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Unformatted text preview: to produce a given
maximum amount of output that we could get if 2we had justunitsient factor 1 and x2 units of factor 2.
amount of output.
To illustrate a production function with more than one input, let’s consider a situation in which the
Isoquants are similar to indi↵erence curves. As we’ve seen earlier, an
production of output requires two curve depicts the di↵erent consumption bundles that are broadly illustrate the techindi↵erence inputs: labor (L) and capital (K). This might just
nological possibilities facing ientsemiconductor manufacturer But there is one important of robots (capital) or
su c a to produce a certain level of utility. contemplating the use
humans (labor). The leftdi↵erenceof Figure 2 erence curves and isoquants. Isoquants are labeled
panel between indi↵ shows the production function as a 3-dimensional graph that
with the amount of output they can produce, not with a utility level. Thus
describes the relationship between of isoquants is ﬁxedoutputtechnology and doesn’tof the two inputs employed by
the quantity of by the and the quantity have the
kind of arbitrary nature that the utility labeling has.
In the two-input case there is a convenient way to depict production relations known as the isoquant.
An isoquant is the set of all possible combinations of inputs 1 and 2 that are just sufﬁcient to produce a
18.3 Examples of Technology
given amount of output. Isoquants are similar to indifference curves. As we’ve seen earlier, an indifference
Since we already know a lot about indi↵erence curves, it is easy to understand how isoquants work. Let’s consider a few examples of technologies
and their isoquants. Fixed Proportions per day; and Q is expressed in thousands of semiconductor chips per day. we can also use a contour plot to represent the production function. However, instead
of calling the contour lines indifference curves, we call them isoquants. Isoquant
means “same quantity”: any combination of labor and capital along a given isoquant
allows the firm to produce the same quantity of output.
To illustrate, let’s consider the production function described in Table 6.4 (the
same function as in Table 6.3). From this table we see that two different combinations
of labor and capital—(L
18) and (L
6)—result in an output of
25 units (where each “unit” of output represents a thousand semiconductors).
Thus, each of these input combinations is on the Q 25 isoquant.
The same isoquant is shown in Figure 6.6 (equivalent to Figure 6.5), illustrating the
total product hill for the production function in Table 6.4. Suppose that you started c06Inputsandproductionfunctions.qxd
isoquant A curve that
shows all of the combinations of labor and capital
that can produce a given
level of output. K, thousands of machine-hours per day A
C 24 E D 18
0 FIGURE 6.6 Isoquants and the Total Product Hill 6 12 18 24 1:29 PM Page 215 6.3 PRODUCTION FUNCTIONS WITH MORE TH...
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- Summer '13