CHAPTER 9
PRODUCTION FUNCTIONS
Because the problems in this chapter do not involve optimization (cost minimization
principles are not presented until Chapter 9) they tend to have a rather uninteresting focus
on functional form.
Computation of marginal and average productivity functions is
stressed along with a few applications of Euler's theorem.
Instructors may want to assign
one or two of these problems for practice with specific functions, but the focus for Part 3
problems should probably be on those in Chapters 10 and 11.
Comments on Problems
9.1
This problem illustrates the isoquant map for fixed proportions production
functions.
Parts (c) and (d) show how variable proportions situations might be
viewed as limiting cases of a number of fixed proportions technologies.
9.2
This provides some practice with graphing isoquants and marginal productivity
relationships.
9.3
This problem explores a specific CobbDouglas case and begins to introduce
some ideas about cost minimization and its relationship to marginal
productivities.
9.4
This problem involves production in two locations and develops the equal
marginal products rule.
9.5
This is a thorough examination of most of the properties of the general twoinput
CobbDouglas production function.
9.6
This problem is an examination of the marginal productivity relations for the CES
production function.
9.7
This illustrates a generalized Leontief production function.
Provides a twoinput
illustration of the general case which is treated in the extensions.
9.8
Application of Euler's theorem to analyze what are sometimes termed the "stages"
of the averagemarginal productivity relationship.
The terms "extensive" and
"intensive" margin of production might also be introduced here, although that
usage appears to be archaic.
Analytical Problems
9.9
Local returns to scale.
This problem introduces the local returns to scale
concept and presents an example of a function with variable returns to scale.
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Chapter 9: Production Functions
9.10
Returns to scale and substitution.
Shows how returns to scale can be
incorporated into a production function while retaining its input substitution
features.
9.11
More on Euler’s Theorem.
Shows how Euler’s Theorem can be used to srudy
the likely signs of cross productivity effects.
Solutions
9.1
a., b.
function 1:
use 10
k
, 5
l
function 2:
use
8
k
, 8
l
c.
Function 1:
2
k
+
l
=
8,000
2.5(2
k
+
l
) = 20,000
5.0
k
+ 2.5
l
= 20,000
Function 2:
k
+
l
=
5,000
4(
k
+
l
) = 20,000
4
k
+ 4
l
= 20,000
Thus, 9.0
k
, 6.5
l
is on the 40,000 isoquant
Function 1:
3.75(2
k
+
l
) = 30,000
7.50
k
+ 3.75
l
= 30,000
Function 2:
2(
k + l
) = 10,000
2
k
+ 2
l
= 10,000
Thus, 9.5
k
, 5.75
l
is on the 40,000 isoquant
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 Fall '10
 Anam,Mahmudul
 Microeconomics, Economics of production, prior consent

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