Marginal Product
What is Marginal Product?
Marginal Product is the additional output produced by adding one more unit of a variable input, holding all other inputs constant.
It is calculated as the change in total product divided by the change in the variable input. Marginal product typically rises at first due to increased efficiency, then falls due to the law of diminishing marginal returns.
Marginal Product: a worked example
A car wash keeps two bays fixed and varies its staff. With 4 workers it cleans 90 cars a day, and with 6 workers it cleans 120. Marginal product over that range is the change in total product divided by the change in labor: 30 extra cars ÷ 2 extra workers = 15 cars per worker. Compare that with average product, which divides total product by all workers: 90 ÷ 4 = 22.5 cars at four workers and 120 ÷ 6 = 20 cars at six. The marginal worker's 15 cars sits below the average of 22.5, which is exactly why the average gets pulled down to 20. If each wash earns $8, the marginal worker brings in 15 × $8 = $120 a day, so hiring pays only while the daily wage sits under $120.
The mistake students make with marginal product
Watching marginal product fall, students conclude the newer hires must be lazier or less skilled and write that on the exam. The model assumes every worker is identical. Marginal product declines because the fixed capital, two wash bays here, is shared among more and more people, leaving each additional worker with less equipment to use. A second slip is reporting the raw extra output as marginal product when labor jumps by more than one worker, instead of dividing that extra output by the number of workers added.
Marginal Product questions
What is the difference between marginal product and average product?
Marginal product measures the extra output from one more unit of input, found by dividing the change in total product by the change in that input. Average product measures output per unit of input, found by dividing total product by the total input used. Whenever marginal product sits above average product, the average rises; whenever it sits below, the average falls, the same arithmetic as one test score pulling a grade average up or down.
How do you calculate marginal product?
Divide the change in total product by the change in the variable input while holding every other input constant. If total product rises from 48 units to 57 units when a third worker joins, marginal product is 9 units. When the input changes by more than one unit, divide by that change instead: 24 extra units produced by 3 extra workers gives a marginal product of 8 units per worker.
What is marginal revenue product and how does it relate to marginal product?
Marginal revenue product equals marginal product multiplied by the output price for a firm selling in a competitive market. A worker who adds 12 units selling at $5 each generates $60 of marginal revenue product, so the firm hires that worker whenever the wage sits below $60. Because marginal product eventually declines, marginal revenue product declines with it, which is why labor demand curves slope downward.
Formula / Example
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