# Factor Demand > AP Microeconomics · Unit 5: Factor Markets > Source: https://www.owlsprep.com/study/ap-microeconomics-u5-factor-demand/ This study guide covers derived demand, marginal revenue product (MRP), the profit-maximizing hiring rule, factor demand curve shape, and shifters of factor demand, aligned to AP Microeconomics Unit 5 learning objectives for exam preparation. **Prerequisites:** Profit maximization for firms; Law of diminishing marginal returns; Difference between perfectly competitive and imperfect product markets ## Learning objectives - Explain why factor demand is classified as derived demand - Calculate marginal revenue product (MRP) and value of marginal product (VMP) - Apply the profit-maximizing hiring rule to find optimal factor quantity - Describe the shape and position of the firm and market factor demand curves - Predict the direction of shifts in factor demand from common changes in market conditions ## 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 (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. Per the official AP Microeconomics CED, factor demand is a core component of Unit 5, making up roughly 10-15% of the unit's exam weight, translating to 2-3 multiple-choice questions per exam, and often a portion of a free-response question. **Derived Demand** — Demand for a factor of production that is derived from consumer demand for the final good the factor produces, rather than being demanded for its own direct value. *Example:* Demand for airline pilots increases when consumer demand for air travel increases. ## MRP and the Profit-Maximizing Hiring Rule The entire logic of factor demand derives directly from the firm's core goal of 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. **Marginal Revenue Product (MRP)** — The additional revenue generated by one extra unit of a factor of production, equal to the product of marginal revenue from output and marginal product of the factor. *Notation:* MRP = MR \times MP **Value of Marginal Product (VMP)** — For perfectly competitive output markets, $MR = P$, so MRP simplifies to VMP. For firms with output market power, $MR < P$, so $MRP < VMP$. *Notation:* VMP = P \times MP The profit-maximizing hiring rule states that a firm hires up to the point where $MRP = MFC$ (marginal factor cost). For perfectly competitive factor markets, $MFC$ equals the market factor price (e.g. $MFC = w$ for labor), so the rule simplifies to: $$MRP = w$$ **Worked example:** 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 $MRP = P \times MP_L$. 2. Calculate MRP of the 3rd line cook: $$MRP_3 = 2 \times 5 = \$10 \text{ per hour}$$ 3. The marginal factor cost of the 3rd line cook equals the market wage: $$MFC = w = \$12 \text{ per hour}$$ 4. Compare values: $MRP_3 = 10 < 12 = MFC$. 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. > **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. ## 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 profit-maximizing (quantity, factor price) pairs. 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. Product market structure 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:** A perfectly competitive firm and a monopolist share the same marginal product of labor schedule: $MP_L = 12 - L$, 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: $$MRP_L = P \times MP_L = 3(12 - L) = 36 - 3L$$ 2. Set $MRP_L = w$ to solve for $L$: $$36 - 3L = 9 \rightarrow 3L = 27 \rightarrow L = 9 \text{ units}$$ 3. For the monopolist: $$MRP_L = MR \times MP_L = 1.5(12 - L) = 18 - 1.5L$$ 4. Set $MRP_L = w$ to solve for $L$: $$18 - 1.5L = 9 \rightarrow 1.5L = 9 \rightarrow L = 6 \text{ units}$$ 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. > **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. ## 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 the variable on the vertical axis. - **Change in demand for the final product**: Increase in final demand raises MRP, shifting factor demand right; fall in final demand shifts left. - **Change in the price of other factors**: If substitute price falls, original factor demand shifts left; if complement price falls, original factor demand shifts right. - **Change in productivity**: Higher productivity raises MP, increasing MRP and shifting demand right; lower productivity shifts left. - **Change in number of firms**: More firms increase market factor demand, shifting the curve right; fewer firms shift left. **Worked example:** Identify the direction of shift for the market demand for commercial drone pilots for each scenario: (1) Consumer demand for real estate aerial photography increases. (2) The price of automated piloting software (a substitute for human pilots) falls. (3) New technology raises each pilot's output by 25%. 1. **Scenario 1**: Increased demand for the final product raises the price of aerial photography, increasing MRP for pilots at every wage. Market demand shifts right. 2. **Scenario 2**: Cheaper substitute software leads firms to substitute automation for human pilots, reducing MRP of human pilots. Demand shifts left. 3. **Scenario 3**: Higher productivity raises marginal product for each pilot, increasing MRP at every wage. Demand shifts right. **Check your understanding** Test your understanding with this AP-style multiple choice question: 1. A bakery sells sourdough loaves in a perfectly competitive output market at \$3 per loaf. The bakery hires bakers at \$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. What is the profit-maximizing hiring decision? - Hire both the 5th and 6th baker - Hire the 5th baker, but not the 6th baker - Do not hire either the 5th or 6th baker - Hire the 6th baker, but not the 5th baker *Why:* Correct. MRP of the 5th baker = $3 \times 6 = $18 > $15$, so hire. MRP of the 6th = $3 \times 4 = $12 < $15$, so do not hire. > **tip** > > This is the most frequently tested MCQ topic for factor demand. Remember: only changes to MR or MP shift the demand curve. A change in the wage never shifts the demand curve—it only causes a movement along it. ## Common pitfalls - **Wrong:** Confusing a movement along the factor demand curve with a shift when the wage changes. - Why it fails: Students mix up quantity demanded vs demand, forgetting the wage is on the vertical axis. - Correct: Always ask: does this change alter MR or MP at every quantity? If not, it is a movement along the curve, not a shift. - **Wrong:** Treating $MRP = VMP$ for all firms, regardless of product market structure. - Why it fails: Students learn VMP from perfect competition examples and incorrectly apply it to firms with market power. - Correct: Before calculating MRP, check for output market power. If the firm has market power, use $MRP = MR \times MP$, not $P \times MP$. - **Wrong:** Assuming a fall in the price of capital always shifts labor demand left. - Why it fails: Students default to the substitute case and forget that capital and labor can be complements. - Correct: First state whether the factors are substitutes or complements, then derive the shift direction from that relationship. - **Wrong:** Comparing average revenue product to the wage instead of marginal revenue product. - Why it fails: Students confuse total profit calculations with marginal profit maximization. - Correct: Always use marginal values: the hiring rule uses MRP = MFC, never average values. - **Wrong:** Drawing the factor demand curve upward-sloping, mixing it up with factor supply. - Why it fails: Students confuse demand and supply sides of the factor market. - Correct: Recall the law of diminishing marginal returns: more of a factor leads to lower MP, so MRP falls, making demand downward-sloping. ## Cheatsheet | Category | Formula/Rule | Key Notes | | --- | --- | --- | | Marginal Revenue Product (MRP) | $MRP = MR \times MP$ | Applies to all firms, all market structures | | Value of Marginal Product (VMP) | $VMP = P \times MP$ | Only for perfectly competitive output markets; $MRP = VMP$ only here | | General Profit-Maximizing Hiring Rule | $MRP = MFC$ | Applies to all firms, all factor market structures | | Hiring Rule (Competitive Factor Market) | $MRP = w$ (labor), $MRP = r$ (capital) | MFC equals factor price for price-taking firms | | Substitute factor price fall | Labor demand shifts left | Cheaper substitutes reduce demand for the original factor | | Complement factor price fall | Labor demand shifts right | Cheaper complements increase demand for the original factor | | Firm Factor Demand Curve | Equals MRP curve | Downward-sloping due to diminishing marginal returns | | Core Property of Factor Demand | Derived demand | Depends entirely on demand for final output | ## What's next This module lays the foundational demand side of factor markets, which is required to analyze factor market equilibrium, factor price determination, and labor market imperfections. Understanding factor demand is also critical for evaluating the economic effects of common policies like the minimum wage, a frequent free-response topic on the AP Microeconomics exam. Next, you will build on this foundation to study factor supply and market equilibrium, before moving on to more advanced topics like monopsony and income distribution. - [Hiring in the Labor Market](https://www.owlsprep.com/study/ap-microeconomics-u5-hiring-in-the-labor-market/) --- From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ap-microeconomics-u5-factor-demand/