Questions: Marginal Revenue Product: Derived Demand for Inputs

Question 1

A new technology improves each worker's marginal product by 30%, while the output price and wage both remain unchanged. What happens to the firm's demand for labor?

• A. Labor demand decreases — each worker produces more, so fewer workers are needed to reach the same output
• B. Labor demand stays unchanged — workers' wages didn't change, so the hiring decision is the same
• C. Labor demand increases — higher marginal product raises MRP, so more workers now pass the MRP ≥ W hiring threshold
• D. Labor demand is unaffected by productivity changes; only the wage determines how many workers to hire

Answer: (C)

MRP = MP × P. If MP rises by 30% and P is unchanged, MRP rises by 30% for every worker. Workers who previously had MRP just below the wage now have MRP above it — they are worth hiring. Workers already hired generate even more value. Both effects push the firm to demand more labor. Option A is the common misconception that higher productivity reduces employment; in a competitive labor market, higher productivity raises MRP (the value of hiring), which increases the incentive to hire. The labor demand curve (which is the MRP curve) shifts rightward.

Question 2

A construction firm currently hires 20 workers, paying each $80/day, and each worker generates exactly $80 in MRP. Suddenly housing demand collapses and the price of new homes falls by 40%. Assuming wages stay at $80 and marginal products are unchanged, what should the firm do?

• A. Keep hiring 20 workers — the wage hasn't changed, so the hiring decision is unchanged
• B. Hire more workers to compensate for lost revenue by increasing total production
• C. Reduce the workforce — the MRP of each worker falls roughly 40%, dropping below the $80 wage
• D. Fire all workers — when output prices fall, no labor can be profitable

Answer: (C)

MRP = MP × P. If P falls by 40%, MRP falls by roughly 40% — from $80 to about $48 per worker. At a wage of $80, no worker is worth their cost (MRP < W), so the firm should reduce its workforce. This illustrates derived demand in action: a collapse in the output market (housing) directly depresses labor demand through the MRP formula, even though labor productivity (MP) and the wage are unchanged. The product market and factor market are inseparably connected through MRP.

Question 3

The marginal revenue product (MRP) curve for labor is the firm's demand curve for labor — the curve that directly determines how many workers the firm wants to hire at any given wage.

• T. True
• F. False

Answer: True

The MRP curve and the labor demand curve are the same thing. At any wage W, the profit-maximizing firm hires workers up to the point where MRP = W. For wages above the current MRP, it doesn't hire more; for wages below, it hires until MRP falls to equal the wage. Reading the MRP curve at each wage level tells you exactly how many workers the firm demands — which is the definition of a demand curve. Anything that shifts MRP (output price changes, productivity shifts) shifts the labor demand curve directly.

Question 4

A firm should hire workers until the total revenue generated by most workers equals the total wage bill — this ensures the firm's labor costs are fully covered by labor's output.

• T. True
• F. False

Answer: False

The correct hiring rule is MRP = W (marginal, not total). Hiring until total revenue = total wage costs would systematically under-hire: it ignores the infra-marginal profit on earlier workers (whose MRP exceeds the wage) and gives no guidance about when to stop hiring as MRP declines. The profit-maximizing rule is to hire each additional worker as long as the marginal value of that worker (MRP) exceeds the marginal cost (wage), and stop when MRP = W. This is exactly analogous to the output rule P = MC — always compare marginal values, not totals.

Question 5

Explain in your own words why labor demand is called 'derived demand.' Use a specific example to show how a change in the product market flows through to the number of workers a firm wants to hire.

Model answer: Labor demand is 'derived' because firms don't want workers for their own sake — they want the output workers produce, and only value workers as long as that output can be sold profitably. The channel is MRP = MP × P: a change in output price P directly changes the MRP of every worker, shifting the labor demand curve. For example, if demand for electric vehicles surges and car prices rise, the MRP of auto assembly workers rises (the same assembly work now generates more revenue per unit), and automakers demand more workers even if wages are unchanged. Conversely, if oil prices collapse and fewer oil rigs are profitable, MRP for rig workers falls and firms lay off workers — not because workers became less productive, but because their output became less valuable. The product market drives the factor market.

This linkage is why recessions in goods markets translate into unemployment: falling output prices depress MRP across industries simultaneously, reducing labor demand economy-wide. It also explains why productivity improvements tend to raise wages in competitive labor markets — higher MP raises MRP, which shifts the labor demand curve outward, bidding up wages. Understanding derived demand is essential for connecting product market analysis to labor market outcomes.