Total Product, Average Product and Marginal Product

Total Product, Average Product and Marginal Product

This section introduces three basic measures that describe what happens inside a production process. A firm combines inputs — labour, capital, raw materials — to create output. These three concepts let us track how output behaves as we change the quantity of one input while holding every other input fixed. Throughout this discussion we treat labour ($L$) as the single variable input and hold capital fixed, which is the standard short-run setting.

Total Product (TP)

Total product is the total quantity of output produced by a given quantity of the variable input during a period, with all other inputs held constant. If a farmer working a fixed plot of land employs a certain number of workers, the total output harvested is the total product of labour. It is also called the total return or total physical product of the variable input. As more units of labour are employed, total product goes on rising — first at an increasing rate and then at a diminishing rate.

Average Product (AP)

Average product measures the output per unit of the variable input. For labour it is:

where $TP$ is total product and $L$ is the number of labour units employed. It tells us how productive the average worker is. If output rises when one more worker is added and the average product goes up, that worker is more productive than the existing average; if the average product falls, the new worker is less productive than the average.

Marginal Product (MP)

Marginal product is the addition to total product when one more unit of the variable input is employed, all other inputs staying constant. For labour:

where $\Delta TP$ is the change in total product and $\Delta L$ is the change in labour (usually one unit). Equivalently, the marginal product of the $L$-th unit is the total product with $L$ units minus the total product with $L-1$ units:

Because inputs cannot be negative, marginal product is not defined at zero employment. A useful identity follows directly: the sum of the marginal products of every unit of the input up to a given level equals the total product at that level. In other words, total product is just the running sum of the marginal products.

The Relationship Between TP, AP and MP

The way the three measures move together follows a simple logic:

1. When MP is greater than AP, AP rises. The extra output from the new unit is above the current average, so it pulls the average up.
2. When MP is less than AP, AP falls. The new unit adds less than the average, so the average is dragged down.
3. When MP equals AP, AP is at its maximum. This is the turning point of the average product.

Average product at any level of employment is simply the average of all the marginal products up to that level. Average and marginal products are together referred to as the average and marginal returns to the variable input.

Graphical Representation

Plotting labour on the horizontal axis and output on the vertical axis gives the shapes analysed in the next sections: …