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# You can scale the production process up and down

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Unformatted text preview: n processes don’t interfere with each other, convexity is a very natural assumption. 3 215 This is depicted in Figure 18.4. 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 di↵erent 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 output. x2 100a2 (25a1 + 75b1, 25a2 + 75b2 ) Isoquant 100b2 100a1 100b1 x1 Figure 3: A production function with two inputs. 3.2 The Marginal Convexity. If you can operate production activities independently, then weighted averages of production plans will also be feasible. Thus the isoquants will have a convex shape. Product Figure 18.4 Suppose that we are operating with some input combination ( x1 , x2 ), and that we consider using a little bit more of factor 1 while keeping factor 2 ﬁxed at the level x2 . How much more output y will we get per additional unit of factor 1? We have to look at the change in output per unit change of factor 1: In this kind of technology, where you can scale the production process up Dy ∂ ( x1 , x ) f ( 1 + D x1 , x processes don’t and down easily and fwhere 2separatexproduction2 ) f ( x1 , x2 ) interfere with each other, = convexity is a= very natural assumption. D x1 ∂ x1 D x1 (1) We call this the marginal product of factor 1 ( MP1 ). The marginal product of factor 2 ( MP2 ) is deﬁned in a similar way. The concept of marginal product is just like the concept of marginal utility that we described in our discussion of consumer theory, except for the ordinal nature of utility. Here, we are discussing physical output: the marginal product of a factor is a speciﬁc number, which can, in principle, be observed. 3.3 The Law of Diminishing Marginal Product As long as we have a monotonic technology, we know that the total output will go up as we increase the amount of factor 1. But it is natural to expect that it will go up at a decreasing rate. Thus we would typically expect that the marginal product of a factor will diminish as we get more and more of that factor. This is called the law of diminishing marginal product (marginal returns). It isn’t really a “law”; it’s just a common feature of most kinds of production processes. It is important to emphasize that the law of diminishing marginal product applies only when all other inputs are being held ﬁxed. 3.3.1 Example: Malthus and Food Crisis The law of marginal product was central to the thinking of economist Thomas Malthus (1766-1834). Malthus predicted that the limited amount of land on our globe would not be able to supply enough food as population grew and more laborers began to farm land. Eventually the marginal productivity of labor fell, and mass hunger and starvation would result. Fortunately, Malthus’ prediction did not turn out to be true, even though he was right about the diminishing marginal returns to labor. Over the past...
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