SD&ZY_20102011/3
12.
Suppose that the longrun world demand and supply elasticities of crude oil are 0.906 and
0.515, respectively.
The current longrun equilibrium price is $30 per barrel and the
equilibrium quantity is 16.88 billion barrels per year.
Derive the linear longrun demand and
supply equations.
Next, suppose the longrun supply curve you derived above consists of
competitive supply and OPEC supply.
If the longrun competitive supply equation is:
7.78 0.29 ,
=
+
C
S
P
what must be OPEC's level of production in this longrun equilibrium?
Solution:
If the demand curve is linear, it is in the form of
.
= +
D
Q
a bP
Also, we know that
16.88
0.906
0.510.
30
=
⇔ =
= 
= 
P
Q
E
b
b
E
Q
P
Rearranging the linear expression for
demand allows us to solve for
a
as follows:
16.88 0.510(30)
32.180.
=

⇒
=
+
=
D
a Q
bP
a
We may now write the linear expression for demand as
32.18 0.510 .
=

D
Q
P
If the supply
curve
is
linear,
it
is
in
the
form
of
.
= +
S
Q
c dP
Also,
we
know
that
16.88
0.515
0.290.
30
=
⇔
=
=
=
P
Q
E
d
d
E
Q
P
Rearranging the linear expression for
demand allows us to solve for
c
as follows:
16.88 0.290(30)
8.18.
=

⇒
=

=
S
c Q
dP
c
We
may now write the linear expression for supply as
8.18 0.290 .
=
+
S
Q
P
OPEC's supply is the
difference between the world supply and competitive supply at $30.
We know that world
supply at $30 is 16.88.
Competitive supply at $30 is
( )
7.78 0.29 30
16.48.
+
=
This implies
that OPEC's supply is 0.4 billion barrels per year at $30 in this longrun equilibrium.
13.
Harding Enterprises has developed a new product called the Gillooly Shillelagh.
The market
demand for this product is given as follows:
Q = 240  4P
a.
At what price is the price elasticity of demand equal to zero?
b.
At what price is demand infinitely elastic?
c.
At what price is the price elasticity of demand equal to one?
d.
If the shillelagh is priced at $40, what is the point price elasticity of demand?
Solution:
The demand curve given in this problem is linear.
The intercepts of the inverse demand curve
on the price and quantity axes are $60 and 240 respectively.
The price elasticity of demand
varies along the length of this demand curve.
Demand is infinitely elastic at the intercept on
the price axis.
Demand is completely inelastic at the intercept on the quantity axis.
Demand is
unit elastic at the halfway point between these two extremes.
a.
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 Spring '11
 appo
 Supply And Demand, Qd

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