The relationship between inputs and outputs (the production technology) expressed numerically or mathematically is called a production function or total product function. The table below illustrates a production function for a small sandwich shop. We assume that all the sandwiches are grilled, and that the firm has only one grill, which can accommodate only two workers comfortably.
As you can see from the data in the table, as more workers are added, the total product (sandwiches per hour) increases, up to a maximum of 42 sandwiches per hour.
But notice how the total output is changing each time another worker is added. For example; when the second worker is added, total product increases from 10 to 25, a change of 15. But when the third worker is added, total product increases from 25 to 35, which is only a change of 10. And this continues, until finally, the 6th worker adds nothing to total product!
We have just done the calculations for what is called marginal product, or the change in total product for a one-unit change in the quantity of an input. In this example, it is the additional sandwiches that can be produced by adding one more worker. Notice that in this example, marginal product increases then decreases.
This is due to the law of diminishing returns, which states that, in the short run, as you continue to add a variable input to a fixed input, at some point the additional output from the variable input will decline. In this example, diminishing returns set in when the third worker is added.
REALITY CHECK: Are you as productive in your tenth straight hour of studying as you were in your first hour? Diminishing returns have set in!
Diminishing returns always apply in the short run, and in the short run every firm will face diminishing returns. This means that every firm will find it progressively more difficult to increase its output as it approaches capacity production.
The figure below graphs the data from Table 6.2.
For more practice drawing the total and marginal product and the production function, try the following EGraph exercises:
For an illustration of diminishing returns and the production function in the case of diminishing returns, try the following EGraph exercises: