THE PRODUCTION FUNCTION

Table 1 shows how the quantity of cookies Helen’s factory produces per hour depends on the number of workers. As you can see in the first two columns, if there are no workers in the factory, Helen produces no cookies. When there is 1 worker, she produces 50 cookies. When there are 2 workers, she produces 90 cookies and so on. Panel (a) of Figure 2 presents a graph of these two columns of numbers. The number of workers is on the horizontal axis, and the number of cookies produced is on the vertical axis. This relationship between the quantity of inputs (workers) and quantity of output (cookies) is called the production function.

One of the Ten Principles of Economics introduced in Chapter 1 is that rational people think at the margin. As we will see in future chapters, this idea is the key to understanding the decisions a firm makes about how many workers to hire and how much output to produce. To take a step toward understanding these decisions, the third column in the table gives the marginal product of a worker. The marginal product of .any input in the production process is the increase in the quantity of output obtained from one additional unit of that input.

TABLE 1 A Production Function and Total Cost: Hungry Helen’s Cookie Factory

Notice that as the number of workers increases, the marginal product declines. The second worker has a marginal product of 40 cookies, the third worker has a marginal product of 30 cookies, and the fourth worker has a marginal product of 20 cookies. This property is called diminishing marginal product. At first, when only a few workers are hired, they have easy access to Helen’s kitchen equipment. As the number of workers increases, additional workers have to share equipment and work in more crowded conditions. Eventually, the kitchen is so crowded that the workers start getting in each others’ way. Hence, as more and more workers are hired, each additional worker contributes less to the production of cookies.

Diminishing marginal product is also apparent in Figure 2. The production function’s slope (rise over run) tells us the change in Helen’s output of cookies (rise) for each additional input of labor (run). That is, the slope of the production function measures the marginal product of a worker. As the number of workers increases, the marginal product declines, and the production function becomes flatter.

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