive, profit-maximizing firm hires workers up to the point where MRP equals the wage rate (MRP = W). If MRP > W, the worker generates more revenue than they cost, so hiring them increases profit. If MRP < W, the worker costs more than they produce. The optimal hiring level L* is the level that maximizes total contribution (Revenue − Labor Cost). For standard diminishing-returns data, this corresponds to the last worker for whom MRP ≥ W.

Labor demand is called "derived demand" because it derives from the demand for the goods workers produce. Firms don't hire workers for their own sake — they hire workers to produce output they can sell. When demand for a product increases (raising its price), the MRP of workers producing that good rises, increasing labor demand. For example, demand for software engineers derives from demand for software products.

When the output price (P) increases, MRP = P × MPL increases at every hiring level. This shifts the labor demand curve to the right, meaning the firm will optimally hire more workers at the same wage rate. Conversely, a decrease in output price reduces MRP and shifts labor demand left. Try changing the output price in this calculator to see how it affects the optimal hiring decision.

MRP (Marginal Revenue Product) equals MR × MPL, while VMP (Value of the Marginal Product) equals P × MPL. For a competitive firm where MR = P, they are identical. For a monopolist, MR < P, so MRP < VMP — a monopolist hires fewer workers than a competitive firm with the same production technology. This calculator assumes competitive output markets, so MRP = VMP throughout.
Disclaimer

This calculator is an educational textbook model with simplified assumptions. It illustrates microeconomic concepts from introductory economics courses (Mankiw Chapter 18). Real-world labor markets involve additional factors such as benefits, training costs, heterogeneous workers, and market power. This tool should not be used for business hiring decisions or professional advice.

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