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 proportutes. 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 CobbDouglas
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 CobbDouglas isoquants have the same nice, wellbehaved shape
ab
f ( x1that )the CobbDouglas indi↵erence curves have; as in the case of utility
, x2 = Ax1 x2
Perfect Substitutes
functions, the CobbDouglas production function is about the simplest exthen we say that it is a CobbDouglas production function. The numbers A > 1, a > 0, and b > 0 are all
ample of wellbehaved 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 CobbDouglas 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...
View
Full
Document
This document was uploaded on 09/21/2013.
 Summer '13
 Microeconomics

Click to edit the document details