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Marginal Revenue Product (MRP) is the additional revenue a firm gains from hiring one more unit of a factor. MRP = MP × Price of output (or MR in imperfect competition). A profit-maximizing firm hires workers until MRP equals the wage, and more generally hires factors until MRP equals factor price. This links factor demand to output demand, explaining why input demand is 'derived' from output demand.
You've already learned two things from your prerequisites. First, marginal product of labor (MPL) tells you how much additional output the next worker produces — it rises at first but eventually falls due to diminishing returns. Second, from profit maximization, you know that firms equate marginal benefit to marginal cost for every decision. MRP applies that same logic to hiring: the "marginal benefit" of hiring a worker is the additional revenue that worker's output generates. Connecting these two ideas gives you the foundation for all of factor market analysis.
Marginal Revenue Product = MPL × P (in a competitive output market). If the tenth worker produces 8 extra units of output, and each unit sells for $15, then MRP = $120. The firm should hire this worker as long as the wage is less than or equal to $120. If the wage is $100, hire. If the wage is $150, don't. The profit-maximizing hiring rule is: hire until MRP = W (wage). This is the factor-market analog of the output-market rule P = MC — the firm equates the marginal value of a resource to its marginal cost.
This rule generates the firm's labor demand curve. As more workers are hired, MPL falls (diminishing returns), so MRP falls. At higher wages, fewer workers pass the MRP ≥ W test, and the firm demands less labor. The downward-sloping MRP curve is literally the firm's demand curve for labor. Anything that shifts it — a change in output price, a technological improvement that raises MPL, or a demand boom that raises the product price — shifts labor demand.
That last point explains derived demand: labor demand is derived from product demand. A construction company doesn't want workers for their own sake — it wants the houses they produce, and only as long as those houses sell profitably. If housing demand falls, output prices drop, MRP falls, and the firm demands fewer construction workers. If housing demand surges, MRP rises and firms compete aggressively to hire workers. Factor markets and product markets are inseparable — a price change in one propagates directly through MRP into the other.
In imperfect competition, the formula adjusts: MRP = MPL × MR, where MR is marginal revenue rather than price. Since a monopolist's MR < P, its MRP is lower than a competitive firm's MRP at every employment level. This means a monopolist in the product market demands less labor and pays lower wages than a competitive industry producing the same output level would — an insight that connects market structure to income distribution.