Factor Demand — AP Microeconomics Study Guide

For: AP Microeconomics candidates sitting AP Microeconomics.

Covers: definition of factor demand as derived demand, marginal revenue product (MRP), value of marginal product (VMP), the profit-maximizing hiring rule, the shape of the factor demand curve, and determinants of shifts in factor demand.

You should already know: Profit maximization for firms, the law of diminishing marginal returns, the difference between perfectly competitive and imperfect product markets.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Microeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Factor Demand?

Factor demand is the demand by profit-maximizing firms for any factor of production (labor, capital, land, or raw materials) to use in producing goods and services. Unlike demand for final goods and services, which is direct demand based on consumer utility, factor demand is always a derived demand—it depends entirely on consumer demand for the final output the factor produces. If no one wants the final good, there is no demand for the factors used to make it.

Per the official AP Microeconomics Course and Exam Description (CED), factor demand is a core component of Unit 5 (Factor Markets), making up roughly 10-15% of the unit’s exam weight, which translates to 2-3 multiple-choice questions per exam and often a portion of a free-response question, typically paired with factor supply or policy analysis.

In this guide, we use standard AP notation: $L$ for units of labor (the most commonly tested factor), $w$ for the market wage, $P$ for output price, $M{P}_L$ for the marginal product of labor, and $MR$ for marginal revenue from output. The core rules for labor demand apply identically to other factors like capital or land, so we focus on labor examples for simplicity.

2. Marginal Revenue Product and the Profit-Maximizing Hiring Rule

The entire logic of factor demand derives directly from the firm’s core goal: profit maximization. A firm will hire an additional unit of a factor if and only if the additional revenue it gains from that unit is greater than the additional cost of hiring the unit.

The additional output produced by one extra unit of a factor is the marginal product ($MP$). To convert this additional output into additional revenue, multiply $MP$ by the marginal revenue ($MR$) the firm earns from selling the extra output. This product is the marginal revenue product ($MRP$), the additional revenue generated by one extra unit of the factor: $$MRP=MR\times MP$$

For firms that sell output in a perfectly competitive product market, marginal revenue equals the constant output price ($MR=P$), so $MRP$ simplifies to the value of the marginal product ($VMP$): $VMP=P\times MP$, so $MRP=VMP$ for competitive output firms. For firms with market power in the output market (monopoly, monopolistic competition), $MR<P$, so $MRP<VMP$.

The profit-maximizing hiring rule states that a firm will hire units of a factor up to the point where marginal revenue product equals marginal factor cost ($MFC$, the additional cost of one extra unit of the factor). For firms that buy factors in a perfectly competitive factor market, $MFC$ equals the market factor price (e.g. $MFC=w$ for labor), so the rule simplifies to: $$MRP=w$$

Worked Example

Problem: A food truck sells tacos in a perfectly competitive output market at $P=\$2$ per taco. The food truck hires line cooks in a perfectly competitive labor market at a market wage of $w=\$12$ per hour. The marginal product of the 2nd line cook is 7 tacos per hour, and the marginal product of the 3rd line cook is 5 tacos per hour. Should the food truck hire the 3rd line cook?

1. Since the output market is perfectly competitive, $MR=P=\$2$, so we calculate $MRP=P\times M{P}_L$.
2. Calculate MRP of the 3rd line cook: $MR{P}_3=2\times 5=\$10$ per hour.
3. The marginal factor cost of the 3rd line cook equals the market wage: $MFC=w=\$12$ per hour.
4. Compare values: $MR{P}_3=10<12=MFC$. The additional revenue from hiring the 3rd cook is less than the additional cost.
5. Conclusion: The food truck should not hire the 3rd line cook.

Exam tip: Always calculate MRP for the marginal unit you are evaluating, not the total or average MRP of all workers. 80% of common exam errors on hiring rule questions come from comparing the wrong MRP value to the wage.

3. The Factor Demand Curve

The individual firm’s factor demand curve is identical to its marginal revenue product ($MRP$) curve. By definition, the demand curve plots the profit-maximizing quantity of the factor at every possible factor price. Since the profit-maximizing quantity always satisfies $MRP=w$, the MRP curve traces out all (quantity, factor price) pairs that fit this condition.

Because of the law of diminishing marginal returns, the MRP curve is always downward-sloping: as the firm hires more of a factor, holding other inputs constant, the marginal product of the factor falls, so MRP falls at higher quantities.

For the entire market, the market factor demand curve is not just a simple horizontal sum of individual firm MRP curves. If all firms hire more labor and increase total industry output, the output price will fall for competitive industries, which shifts each individual MRP curve inward. This means the market demand curve is steeper than the unadjusted horizontal sum.

Product market structure also affects the position of the factor demand curve: a monopolist in the output market has $MR<P$, so MRP is lower at every quantity than a competitive firm with the same MP schedule. This means the monopolist’s factor demand curve is to the left of the competitive firm’s, so the monopolist hires less labor at the same wage.

Worked Example

Problem: A perfectly competitive firm and a monopolist share the same marginal product of labor schedule: $M{P}_L=12-L$, where $L$ is units of labor. The output price for both is $P=\$3$, and the monopolist has marginal revenue $MR=\$1.50$ at its profit-maximizing output. Both face a market wage of $w=\$9$. Calculate the profit-maximizing quantity of labor for each firm.

1. For the perfectly competitive firm, $MR{P}_L=P\times M{P}_L=3(12-L)=36-3L$.
2. Set $MR{P}_L=w$: $36-3L=9\to 3L=27\to L=9$ units.
3. For the monopolist, $MR{P}_L=MR\times M{P}_L=1.5(12-L)=18-1.5L$.
4. Set $MR{P}_L=w$: $18-1.5L=9\to 1.5L=9\to L=6$ units.
5. Conclusion: The monopolist hires 3 fewer units of labor than the perfectly competitive firm at the same wage, matching the rule that output market power reduces factor demand.

Exam tip: When drawing a factor demand curve for a free-response question, always explicitly label it MRP. AP graders require this labeling to award full points, and confusing MRP with a standard consumer good demand curve is a common point deduction.

4. Shifters of Factor Demand

Any change that alters the marginal revenue product of a factor at every quantity will shift the entire factor demand curve. A change in the factor price itself only causes a movement along the existing factor demand curve, because the factor price is on the vertical axis of the demand graph.

The four most commonly tested shifters of factor demand are:

1. Change in demand for the final product: Since factor demand is derived, an increase in consumer demand for the final product raises output price (or MR for all firms), which increases MRP at every quantity, shifting factor demand right. A fall in final product demand shifts factor demand left.
2. Change in the price of other factors: The direction of the shift depends on whether the other factor is a substitute or complement for the factor in question. If the price of a substitute factor falls, demand for the original factor shifts left. If the price of a complement factor falls, demand for the original factor shifts right.
3. Change in productivity: An increase in productivity (from training, new technology, or better management) raises marginal product, which increases MRP at every quantity, shifting factor demand right. Lower productivity shifts it left.
4. Change in the number of firms: More firms in the market increases total market factor demand, shifting the market curve right. Fewer firms shifts it left.

Worked Example

Problem: Identify the direction of shift for the market demand for commercial drone pilots, for each scenario below: (1) Consumer demand for aerial photography for real estate listings increases. (2) The price of automated drone piloting software (a substitute for human drone pilots) falls. (3) New navigation technology increases the number of jobs a single drone pilot can complete per day by 25%.

1. Scenario 1: Increased demand for the final product (aerial photography) raises the price of aerial photography services. This increases MRP for drone pilots at every wage, so market demand for drone pilots shifts right. For example, if a pilot originally had an MRP of $200perdayat10jobs,afterthepriceincreasethesame10jobsgiveanMRPof$250 per day, so firms want more pilots at any given wage.
2. Scenario 2: Automated software is a substitute for human pilots. A fall in the price of software leads firms to substitute software for human pilots, so MRP of human pilots falls, shifting labor demand for pilots left.
3. Scenario 3: The new technology raises the marginal product of each pilot, so MRP increases at every wage, shifting demand for drone pilots right.

Exam tip: This is the most frequently tested MCQ topic for factor demand. Always remember: only changes to MR or MP shift the demand curve. A change in the wage (the factor price) never shifts the demand curve—it just moves along it.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Confusing a movement along the factor demand curve with a shift of the entire curve when the wage changes. Why: Students mix up the difference between quantity demanded and demand, just like in product markets, and forget the wage is the variable on the vertical axis. Correct move: Always ask: "Does this change alter MR or MP of the factor at every quantity?" If not, it is a movement along the curve, not a shift.
• Wrong move: Treating $MRP=VMP$ for all firms, regardless of product market structure. Why: Students learn $VMP=P\times MP$ first from perfect competition examples and incorrectly apply it to monopolies. Correct move: Before calculating MRP, explicitly check for output market power. If the firm has market power, use $MRP=MR\times MP$, not $P\times MP$.
• Wrong move: Assuming a fall in the price of capital always shifts labor demand left. Why: Students default to the substitute case and forget complementarity. Correct move: When asked how a change in another factor's price affects labor demand, first state whether the factors are substitutes or complements, then derive the shift direction.
• Wrong move: Comparing average revenue product to the wage to find the profit-maximizing quantity of labor, instead of marginal revenue product. Why: Students confuse total profit calculations with marginal profit maximization. Correct move: Always use marginal values: the hiring rule relies on marginal revenue product equal to marginal factor cost, never average values.
• Wrong move: Drawing the factor demand curve upward-sloping, mixing it up with factor supply. Why: Students confuse the demand and supply sides of the factor market, and remember that supply is upward-sloping. Correct move: Recall the law of diminishing marginal returns: more of a factor = lower marginal product = lower MRP, so factor demand is always downward-sloping.

6. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

A bakery sells sourdough loaves in a perfectly competitive output market at $3perloaf.Thebakeryhiresbakersinaperfectlycompetitivelabormarketat$15 per hour. The marginal product of the 5th baker is 6 loaves per hour, and the marginal product of the 6th baker is 4 loaves per hour. Which of the following is the profit-maximizing hiring decision for the bakery? A) Hire both the 5th and 6th baker B) Hire the 5th baker, but not the 6th baker C) Do not hire the 5th or the 6th baker D) Hire the 6th baker, but not the 5th baker

Worked Solution: We use the profit-maximizing hiring rule: hire a worker only if their MRP is at least equal to the wage. For a perfectly competitive output market, $MRP=P\times M{P}_L$. MRP of the 5th baker is $3\times 6=\$18$, which is greater than the $\$15$ wage, so the 5th baker should be hired. MRP of the 6th baker is $3\times 4=\$12$, which is less than $\$15$, so the 6th baker should not be hired. The correct answer is B.

Question 2 (Free Response)

A firm produces custom bicycle frames and has monopoly power in the output market. The firm hires workers in a perfectly competitive labor market at an hourly wage of $\$20$. The firm's marginal product of labor is given by $M{P}_L=20-2L$, where $L$ is the number of workers. The firm's marginal revenue from output is $\$2$ per frame. (a) Write the equation for the firm's marginal revenue product of labor ($MR{P}_L$). (b) Calculate the profit-maximizing number of workers for the firm. (c) If the firm instead were perfectly competitive, and sold output at $P=\$3$ per frame, would it hire more or fewer workers than the monopoly? Explain, and calculate the profit-maximizing quantity of labor to support your answer.

Worked Solution: (a) By definition, $MR{P}_L=MR\times M{P}_L$. Substituting the given values: $$MR{P}_L=2(20-2L)=40-4L$$ (b) Set $MR{P}_L=w$ for profit maximization: $$40-4L=20\to 4L=20\to L=5\text{ workers}$$ (c) For a perfectly competitive firm, $MR=P=3$, so: $$MR{P}_L=3(20-2L)=60-6L$$ Set equal to $w=20$: $$60-6L=20\to 6L=40\to L\approx 6.67\text{ workers}$$ The perfectly competitive firm hires more workers than the monopolist. This is because $MR=P>MR$ for a monopolist, so MRP is higher at every quantity of labor, leading to a higher profit-maximizing quantity at the same wage.

Question 3 (Application / Real-World Style)

A delivery company is hiring additional drivers to complete local routes. Each driver costs $\$180$ per day (wage plus insurance and vehicle costs). The marginal number of deliveries per day for each additional driver is: 1st driver: 100 deliveries, 2nd driver: 90 deliveries, 3rd driver: 80 deliveries. The company earns $\$2$ of net revenue per delivery (after covering fuel and other non-labor costs). How many drivers should the company hire to maximize profit? Interpret your result in context.

Worked Solution: Calculate MRP for each driver, where $MR=\$2$ per delivery:

• MRP 1st driver: $2\times 100=\$200>\$180$
• MRP 2nd driver: $2\times 90=\$180=\$180$
• MRP 3rd driver: $2\times 80=\$160<\$180$

The profit-maximizing rule says to hire all drivers where $MRP\ge w$, so the company should hire 2 drivers. In context, the first driver adds $\$20$ to total profit, the second adds exactly enough revenue to cover its cost, and the third would reduce total profit by $\$20$, so stopping at 2 drivers is optimal.

7. Quick Reference Cheatsheet

8. What's Next

This chapter lays the foundational demand side of factor markets, which is required to analyze factor market equilibrium, minimum wage effects, and income inequality—all core tested topics in Unit 5. Without mastering the profit-maximizing hiring rule and the properties of the MRP factor demand curve, you cannot correctly analyze how changes to policy or market conditions affect employment and wages. Factor demand is also a critical prerequisite for analyzing imperfectly competitive factor markets like monopsony, where the firm has market power on the demand side, requiring adjustments to the profit-maximizing rule to account for MFC being higher than the market wage. The concept of derived demand also connects to general equilibrium analysis across the entire economy, a recurring theme on the AP exam.

Factor Supply and Competitive Factor Market Equilibrium Monopsony in Factor Markets Labor Market Policy and Income Inequality