Econ 3130, Spring 2012, R. Masson
Chapter 4: p. 1
Chapter 4: Utility
I.
What is the role of this chapter?
A. One way to generate indifference curves which are “well behaved” (e.g., not crossing) is
the use of mathematics
1. We can mathematically generate “Utility” as a function U=U(x
1
,x
2
) which has
indifference curves in two-space as in Chapter 3
a.
NB:
The graphical functional forms are limited only by the imagination,
mathematical functional forms are restricted by tractability
B. Second, we may want to address the concept of indifference curves with more than two
goods
1. If we have x
1
,x
2
,x
3
an indifference relationship is no longer a curve, it is a surface and
cannot easily be graphed
a. Recall gin, vermouth and whiskey
C. Third we may want to use econometrics, which requires formulae
1. Characteristics of the formulae may be important to model.
2. Example
a. Suppose we want to estimate demand for x
1
and x
2
given M,p
1
,p
2
(1) We could regress x
1
on d
1
(M,p
1
,p
2
) where d
1
is some functional form, for
example the regression x
1
=
±
0
+
±
1
M+
±
2
p
1
+
±
3
p
2
(a) One would have linear demand.
The slope of the demand curve would be
0
x
1
/
0
p
1
=
±
2
, where
±
2
<0
(b) For most goods (“normal goods”) one would expect
±
1
>0
(c) One would also expect
±
3
>0 (as costs of substitutes rise, buy less
substitute and more x
1
)
(2) At the same time we could regress x
2
on some d
2
(M,p
1
,p
2
)
(3) But there is a problem if we run two separate regressions, there is no
guarantee that
(
is the value from the estimated demand
function for some specific M,p
1
,p
2
) unless we impose some mathematical