Marginal Productivity

Business Calculus · Axiom Academy

How additional inputs affect production output What is Marginal Productivity? Marginal productivity measures how much additional output is produced when one input increases by one unit, while all other inputs remain constant. It's the partial derivative of the production function with respect to that input. Marginal Product of Labor (MP L ) Additional output from one more unit of labor, holding capital constant. Marginal Product of Capital (MP K ) Additional output from one more unit of capital, holding labor constant. For a Cobb-Douglas production function : Multiply by α, reduce labor exponent by 1 Multiply by β, reduce capital exponent by 1 Example: Manufacturing Company A factory's production is modeled by: where L = labor hours (hundreds) and K = capital (millions of dollars). Adding 100 more labor hours increases output by ~7.5 units Adding 1M more capital increases output by ~10 units Capital has higher marginal productivity at this point A fundamental principle: as you increase one input while holding others constant, the marginal product of that input eventually decreases . As labor increases (with capital fixed), total output grows but marginal product declines. Think about a factory: with a fixed number of machines (capital), adding more workers helps initially. But eventually, workers start getting in each other's way, waiting for machines, or having less equipment to work with—so each additional worker adds less to output.

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