3.1 The Production Function

Inputs become output

The production function shows the relationship between the quantity of inputs (like labor and capital) and the quantity of output a firm can produce. In the short run, at least one input — usually capital — is fixed, while labor is the variable input firms adjust to change output.

Total, Marginal, and Average Product

Total product (TP) is total output from a given amount of labor. Marginal product (MP) is the extra output from adding one more worker (ΔTP/ΔL). Average product (AP) is output per worker (TP/L). MP tells you whether TP is rising or falling.

Diminishing marginal returns

As more variable input (labor) is added to a fixed input (capital), marginal product eventually decreases — this is the law of diminishing marginal returns. It happens because each new worker has less capital/equipment to work with, so extra output per worker shrinks even while total output may still rise.

Key terms

Production function

The relationship between the quantity of inputs used and the quantity of output produced.

Total Product (TP)

The total quantity of output produced with a given amount of input.

Marginal Product (MP)

The additional output produced by adding one more unit of a variable input; MP = ΔTP/ΔL.

Average Product (AP)

Output per unit of variable input; AP = TP/L.

Law of Diminishing Marginal Returns

As more variable input is added to a fixed input, marginal product eventually decreases.

Try an AP-style question

The short run is defined as a period when…

1. costs are zero
2. all inputs are variable
3. at least one input is fixed
4. firms can enter freely