Principles of Microeconomics / Unit 17 MIC 1617 worked example, 60 to 90 seconds
Sample Question Four: The Cost-Minimizing Combination
The idea
A firm producing a given output at least cost uses inputs so that the marginal product per dollar is equal across them: marginal product of labor over the wage equals marginal product of capital over the rental. If one ratio is higher, the last dollar spent on that input buys more output, so shift spending toward it, which lowers its marginal product and raises the other's until they match. Compute both ratios, compare, and say which input to use more of.
In practice
Worked example: the last worker adds twenty units and costs ten dollars, two units per dollar; the last machine-hour adds forty-five units and costs fifteen dollars, three units per dollar. Capital's ratio is higher, so the firm is not at least cost; it should use more capital and less labor. As it does, capital's marginal product falls and labor's rises, and the ratios converge; at, say, thirty units for fifteen dollars and twenty for ten, both are two per dollar and the combination is cost-minimizing.
Where people slip
Compare marginal product per dollar, never marginal product alone; a machine with the higher marginal product is not worth more if it costs proportionally more. And the rule is the consumer's utility-per-dollar rule with output in place of utility, which is why the exam tests both.
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