AP Microeconomics: Derived Demand for Labor and MRP = MFC Rule

AP Microeconomics – Derived Demand for Labor and MRP = MFC Rule

What This Is

Derived demand for labor is the demand for workers that comes from the demand for the product they help produce. Firms hire labor up to the point where the Marginal Revenue Product of Labor (MRP?) equals the Marginal Factor Cost (MFC)—the “MRP = MFC” rule. This concept shows how changes in product markets (price, technology, input prices) ripple through to the labor market, and it is a staple of AP?Micro?economics FRQs and multiple?choice items.

Key Terms & Formulas

• Derived Demand – Labor demand that is derived from the demand for the firm’s output, not from workers’ preferences.
• Marginal Physical Product of Labor (MP?) – Extra output produced by one more unit of labor; MP? = ?Q / ?L.
• Marginal Revenue Product of Labor (MRP?) – Extra revenue a firm earns from hiring one more worker. MRP? = MP? × MR (where MR = marginal revenue of the product).
• Marginal Factor Cost (MFC) – The additional cost of hiring one more unit of labor. In a perfectly competitive labor market, MFC = w (the market wage). In a monopsony, MFC > w and the MFC curve lies above the wage line.
• MRP? Curve – Graph of MRP? (vertical axis) vs. quantity of labor (horizontal axis). Downward?sloping because MP? diminishes and/or MR falls as output expands.
• MFC Curve – Horizontal line at the market wage in a competitive labor market; upward?sloping (steeper) in a monopsony.
• Profit?Maximizing Rule (MRP? = MFC) – The firm hires labor until the value of the last worker’s output equals the cost of that worker.
• Labor Supply Curve (S?) – Shows the relationship between the wage rate and the quantity of labor workers are willing to supply. Axes: Wage (vertical), Labor (horizontal).
• Shift Shifters of Derived Demand – Changes in product price, technology, input prices, or number of firms that shift the MRP? curve left (decrease) or right (increase).
• Elasticity of Derived Demand – ? = %?L? / %?w; more elastic when product demand is elastic, labor share in total cost is low, and substitutes are easy to find.

Step?by?Step / Process Flow (Solving a Typical AP Problem)

1. Identify the product market condition – e.g., price of the final good rises, a new technology is adopted, or an input price falls.
2. Calculate/Sketch MP? – Use the production function or given data to find the marginal physical product for each additional worker.
3. Derive MRP? – Multiply each MP? by the marginal revenue (price if the firm is a price taker; otherwise use MR). Plot MRP? on a graph (vertical axis = $/worker, horizontal axis = # of workers).
4. Draw the MFC curve – If the labor market is competitive, draw a horizontal line at the given wage. If it’s a monopsony, draw an upward?sloping MFC that starts at the wage line and rises faster than the labor supply curve.
5. Find the intersection – The point where MRP? = MFC gives the profit?maximizing quantity of labor (L). Mark the corresponding wage (w) on the vertical axis.
6. Interpret the result – Explain how a change in the product market (step?1) shifts MRP?, moves the intersection, and thus changes both employment and wages.

Common Mistakes

AP Exam Insights

1. Multiple?Choice Focus: Look for items that ask you to identify the correct labor?market diagram (MRP? vs. MFC) or to choose the outcome of a shift (e.g., “If the price of smartphones rises, the derived demand for assembly?line workers will …”).
2. FRQ Prompt Pattern: You’ll often be given a table of output, labor, and price, then asked to (a) compute MP?, (b) compute MRP?, (c) draw the MRP? and MFC curves, and (d) explain how a change (e.g., a new robot) affects equilibrium employment and wages.
3. Tricky Distinction: “A change in the wage rate”-movement along the labor?demand curve; “a change in product price”-shift of the derived?demand (MRP?) curve. Remember to label both curves on the same graph.
4. Monopsony vs. Competitive Labor Market: The exam loves to contrast the two. In a monopsony, the profit?maximizing wage is below the marginal factor cost at the chosen employment level; in a competitive market, wage = MFC.

Quick Check Questions

1. MC: A firm’s product price rises from $10 to $12. All else equal, what happens to the MRP? curve?

2. Answer: It shifts right/upward because MR (and thus MRP?) increases.

3. FRQ?style: A bakery uses 1, 2, and 3 workers to produce 20, 35, and 45 loaves of bread per day. The market price of bread is $5 per loaf.
   a) Compute MP? for the 2nd and 3rd workers.
   b) Compute MRP? for the 2nd and 3rd workers.
   c) If the wage is $30, how many workers should the bakery hire?

4. Answer: a) MP? = 15 loaves, MP? = 10 loaves. b) MRP? = 15×5 = $75, MRP? = 10×5 = $50. c) Hire 2 workers because MRP? ($75) > wage ($30) but MRP? ($50) > wage still, actually both > wage, so hire 3? Wait, check: MRP? = $50 > $30, so hire 3 workers. (If wage were $60, only 2 workers.) Explanation: Hire until MRP?-wage; the last hired worker’s MRP? must be at least the wage.

5. MC: In a monopsonistic labor market, the firm’s labor supply curve is upward?sloping. Which statement is true at the profit?maximizing point?

6. Answer: The wage paid is lower than the marginal factor cost (MFC > wage).

Last?Minute Cram Sheet (10 One?Liners)

1. Derived demand = demand for a factor that comes from product demand.
2. MRP? = MP? × MR (use price for MR if the firm is a price taker).
3. Profit?max rule: Hire labor until MRP? = MFC.
4. Competitive labor market: MFC = wage (horizontal line).
5. Monopsony: MFC lies above the wage line; the firm pays a lower wage than the cost of the last worker.
6. A rise in product price-rightward shift of MRP? (higher revenue per unit of output).
7. A technological improvement that raises MP?-rightward shift of MRP? (more output per worker).
8. Elasticity of derived demand is higher when product demand is elastic, labor’s share of total cost is low, and substitutes are easy.
9. “Supply increases” = curve shifts right, not up. A price change moves you along the curve.
10. In a monopsony, the equilibrium wage is not where the labor?supply curve meets the MRP? curve; it’s where MFC meets MRP?.