Principles of Microeconomics / Unit 13 MIC 1208 worked example, 60 to 90 seconds
The Two Rules Lead to the Same Outcome
The idea
The hiring rule and the output rule are one rule in two units. Hiring a worker whose marginal revenue product exceeds the wage is producing units whose price exceeds marginal cost, because a unit's marginal cost is the wage divided by marginal product. Check it: compute marginal cost per unit for the last worker hired and the first not hired, and compare each with the price. Both rules must give the same workers and output.
In practice
Worked example: at one hundred fifty a day and ten dollars a wash, the car wash hires four workers, since the fourth's marginal revenue product of one eighty beats the wage and the fifth's one forty does not. Now the output rule. The fourth worker adds eighteen cars for one hundred fifty dollars, a marginal cost of eight dollars thirty-three a wash, below the ten-dollar price: produce them. The fifth adds fourteen cars for one hundred fifty, ten dollars seventy-one a wash, above the price: do not. Both rules stop at four workers and ninety-six cars.
Where people slip
Marginal cost per unit is the wage divided by marginal product, so it rises as marginal product falls; that is the link between unit six's rising marginal cost and this unit's falling marginal product. And the rules cannot disagree; if they seem to, a marginal was computed from an average.
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