A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.

Marginal Revenue Product: Derived Demand for Inputs

College Depth 92 in the knowledge graph ☐ I know this ☆ Set as goal
2topics build on this
461prerequisites beneath it
See this on the map →
Profit MaximizationTotal, Average, and Marginal Product of Labor→→Wage Determination and Labor Market Equilibrium
factor-demand derived-demand labor-demand

Core Idea

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.

Explainer

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.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Literal Equations → Slope-Intercept Form → Point-Slope Form → Writing Linear Equations → Parallel and Perpendicular Line Slopes → Graphing Linear Equations → Piecewise Functions → One-Sided Limits → Continuity Definition → Limits and Continuity in Multiple Variables → Functions of Several Variables → Continuity in Multiple Variables → Partial Derivatives: Definition and Computation → Differentiability in Multiple Variables → Differentiability in Multivariable Functions → Total Differential and Linear Approximation → Chain Rule for Multivariable Functions → Implicit Differentiation → Related Rates → Optimization Problems → Critical Points of Multivariable Functions → Critical Points and Classification of Extrema → Second Partial Test for Local Extrema (Hessian) → The Hessian Matrix and Second Derivative Test → Unconstrained Optimization: Finding Extrema → Optimization in Multiple Variables → Lagrange Multipliers → Constrained Optimization and Lagrange Multipliers → Utility and Preferences → Marginal Utility and Diminishing Returns → Profit Maximization → Marginal Revenue Product: Derived Demand for Inputs

Longest path: 93 steps · 461 total prerequisite topics

Prerequisites (2)

Leads To (1)