Unformatted text preview: when fast-foodcorrespond to the
highlighted input combinations in Table 6.4. When both inputs have positive marfaced shortage of young, low-wage employees, the ﬁrms may respondmore of each input increases theby recruiting older
ginal products, using by automating or amount of output attainable.
people to ﬁll these positions. As we discuss in Chapters 7Hence, isoquants Qtaking this ﬂexibility in6.8, correspond to larger
and 8, by 2 and Q3, to the northeast of Q1 in Figure the production
and larger quantities of output.
An isoquant can also be represented algebraically, in the form of an equation,
process into account, managers can choose input combinations that minimize cost and maximize proﬁt. as 3.1 well as graphically (like the isoquants in Figure 6.8). For a production function like the
ones we have been considering, where quantity of output Q depends on two inputs
(quantity of labor L and quantity of capital K ), the equation of an isoquant would express K in terms of L. Learning-By-Doing Exercise 6.1 shows how to derive such an
equation. Properties of Technology As in the case of consumers, it is common to assume certain properties about technology. First we will
generally assume that technologies are monotonic: if you increase the amount of at least one of the inputs,
it should be possible to produce at least as much output as you were producing originally. This is sometimes
referred to as the property of free disposal: if the ﬁrm can costlessly dispose of any inputs, having extra
inputs around can’t hurt it.
Second, we will often assume that the technology is convex. This means that if you have two extreme
ways to produce y units of output, ( x1 , x2 ) and (z1 , z2 ), then their weighted average will produce at least y
units of output. One argument for convex technologies goes as follows. Suppose that you have a way to
produce 1 unit of output using a1 units of factor 1 and a2 units of factor 2 and that you have another way
to produce 1 unit of output using b1 units of factor 1 and b2 units of factor 2. We call these two ways to
produce output production techniques.
Furthermore, let us suppose that you are free to scale the output up by arbitrary amounts so that
(100a1 , 100a2 ) and (100b1 , 100b2 ) will produce 100 units of output. But now note that if you have 25a1 + 75b1
units of factor 1 and 25a2 + 75b2 units of factor 2 you can still produce 100 units of output: just produce 25
units of the output using the “a” technique and 75 units of the output using the “b” technique.
This is depicted in Figure 3. By choosing the level at which you operate each of the two activities, you
can produce a given amount of output in a variety of different ways. In particular, every input combination
along the line connecting (100a1 , 100a2 ) and (100b1 , 100b2 ) will be a feasible way to produce 100 units of
In this kind of technology, where you can scale the production process up and down easily and where
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