Exercises: Marginal Revenue Product and Labor Demand

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 $\$15$ 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.

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 $\$10$ (the car wash market is perfectly competitive). The table shows how the number of workers affects total washes per hour.

(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.

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 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.

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.

(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 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.