Econ 301 – F07
Answers to PROBLEM SET 4  due in class on Thursday Oct 25
Wissink
1.
Derive/recall the demand functions for x & y for the utility function u(x, y) = xy.
Calculate the own
price elasticity of demand for x using the demand function for x you derived.
Calculate the crossprice
elasticity of demand for x with respect to Py.
Calculate the income elasticity of demand for x.
[ANSWER]
With the utility function, u(x,y)=xy, we get x*=I/2Px and y*=I/2Py.
The own price elasticity of demand for x, the crossprice elasticity of demand for x with respect to Py,
and the income elasticity of demand for x are in the followings:
1
2
/
2
1
0
0
1
2
/
2
,
,
2
,
=
×
=
×
∂
∂
=
=
×
=
×
∂
∂
=
=
×

=
×
∂
∂
=
Px
I
I
Px
x
I
I
x
x
Py
x
Py
Py
x
Px
I
Px
Px
I
x
Px
Px
x
D
I
x
D
y
x
D
Px
x
η
η
η
2.
Suppose there are two markets: the market for Butter, B, and market for Guns, G. Suppose the
demand curve in each market is linear where P=price and Q=quantity.
That is:
P
B
= K – sQ
B
and
P
G
=
F  tQ
G
.
Suppose these two demand curves intersect the price axis at the same value, i.e., K = F.
Using the exact point elasticity formula, show that if quantities are selected such that prices are equal in
these two markets, then so are their ownprice elasticities of demand.
[ANSWER]
With K=F, we get sQ
B
=tQ
G.
from the following: P
B
=P
G
=> KsQ
B
= F – tQ
G
=> sQ
B
=tQ
G.
The ownprice elasticity of demand for Butter is 1/s*P
B
/Q
B
= P
B
/(s*Q
B
) and the ownprice elasticity of
demand for Guns is 1/t*P
G
/Q
G
= P
G
/(t*Q
G
) = P
B
/(s*Q
B
) since sQ
B
=tQ
G
and P
B
=P
G
.
3.
Suppose that on January 1st 2007, the Ithaca Transit Authority increased fares on all its bus lines
from 40 cents to 60 cents.
Private bus companies in Ithaca did not change their fares.
The Daily Sun of
January 8th reports that the total number of rides on cityowned buses decreased from 2200 to 1800 per
day; on those city lines competing with private bus lines, the number of rides decreased from 1150 to
850 per day.
a.
Compute the own price elasticity of demand (over the oneweek period) for all cityowned bus lines.
Compute the own price elasticity of demand for cityowned lines competing with private companies.
b.
Is the demand for bus rides elastic or inelastic?
Explain.
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 Fall '07
 WISSINK
 Microeconomics, Price Elasticity, Supply And Demand, Utility, MPl, APL

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