Marginal Revenue Product and Labor Demand
A pizza shop in Chicago posts a "Now Hiring" sign. Should the owner hire one more cook? The answer isn't "yes, because we're busy." It depends on a comparison: what the new cook adds to the shop's revenue versus what the cook costs. Later on this page we'll settle exactly when the owner should stop hiring.
Derived Demand and MRP
Nobody hires a cook just for fun. A firm hires workers because of what they help produce and sell. Economists call this derived demand: the demand for labor comes from (is derived from) the demand for the product the labor makes. If nobody wanted pizza, no one would want to hire pizza cooks.
So how much is one more worker worth to a firm? Two things matter:
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How much extra output the worker produces: the marginal product of labor, $MP_L = \Delta TP / \Delta L$.
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How much extra revenue each extra unit of output brings in: marginal revenue, $MR$.
In a perfectly competitive product market, the firm is a price taker, so $MR = P$. Then $MRP = MP_L \times P$. (This is sometimes called the value of marginal product.)
Define marginal revenue product of labor* (MRP) in your own words. Then write the formula for MRP using the marginal product of labor ($MP_L$) and marginal revenue…
Define marginal revenue product of labor (MRP) in your own words. Then write the formula for MRP using the marginal product of labor ($MP_L$) and marginal revenue ($MR$). Explain in one sentence why we say the demand for labor is a "derived demand."
A pizza shop in Chicago sells every pizza for $\$15…
A pizza shop in Chicago sells every pizza for $\$15$ in a perfectly competitive product market. Hiring one more cook increases output by 4 pizzas per hour. Calculate the marginal revenue product of that cook, and state the formula you used.
The Hiring Rule: MRP = MFC
Now the owner's question. Hire a worker if the worker adds more to revenue than to cost. The extra cost of one more worker is the marginal factor cost (MFC) (also called marginal resource cost, MRC).
In a perfectly competitive labor market, the firm is a wage taker: it can hire as many workers as it wants at the market wage $W$. So each worker costs exactly $W$, and $MFC = W$.
Why? If $MRP > W$, one more worker adds more revenue than cost, so profit rises. If $MRP < W$, that worker costs more than they bring in, so profit falls. This is the same marginal logic as $MB = MC$.
Because of diminishing marginal returns, $MP_L$ falls as more workers are hired, so MRP slopes downward.
To the left of $L^*$, MRP is above the wage, so hiring pays. To the right, MRP is below the wage, so stop.
A firm hires labor in a perfectly competitive labor market where the market wage is $\$16…
A firm hires labor in a perfectly competitive labor market where the market wage is $\$16$ per hour. State the profit-maximizing hiring rule for this firm. Then say whether the firm should hire one more worker if that worker's MRP is $\$20$ per hour, and explain why.
A car wash in Phoenix sells each wash for $\$10…
A car wash in Phoenix sells each wash for $\$10$ (the car wash market is perfectly competitive). The table shows how the number of workers affects total washes per hour.
| Workers | Total washes per hour |
|---|---|
| 0 | 0 |
| 1 | 6 |
| 2 | 11 |
| 3 | 15 |
| 4 | 18 |
| 5 | 20 |
(a) Compute the marginal product and the MRP for each worker.
(b) The wage is $\$25$ per hour in a perfectly competitive labor market. How many workers should the car wash hire? Explain using the rule MRP = MFC.
What Shifts Labor Demand?
Since the MRP curve is the firm's labor demand curve, we can read it like any demand curve.
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A change in the wage causes a movement along the curve (a change in the quantity of labor demanded).
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A change in anything that alters MRP at each quantity of labor shifts the curve (a change in labor demand).
Labor supply shifts too. A change in the wage moves you along the supply curve, but a change in any of these determinants shifts it:
The market wage and employment come from the intersection of market labor demand and supply:
| Change | Curve that shifts | Wage | Employment |
|---|---|---|---|
| Demand increases | Demand right | Up | Up |
| Demand decreases | Demand left | Down | Down |
| Supply increases | Supply right | Down | Up |
| Supply decreases | Supply left | Up | Down |
Emma owns a food truck in Houston. Explain what happens to her demand for cooks (shift of the labor demand curve, or movement along it) in each case, and give a reason:…
Emma owns a food truck in Houston. Explain what happens to her demand for cooks (shift of the labor demand curve, or movement along it) in each case, and give a reason:
(a) The price of tacos rises because of a surge in customer demand.
(b) A new grill is purchased that makes each cook able to prepare more tacos per hour.
(c) The market wage for cooks rises.
A local labor market for warehouse workers in Denver is perfectly competitive. Use supply and demand reasoning to explain what happens to the equilibrium wage and the…
A local labor market for warehouse workers in Denver is perfectly competitive. Use supply and demand reasoning to explain what happens to the equilibrium wage and the equilibrium quantity of workers in each case:
(a) A new law requires more training, so fewer people are willing to work as warehouse workers at each wage.
(b) Online shopping grows, increasing the price of the products the warehouses ship.
State for each case which curve shifts and in which direction.
Hiring Several Inputs
Most firms use labor and capital. The profit-maximizing rule applies to each input: hire until $MRP = $ input price. For labor, $MRP_L = w$. For capital, $MRP_K = r$, the rental price of a machine.
In perfect competition, $MRP_L = MP_L \times P = w$ and $MRP_K = MP_K \times P = r$. Dividing each equation by $P \times$ its input price gives $MP_L / w = 1/P$ and $MP_K / r = 1/P$. Since both ratios equal $1/P$, they equal each other, which gives the least-cost rule:
$$\frac{MP_L}{w} = \frac{MP_K}{r}$$Each side is the extra output per dollar spent on that input. If one input gives more output per dollar, shift spending toward it until the ratios are equal.
A landscaping company in Atlanta sells its services in a perfectly competitive market at a price of $\$40…
A landscaping company in Atlanta sells its services in a perfectly competitive market at a price of $\$40$ per lawn. It hires workers in a perfectly competitive labor market at a wage of $\$60$ per hour. The table shows the output of lawns per hour.
| Workers | Lawns per hour |
|---|---|
| 1 | 3 |
| 2 | 5.5 |
| 3 | 7.5 |
| 4 | 9 |
| 5 | 10 |
| 6 | 10.5 |
(a) Compute the marginal product and the MRP of each worker (the first worker's marginal product is 3 lawns).
(b) Find the profit-maximizing number of workers.
(c) Now the price of a lawn service falls to $\$30$. Find the new profit-maximizing number of workers and explain how this illustrates that labor demand is derived.
(d) Explain why the MRP curve is the firm's labor demand curve in this market.
A firm uses labor and capital (machines) to produce a good sold in a perfectly competitive product market at a price of $\$8$. The wage is $\$24$ per hour and the rental…
A firm uses labor and capital (machines) to produce a good sold in a perfectly competitive product market at a price of $\$8$. The wage is $\$24$ per hour and the rental price of a machine is $\$40$ per hour. At the firm's current input mix, the marginal product of the last worker is 4 units per hour and the marginal product of the last machine is 4 units per hour.
(a) Compute the MRP of labor and the MRP of capital at the current mix.
(b) Is the firm hiring the profit-maximizing amount of each input? Explain using MRP and the input prices.
(c) Compute $MP_L / w$ and $MP_K / r$. Based on these, should the firm use more labor and less capital, more capital and less labor, or neither? Justify your answer.
(d) Explain how a decrease in the wage, with the rental price unchanged, would affect the firm's demand for capital. Name the effect that causes it.
Summary
Back to the pizza shop: the owner should keep hiring cooks as long as each new cook's MRP is at least the wage, and stop once it falls below.