Principles of Microeconomics / Unit 6 MIC 0533 worked example, 60 to 90 seconds
Applying the Input Rule
The idea
Given the marginal product and price of each input at the firm's current mix, divide each marginal product by its price. If the ratios are equal, the firm is minimizing cost for that output and should change nothing. If they differ, the firm should use more of the input with the higher marginal product per dollar and less of the other; as it does, the higher ratio falls through diminishing returns and the lower one rises, until they meet. The answer is a direction, never "use only the cheaper input".
In practice
Worked example: a workshop's last worker adds sixty units at a price of twelve dollars, five units per dollar, and its last machine adds forty units at four dollars, ten units per dollar. Capital gives more per dollar, so the firm should use more capital and less labor to make its current output at lower cost. A second workshop's last worker adds thirty units at ten dollars and its last machine fifteen at five dollars, three per dollar each: it is already at least cost.
Where people slip
Two errors. Comparing marginal products without dividing by price, which would have favored labor's sixty over capital's forty. And concluding that the cheaper input should replace the other entirely; diminishing returns lower capital's marginal product as more is used, and the shift stops when the ratios meet.
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