Questions: Total, Average, and Marginal Product of Labor

Question 1

A firm currently employs 8 workers with an average product of 30 units per worker. The 9th worker would add 24 units of output. What happens to the average product after hiring the 9th worker?

• A. AP rises, because the firm is producing more total output
• B. AP falls, because the marginal worker produces less than the current average
• C. AP stays the same, because average product depends only on capital, not labor
• D. AP rises to 24, matching the marginal worker's output

Answer: (B)

When marginal product is below average product (24 < 30), the new worker pulls the average down — just as a below-average test score lowers your overall average. AP will fall. This is a mathematical identity: MP > AP implies AP is rising; MP < AP implies AP is falling; MP = AP at exactly AP's peak. Option A confuses rising total output (which is true — output went from 240 to 264) with rising average output per worker (which is false).

Question 2

A bakery employs 10 workers. The 11th worker would add 45 loaves per day. Each loaf sells for $2, and the daily wage is $120. Should the bakery hire the 11th worker?

• A. Yes — marginal product is still positive, so the worker adds to total output
• B. Yes — the firm should hire until output is maximized
• C. No — the value of the 11th worker's output is less than the wage
• D. No — diminishing returns means the bakery is already overstaffed

Answer: (C)

The marginal revenue product of the 11th worker is MP × price = 45 × $2 = $90, which is less than the $120 wage. Hiring this worker adds $90 in revenue but costs $120, reducing profit by $30. The firm stops hiring when MRP = wage, not when MP = 0. Option A is the classic misconception: positive MP means output rises, but the worker may still cost more than they produce. Diminishing returns (option D) is irrelevant on its own — what matters is whether MRP covers the wage.

Question 3

Diminishing marginal returns occurs when additional workers cause total output to fall.

• T. True
• F. False

Answer: False

Diminishing marginal returns means each additional worker adds less output than the one before — MP is declining but still positive. Total output continues to rise, just at a decreasing rate. Output only falls if MP becomes negative, which requires additional workers to actively impede production (e.g., severe crowding). The distinction matters: a firm experiencing diminishing returns still benefits from each worker; it just benefits less with each hire.

Question 4

The marginal product curve must intersect the average product curve exactly at average product's maximum.

• T. True
• F. False

Answer: True

This is a mathematical identity, not a coincidence. When a new worker produces more than the current average (MP > AP), they pull the average up — AP is rising. When a new worker produces less than the average (MP < AP), they drag it down — AP is falling. Therefore, at the exact moment AP transitions from rising to falling (its maximum), MP must equal AP. This logic applies to any average-marginal pair: class averages, batting averages, etc.

Question 5

Why do profit-maximizing firms stop hiring workers before marginal product reaches zero?

Model answer: A firm compares the value of an additional worker's output — the marginal revenue product (MP × output price) — against the wage. When MRP exceeds the wage, hiring adds more to revenue than to cost. When MRP falls below the wage, the last worker costs more than they generate. The firm stops where MRP = wage. Since wages are positive and output prices are positive, MRP reaches zero only when MP = 0, so firms always stop well before MP hits zero.

The intuition 'hire until MP = 0' ignores the cost of labor. Diminishing returns drive MP down, but the firm must stop as soon as the dollar value of that declining MP falls below the wage — typically at a substantial positive MP level. Only if labor were free (wage = 0) would a firm rationally hire until MP = 0.