[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

The relationship between the quantity of inputs used in production
and the level of output is called the production function. Figure 6.1
shows the farmer’s production function; the data supporting the figure
are set forth in Table 6.1. The increase in output corresponding to a
unit increase in any factor of production, labor in this case, is the marginal
product of that factor. For example, when the number of hours
worked per year rises from 8,000 to 9,000, output increases by 10,000
bushels, from 155,000 to 165,000. The marginal product of an extra
1,000 hours of labor is thus 10,000 bushels. The marginal product is
given in the last column of the table. Diagrammatically, it is given by
the slope of the production function. The slope of a curve is the change
along the vertical axis (the increase in output) from a unit increase
along the horizontal axis (the increase in labor input).
Diminishing Returns In the case of the wheat farmer, as more
labor is added to a fixed amount of land, the marginal product of labor
diminishes. This is another application of the concept of diminishing
returns, which we originally encountered in Chapter 2. In the case of a
firm’s production function, diminishing returns implies that each additional
unit of labor generates a smaller increase in output than the last.
Increasing the number of hours worked from 7,000 to 8,000 raises
output by 15,000 bushels, but increasing the hours worked from 8,000
to 9,000 raises output by only 10,000 bushels. Diminishing returns sets
in with a vengeance at higher levels of input; moving from 10,000 to
11,000 hours worked adds nothing. Diagrammatically, diminishing
returns are represented by the slope’s flattening out as the amount of
labor increases. It is clear that because of diminishing returns, increases
in input lead to less than proportionate increases in output; doubling
the input results in output that is less than twice as large.
OUTPUT OF WHEAT (THOUSANDS OF BUSHELS)
170
165
155
140
120
95
0
Figure 6.1
Production
function
Slope in this region
= 15 bushels per hour of labor
= marginal product of an hour
of labor (increasing labor input
by 1,000 hours increases
output by 15,000 bushels)
5 6 7 8 9 10 11
THOUSANDS OF HOURS WORKED
PRODUCTION FUNCTION WITH
DIMINISHING RETURNS TO AN INPUT
As the amount of the input (labor) increases, so does
the output (wheat). But there are diminishing returns
to labor: each increase in labor results in successively
smaller increases in wheat output. Since the slope
of the curve is the marginal product of labor, the slope
on the graph flattens out as the amount of labor
increases.
Table 6.1
LEVEL OF OUTPUT WITH DIFFERENT AMOUNTS OF LABOR
Marginal Product
Amount of
(additional bushels pro-
Number of wheat produced duced by 1,000 additional
hours worked (bushels) hours of labor)
5,000 95,000
6,000 120,000 25,000
7,000 140,000 20,000
8,000 155,000 15,000
9,000 165,000 10,000
10,000 170,000 5,000
11,000 170,000 0
PROFITS, COSTS, AND FACTORS OF PRODUCTION ∂ 133