2 Marginal Product and Productivity

Production and the short run

A firm’s Production function describes the maximum output it can produce from given quantities of inputs using its available technology. In the short run, at least one input—often a factory, equipment, or workspace—is fixed, while another input, such as labor, can vary. Productivity measures how effectively inputs are converted into output.

Total, average, and marginal product

Total product ($TP$) is the total quantity of output produced. Average product ($AP$) is output per unit of an input, while Marginal product ($MP$) is the extra output resulting from an additional unit of that input, holding other inputs constant.

For labor, the measures are:

• Average product of labor: $AP_L = \frac{Q}{L}$

• Marginal product of labor: $MP_L = \frac{\Delta Q}{\Delta L}$

Here, $Q$ is total output and $L$ is the quantity of labor. If labor is measured in whole workers, marginal product is the change in output when the next worker is added.

For a bakery with a fixed kitchen, the example values are:

• $0$ workers: total product $0$; marginal and average product are not given.

• $1$ worker: total product $8$, marginal product $8$, and average product $8$.

• $2$ workers: total product $20$, marginal product $12$, and average product $10$.

• $3$ workers: total product $30$, marginal product $10$, and average product $10$.

• $4$ workers: total product $36$, marginal product $6$, and average product $9$.

The third worker raises output from $20$ to $30$ units, so that worker’s marginal product is $30 - 20 = 10$ units. With $3$ workers, average product is $\frac{30}{3} = 10$ units per worker.

How product measures relate

Marginal product is the slope of the total-product curve: a steeper curve means a larger marginal product. When marginal product is positive, adding the input increases total output. When marginal product is zero, total product has reached a peak; when marginal product is negative, adding the input reduces output.

Marginal product also indicates whether average product rises or falls. If the next unit’s marginal product is above the current average, it pulls the average up; if it is below the average, it pulls the average down. In a smooth production curve, marginal product crosses average product at average product’s maximum.

In the bakery example, the fourth worker’s marginal product is $6$, below the previous average of $10$, so average product falls to $9$.

Diminishing returns and input choices

A firm may initially gain from specialization as it adds workers. But when equipment or workspace is fixed, adding more workers eventually means sharing or crowding the same resources. Diminishing marginal product occurs when each additional unit of a variable input adds less output than the previous unit. Total product can still rise during this phase: the additional input contributes output, but progressively less. If marginal product eventually becomes negative, the input has been added beyond the point where it helps production.

These measures can help managers compare input choices. Average product summarizes output per worker, while marginal product estimates the extra output from the next worker. A manager considering another worker can compare that worker’s expected contribution with the cost of employing them and the value of the added output. With other inputs unchanged, diminishing marginal product signals that further increases in labor yield smaller additions to production.

To sustain higher productivity, the firm may need to change its mix of inputs—for example, by adding equipment or improving the production process. The relevant production function and productivity measures depend on the product and the inputs being considered.