The Production Function

How economists describe the relationship between inputs like labour and capital and the output a firm produces, and the law of diminishing returns.

Firms turn inputs, such as workers, machines, land and materials, into outputs, such as goods and services. The relationship between inputs and output is described by a production function.

Inputs

Economists often simplify inputs into two main categories:

Labour: the work of employees.
Capital: machines, equipment, buildings and tools.

A production function answers: with a given amount of labour and capital, how much can a firm produce?

Marginal product

The marginal product of an input is the extra output produced by adding one more unit of it, holding other inputs fixed. For example, the marginal product of labour is the extra output from hiring one more worker.

Diminishing returns

A central idea is the law of diminishing marginal returns: if you keep adding more of one input while holding others fixed, the extra output from each additional unit eventually falls.

Imagine a small restaurant kitchen with two stoves:

The first cook produces many meals.
A second cook adds a lot more.
A third cook helps, but starts waiting for stoves.
A fifth or sixth cook gets in the way, adding very little.

The kitchen’s fixed capital, the stoves and space, limits how productive extra cooks can be.

Short run and long run

In the short run, some inputs, like the size of a factory, are fixed, so diminishing returns apply. In the long run, firms can adjust all inputs, building bigger kitchens or factories.

Technology

Better technology shifts the production function upward: the same inputs produce more output. This is why technological progress is central to long-run growth.

Workers on a farm

A farmer with one hectare of land hires one worker, then two, then three. The first worker greatly increases the harvest. The second adds less. By the fifth worker, the land is crowded, and extra output is tiny. More land or better seeds would be needed to make additional workers productive.

Thinking diminishing returns means output falls

Diminishing returns means each additional unit of input adds less extra output than the one before, not that total output falls. Total output usually keeps rising, just more slowly.

Key takeaways

A production function shows how inputs like labour and capital produce output.
Marginal product is the extra output from one more unit of an input.
Diminishing marginal returns mean extra output falls as one input increases with others fixed.
Better technology shifts the production function up, allowing more output from the same inputs.