The technology exhibits increasing returns to scale

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Unformatted text preview: creases by more than t. Later on, for larger levels of output, increasing scale by t may just increase output by the same factor t. 4 Examples of Technology Since we already know a lot about indifference curves, it is easy to understand how isoquants work. Let’s consider a few examples of technologies and their isoquants. 4.1 Fixed Proportions and Perfect Substitutes Suppose that we are producing holes and that the only way to get a hole is to use one man and one shovel. Extra shovels arent worth anything, and neither are extra men. Thus the total number of holes that you can produce will be the minimum of the number of men and the number of shovels that you have. We write the production function as f ( x1 , x2 ) = min{ x1 , x2 }. The isoquants look like those depicted in the left panel of Figure 4. Note that these isoquants are just like the case of perfect complements in consumer theory. Suppose now that we are producing homework and the inputs are red pencils and blue pencils. The amount of homework produced depends only on the total number of pencils, so we write the production function as f ( x1 , x2 ) = x1 + x2 . The resulting isoquants are just like the case of perfect substitutes in consumer theory, as depicted in the right panel of Figure 4. 6 EXAMPLES OF TECHNOLOGY 335 336 TECHNOLOGY (Ch. 18) x2 x2 Isoquants Isoquants x1 x1 Figure Perfect substitutes. Isoquants for the case of perfect substiFigure (Left) Fixed proportion propor-tutes. Figure Fixed proportions. 4:Isoquants for the case of fixedproduction function; (Right) Perfect substitutes. 18.3 tions. 18.2 changes in the inputs. We’ll examine their impact in more detail later on. 4.2 Cobb-Douglas The isoquants look like those depicted in Figure 18.2. Note In some of the examples, we will choose to set A = 1 in order to simplify that these isoquants are just like the case of perfect complements in consumer calculations. the theory. If the production function has the form The Cobb-Douglas isoquants have the same nice, well-behaved shape ab f ( x1that )the Cobb-Douglas indi↵erence curves have; as in the case of utility , x2 = Ax1 x2 Perfect Substitutes functions, the Cobb-Douglas production function is about the simplest exthen we say that it is a Cobb-Douglas production function. The numbers A > 1, a > 0, and b > 0 are all ample of well-behaved isoquants. Suppose nowconstants. producing homework and the inputs are red positive that we are pencils and blue pencils. The amount of homework produced depends only The neat thing about Cobb-Douglas production functions is that they can exhibit in- creasing, decreason the total number of pencils, so we write the production function as 18.4 Properties of Technology ing, ) = x1 + x2 . The resulting isoquants f (x1 , x2or constant returns to scale: are just like the case of perfect substitutes in consumer theory, as depicted in Figure 18.3. As in the case of consumers, it is common to assume certain properties a+b f (tx1 , tx2 ) = A(tx1...
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This document was uploaded on 09/21/2013.

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