How is the demand for a factor like labor derived, and what does marginal revenue product tell a firm about hiring?
Topic 5.1 Introduction to Factor Markets: explain that factor demand is derived demand, define and calculate marginal revenue product, and state the hiring rule that marginal revenue product equals marginal factor (resource) cost.
A focused answer to AP Microeconomics Topic 5.1, covering derived demand, marginal product and marginal revenue product, marginal factor (resource) cost, and the profit-maximizing hiring rule that marginal revenue product equals marginal factor cost, with worked exam-style questions.
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What this topic is asking
Topic 5.1 opens Unit 5 by turning the firm's output decisions into input (factor) decisions. The College Board wants you to explain that factor demand is derived demand, define and calculate marginal revenue product, define marginal factor cost, and state the profit-maximizing hiring rule: hire a factor until its marginal revenue product equals its marginal factor cost. Labor is the standard example, but the logic applies to any factor.
Derived demand
So if demand for the product rises, demand for the workers who make it rises too, and if the product's price collapses, so does the demand for its inputs. This is why factor markets are taught after the product markets of Units 3 and 4: the value of an input depends entirely on the value of what it produces. Derived demand also explains why a more productive or higher-priced product supports higher wages.
Marginal revenue product
Marginal revenue product combines two ideas you already know: the marginal product from Topic 3.1 (how much extra output a worker adds) and marginal revenue from Topic 3.5 (how much each unit of output is worth). Because marginal product eventually falls (diminishing marginal returns), the marginal revenue product also falls as more of the factor is hired, which is why the factor demand curve slopes downward. For a firm that is a price maker in its product market, marginal revenue is below price, so its MRP falls faster than for a competitive seller.
The hiring rule
The hiring rule is the factor-market twin of the output rule. Marginal factor cost (MFC) is the extra cost of one more unit of the factor; in a competitive labor market each extra worker costs the same wage, so MFC equals the wage. The firm hires each worker whose marginal revenue product is at least the wage and stops when the next worker's MRP would fall below it, exactly where . This both sets how many workers to hire and, across the market, helps determine the equilibrium wage.
Try this
Q1. State why factor demand is called a derived demand. [1 point]
- Cue. Firms demand factors not for their own sake but for the output and revenue they produce, so demand for the product drives demand for the factor.
Q2. A worker's marginal product is 6 units and the product sells competitively at $7. State the worker's marginal revenue product. [1 point]
- Cue. MRP = MP \times P = 6 \times 7 = \42$.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2019 (style)1 marksMultiple choice. The marginal revenue product of labor is (A) the wage rate. (B) the extra output from one more worker. (C) the extra revenue from one more worker. (D) total revenue divided by the number of workers. (E) the price of the product.Show worked answer →
The answer is (C). Marginal revenue product is the additional revenue a firm earns from employing one more unit of a factor; for a competitive seller it equals marginal product times the product price.
(A) is the cost of labor, not its revenue. (B) is the marginal product, before converting to revenue. (D) is average revenue product, not marginal. (E) alone is not the marginal revenue product.
AP 2021 (style)4 marksFree response. A firm sells its output in a competitive market at 30, how many workers will the firm hire? (d) Explain why labor demand is called a derived demand.Show worked answer →
A four-point factor-market FRQ.
(a) (1 point): marginal revenue product = marginal product x price: 10x5=50, 8x5=40, 6x5=30, 4x5=20.
(b) (1 point): hire up to the point where marginal revenue product equals marginal factor cost (the wage in a competitive labor market).
(c) (1 point): with a wage (marginal factor cost) of 30: workers 1 (50), 2 (40), and 3 (30) qualify; the fourth (20) does not, so hire 3 workers.
(d) (1 point): labor demand is derived because firms demand labor not for its own sake but for the output (and revenue) it produces; demand for the product drives demand for the factor.
Related dot points
- Topic 5.2 Changes in Factor Demand and Factor Supply: identify the determinants that shift factor demand and factor supply, and predict the effect on the equilibrium factor price and quantity.
A focused answer to AP Microeconomics Topic 5.2, covering the determinants that shift factor (labor) demand and supply, including product demand, productivity, prices of other factors, and the number of workers, and how shifts change the equilibrium wage and employment, with worked exam-style questions.
- Topic 5.3 Profit-Maximizing Behavior in Perfectly Competitive Factor Markets: apply the marginal revenue product equals wage rule for a wage-taking firm, and use the least-cost and profit-maximizing input combination rules across multiple factors.
A focused answer to AP Microeconomics Topic 5.3, covering the hiring rule for a firm in a competitive factor market, the least-cost combination of inputs rule, the profit-maximizing input rule, and how a firm chooses between labor and capital, with worked exam-style questions.
- Topic 5.4 Monopsonistic Markets: explain why a monopsonist's marginal factor cost lies above the labor supply curve, find the monopsony wage and employment, and compare them with the competitive outcome.
A focused answer to AP Microeconomics Topic 5.4, covering monopsony as a single buyer of a factor, why marginal factor cost lies above the supply curve, how the monopsonist sets employment where marginal revenue product equals marginal factor cost and the wage off the supply curve, and the resulting lower wage and employment, with worked exam-style questions.
- Topic 3.1 The Production Function: define total, marginal, and average product, explain the law of diminishing marginal returns, and relate the product curves to one another.
A focused answer to AP Microeconomics Topic 3.1, covering the production function, total product, marginal product and average product, the law of diminishing marginal returns, and how the product curves relate to one another, with worked exam-style questions.
- Topic 3.5 Profit Maximization: explain the marginal revenue equals marginal cost rule, apply it to find the profit-maximizing output, and use the average total cost curve to measure profit or loss.
A focused answer to AP Microeconomics Topic 3.5, covering the profit-maximizing rule that marginal revenue equals marginal cost, how to find the optimal output, and how to measure total profit or loss using price and average total cost, with worked exam-style questions.
Sources & how we know this
- AP Microeconomics Course and Exam Description — College Board (2023)