The production function

Production turns inputs (labour, capital, land) into output. Put oranges into a juicer and juice comes out: the oranges are the input, the juice the output, and more oranges give more juice. A firm sells its output to earn revenue; its profit = revenue − cost. We assume the firm wants to maximise profit.

The production function gives the maximum output a firm can produce with each combination of inputs: q = f(L, K), where L is labour and K is capital. It is defined for a given technology: if technology improves, there is a new production function, with more output from the same inputs.

A production function can be shown as a table: one input along the top, the other down the side, and the output for each combination inside. With zero labour or zero capital, output is usually zero: both are needed.

An isoquant joins all the input combinations that give the same output. For example, 20 units of output might come from (6 workers, 1 machine), (3 workers, 2 machines) or (2 workers, 3 machines). To produce the same output with less labour, the firm needs more capital, so an isoquant slopes downward.