Lecture 6
Income and Substitution I
Work less, wear less, eat less, and we shall be a great deal wiser,
healthier, and wealthier than by taking the course we now do.
Brigham Young, Journal of Discourses, vol. 12, p. 122.
The Economics Outline
1. Changes in Income
2. Changes in Price
3. Income and Substitution Effects
The Mathematics Outline
1. Comparative Statics
2. Partial Derivatives
Changes in Income
A change in income will shift out the budget constraint and allow the individual to attain
a higher level of utility.
However, an increase in income does not necessarily mean that
the individual will buy more of any given good.
It is through changes in income that we
define
normal
goods and
inferior
goods.
Mathematically we have
:
If
0
≥
, then x
*
∂
∂
I
x
i
i
is a
normal
good.
[See Figure 5.1 in Nicholson]
If
0
<
then x
*
∂
∂
I
x
i
i
is an
inferior
good
[See Figure 5.2 in Nicholson]
Changes in Price
A change in price will result in a change in the quantity demanded.
To determine the
magnitude of the change you would take the derivative,
i
i
P
x
∂
*
∂
.
One would think that,
at a minimum, you could say that
0
*
<
∂
i
i
P
x
∂
.
This just says that the demand curve is
downward sloping.
However, it turns out that there are conditions under which the
demand curve could be upward sloping.
In other words, without knowing the specifics of
the case I cannot tell if the derivative,
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 Spring '11
 Stevens
 Dr. Steven Waters

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