Production Function
Plain definition
A production function shows the maximum output a firm can produce from each combination of inputs — typically written Q = f(L, K) for labor and capital. It is a purely technological relationship: given today's methods, these inputs yield at most this much output.
In economics
The production function is the firm's counterpart to the consumer's utility function. Its shape determines costs: diminishing marginal returns to a variable input make the marginal cost curve slope upward. In the short run at least one input is fixed; in the long run all inputs — and the technology itself — can change.
Example
A bakery's production function might show that 2 workers and 1 oven yield at most 200 loaves a day, while 3 workers and 1 oven yield 260 — the extra 60 loaves are the marginal product of the third worker, already smaller than the second worker's contribution.
The production function is often confused with a cost function. The production function is technological — it relates physical inputs to physical output, with no prices involved. Costs enter only when input prices are attached to those quantities. A firm can be technically efficient (on its production function) yet economically wasteful (using an expensive input mix).