Problem Set 3  Solutions
1.
If two goods are perfect
complements then a change in
the price of one good without a
change in wealth will not affect
demand for the other good.
The
problem is that when the price of
a good changes the effect on
demand for the good is
composed of a substitution
effect (demand change from
pure price change) and an
income effect (price change
affects income, which then
affects demand).
In order to see
the substitution effect, we need to change price while holding utility constant and then
see if the quantities demanded change.
In the graph we start at point A with the steep
budget constraint.
Now Px falls and we draw a new budget constraint reflecting the same
amount of Y and a larger quantity of X (dashed line).
Notice the consumer has purchased
more of X and Y but we don’t know if this is the substitution effect or income effect.
If
we draw a third budget constraint reflecting the new price scheme but tangent to the
original utility curve (dotted line) we see that demand does not change.
This implies
there is no substitution effect and the increased demand results only from the income
effect.
We start at point A on
indifference curve U
0
and with
the steep budget constraint
(dotted).
The consumer chooses
bundle A because the MRS <
Px/Py (the ratio of marginal
utilities is less than the ratio of
prices).
Then Px decreases and
we draw two new budget lines,
one tangent to the original
indifference curve and the other
reflecting the original wealth and
new price of good X.
In both
cases the consumer only
consumes good X (MRS > ratio of prices).
The substitution effect is the quantity from
the origin to C, while the income effect is from C to B.
Other cases:
Note that if the MRS is smaller than the price ratio before and after a change in Px, then
there is no change: both the income and substitution effects are zero. If the MRS is bigger
X
Current BC
BC utility compensated
BC after price change
Y
M
Curr
M
Util
A
B
X
UTILITY CURVES!
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 Spring '11
 BaumSnow
 Microeconomics, ev, price change

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