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1
Econ 100
Winter 2012
Problem set 1
1.
Find the derivative with respect to
x
for the following functions.
a.
( )
32
f
x
ax
bx
x
=
+
+
;
b.
( )
ln
f
x
ax
x
=
;
2.
What is the price elasticity of the demand curve Q(p) = a  b
ln
(p)?
3.
Suppose that the demand for water balloons fit the function D(p,p
s
) =
D
(
p
,
p
s
)
=
.2
p
"
.5
p
s
"
.2
where
p
is the price of water balloons and
ps
is the price of super soakers (an advanced squirt
gun technology).
Based upon this demand curve, are super soakers a compliment or a substitute for water
balloons?
Demonstrate why.
The partial derivative of demand with respect to the price of squirt guns is
For any positive price of water balloons and squirt guns, this is negative.
So
quantity of water balloons goes down with an increase in the price of squirt guns.
So squirt guns are a
complement
to water balloons.
dQ
(
p
)
dp
=

b
p
dQ
(
p
)
dp
p
Q
=

b
Q
=

b
a

b
ln
p
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4.
Suppose that the current price of oil is $60 per barrel and the quantity sold is 90 million
barrels per day. Assume that the supply and demand curves for oil are linear.
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 Fall '11
 JAMESBUSHNELL
 Microeconomics, Price Elasticity

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