CHAPTER 10
COST FUNCTIONS
The problems in this chapter focus mainly on the relationship between production and
cost functions.
Most of the examples developed are based on the CobbDouglas function
(or its CES generalization) although a few of the easier ones employ a fixed proportions
assumption.
Two of the problems (10.7 and 10.8) make use of Shephard's Lemma since
it is in describing the relationship between cost functions and (contingent) input demand
that this envelopetype result is most often encountered. The analytical problems in this
chapter focus on various elasticity concepts, including the introduction of the Allen
elasticity measures.
Comments on Problems
10.1
Famous example of Viner's draftsman.
This may be used for historical interest or
as a way of stressing the tangencies inherent in envelope relationships.
10.2
An introduction to the concept of “economies of scope”. This problem illustrates
the connection between that concept and the notion of increasing returns to scale.
10.3
A simplified numerical CobbDouglas example in which one of the inputs is held
fixed.
10.4
A fixed proportion example.
The very easy algebra in this problem may help to
solidify basic concepts.
10.5
This problem derives cost concepts for the CobbDouglas production function
with one fixed input.
Most of the calculations are very simple.
Later parts of the
problem illustrate the envelope notion with cost curves.
10.6
Another example based on the CobbDouglas with fixed capital.
Shows that in
order to minimize costs, marginal costs must be equal at each production facility.
Might discuss how this principle is applied in practice by, say, electric companies
with multiple generating facilities.
10.7
This problem focuses on the CobbDouglas cost function and shows, in a simple
way, how underlying production functions can be recovered from cost functions.
10.8
This problem shows how contingent input demand functions can be calculated in
the CES case.
It also shows how the production function can be recovered in such
cases.
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Chapter 10: Cost Functions
Analytical Problems
10.9
Generalizing the CES cost function.
Shows that the simple CES functions used
in the chapter can easily be generalized using distributional weights.
10.10
Input demand elasticities.
Develops some simple input demand elasticity
concepts in connection with the firm’s contingent input demand functions (this is
demand with no output effects).
10.11
The elasticity of substitution and input demand elasticities.
Ties together the
concepts of input demand elasticities and the (Morishima) partial elasticity of
substitution concept developed in the chapter. A principle result is that the
definition is not symmetric.
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 Fall '10
 Anam,Mahmudul
 Microeconomics, prior consent, U.S. Edition

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