Derived Demand & Marginal Revenue Product

You’ll be able to

Explain why the demand for a factor of production is a derived demand
Calculate marginal revenue product and marginal resource cost
Apply the profit-maximizing hiring rule MRP = MRC

Factor demand is derived demand

The demand for a factor of production — labor, land, capital — is a derived demand: firms want inputs not for their own sake but because of the output they help produce. The demand for autoworkers is derived from the demand for cars; if car demand rises, so does the demand for the workers who build them. This means anything that raises the value of the product — higher product price or higher productivity — raises factor demand, while a fall in product demand reduces it. Factor markets are the mirror image of product markets, with firms now the buyers and households the sellers.

Marginal revenue product

A firm decides how many workers to hire by comparing what each adds to revenue with what each adds to cost. The marginal revenue product (MRP) of a worker is the extra revenue from hiring one more — the worker’s marginal product (MP) times the marginal revenue the firm earns per unit. In a competitive product market, where price equals marginal revenue, this simplifies to MRP = MP × P. Because marginal product falls under diminishing returns, MRP declines as more workers are hired — so the MRP curve is the firm’s demand curve for labor.

The hiring rule: MRP = MRC

The extra cost of hiring one more unit of a factor is its marginal resource cost (MRC) (also called marginal factor cost). In a competitive labor market, the firm is a wage taker, so each additional worker costs the same market wage: MRC = wage. The profit-maximizing firm hires up to the point where MRP = MRC — where the last worker’s contribution to revenue just equals the cost of employing them. Hire while MRP > MRC (the worker adds more than they cost) and stop once MRP < MRC.

Factor hiring

MRP = MP × MR (= MP × P in a competitive product market) · Hire until MRP = MRC

MRP is the extra revenue from one more unit of the factor; MRC is its extra cost. In a competitive labor market MRC equals the market wage.

Worked example

A firm sells its output in a competitive market at $5 per unit. The third worker has a marginal product of 8 units, and the fourth worker has a marginal product of 6 units. The market wage is $35. Should the firm hire the fourth worker?

1.MRP of the fourth worker = MP × P = 6 × $5 = $30.
2.The marginal resource cost is the market wage: MRC = $35.
3.Compare: MRP ($30) < MRC ($35), so the fourth worker adds less to revenue than to cost.
4.(For context, the third worker’s MRP = 8 × $5 = $40 > $35, so hiring the third was profitable.)

Answer: No — the firm should not hire the fourth worker, because that worker’s MRP ($30) is below the wage/MRC ($35). The firm hires only up to the point where MRP = MRC, which lies between the third and fourth workers here.

Checkpoint

The demand for skilled welders increases sharply after the demand for new ships rises. This illustrates that the demand for labor is:

Watch out

MRP uses marginal revenue, not price, in general: MRP = MP × MR. It equals MP × P only when the product market is perfectly competitive (where MR = P). For a firm with market power, MR < P, so MRP is smaller than MP × P.

Checkpoint

A firm hires labor in a competitive labor market at a wage of $40. The next worker would add 12 units of output, and the firm sells each unit for $4 in a competitive product market. To maximize profit, the firm should:

On the exam

The hiring rule MRP = MRC is the factor-market twin of the product-market rule MR = MC. In a competitive labor market, set MRP = wage. Always confirm whether the product market is competitive before using MRP = MP × P.

Answer the 2 checkpoints as you read.