How does a firm in a competitive factor market decide how much of each input to hire, and how does it least-cost combine inputs?
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.
Reviewed by: AI editorial process; not yet individually human-reviewed
Have a quick question? Jump to the Q&A page
Jump to a section
What this topic is asking
Topic 5.3 sharpens the hiring decision when a firm is a wage taker in a competitive factor market and uses more than one input. The College Board wants you to apply the marginal revenue product equals wage rule, and use the least-cost combination of inputs rule and the profit-maximizing input rule to decide how much labor and capital to use. It is the multi-input version of Topic 5.1.
The hiring rule for a wage taker
Because the firm is too small to affect the factor price, its labor supply curve is horizontal at the market wage, and the marginal factor cost is constant and equal to that wage. This makes the single-input hiring rule simple: keep hiring while the marginal revenue product is at least the wage, and stop where they are equal.
The least-cost combination of inputs
When a firm uses several inputs to make a given output, it should combine them to minimize cost.
If the ratios are not equal, the firm can produce the same output more cheaply by shifting spending toward the input with the higher marginal product per dollar. As it uses more of that input, its marginal product falls (diminishing returns), and as it uses less of the other, that input's marginal product rises, until the per-dollar ratios equalise. This is the input-side analogue of the consumer's utility-maximizing rule in Topic 1.6.
The profit-maximizing input combination
The distinction matters: the least-cost rule tells you the cheapest way to make a given output, while the profit-maximizing rule also tells you the right output to make. The profit-maximizing condition implies the least-cost condition, but not the reverse.
Try this
Q1. State the hiring rule for a firm in a competitive labor market. [1 point]
- Cue. Hire labor until the marginal revenue product of labor equals the wage ().
Q2. A firm has marginal product per dollar of 3 for labor and 5 for capital. State which input it should use more of. [1 point]
- Cue. More capital, because it gives more output per dollar (5 versus 3); shift spending toward capital until the ratios equalise.
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. A firm minimizes the cost of producing a given output when (A) the marginal products of all inputs are equal. (B) the marginal product per dollar is equal across all inputs. (C) it uses only the cheapest input. (D) the wage equals the rental rate. (E) marginal revenue product is zero.Show worked answer β
The answer is (B). The least-cost rule requires the marginal product per dollar (marginal product divided by input price) to be equal across all inputs, so the last dollar spent on each input adds the same output.
(A) ignores prices; a high-marginal-product input may be costly. (C) wastes the productivity of other inputs. (D) is irrelevant. (E) is not a cost-minimizing condition.
AP 2021 (style)4 marksFree response. A firm uses labor and capital. The marginal product of labor is 20 and the wage is 20. (a) Calculate the marginal product per dollar for each input. (b) State whether the firm is minimizing cost and why. (c) State which input the firm should use more of. (d) State the least-cost rule.Show worked answer β
A four-point input-combination FRQ.
(a) (1 point): labor: 20 / 20 = 1.5 units per dollar.
(b) (1 point): not minimizing cost, because the marginal product per dollar is not equal across inputs (2 for labor vs 1.5 for capital).
(c) (1 point): use more labor (and less capital), because labor gives more output per dollar; doing so raises labor's contribution and lowers capital's until the ratios equalise.
(d) (1 point): the least-cost rule is marginal product of labor / wage = marginal product of capital / rental rate (marginal product per dollar equal across inputs).
Related dot points
- 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.
- 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 5.4 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 3.5 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.
- Topic 3.2 Short-Run Production Costs: define fixed, variable, total, marginal, and average costs, calculate each from data, and explain the shapes of the short-run cost curves and how marginal cost relates to the averages.
A focused answer to AP Microeconomics Topic 3.2, covering fixed, variable, and total cost, average fixed, average variable, average total, and marginal cost, how to calculate each, and the shapes and relationships of the short-run cost curves, with worked exam-style questions.
Sources & how we know this
- AP Microeconomics Course and Exam Description β College Board (2023)