the two equations. For example substitute eqn (2) in (1) to get 55
−
3(35
−
2
Q
B
)
−
Q
B
=0
.
This delivers
Q
∗
B
=10
.
Substitute back in eqn (2) to see that
Q
∗
A
=15
.
(b2) (3 marks). The optimal prices with price discrimination are
P
∗
A
=55
−
15 = 40 and
P
∗
B
=35
−
1
2
∗
10 = 30
.
The cost or arbitrage must therefore exceed $10 per unit to make
this form of price discrimination work.
Question 22
(a) (4 marks) It means two changes (1) getting rid of the price guarantee of
P
=20per
bushel (That is, do not interbene in the market by o
f
ering
P
=20
.
Market forces will
determine the price); (2). Allow farmers to start growing wheat (i.e. allow entry).
(b)(6marks)withapriceof
P
= 20 individual
f
rms o
f
er
q
i
such that
P
=
MC
(
q
i
)=
q
i
−
4
.
Since the supply of an individual
f
rm is given by
P
=
q
i
−
4or
q
i
=
P
+4=24themarket
supply is given by
Q
=10
,
000
P
+40
,
000
.
With
P
=20weget
Q
=240
,
000
.
Two remarks [not needed in your answer]
•
Another way: individual supply determined by
P
=
q
i
−
4so
q
i
=24i
f
P
=20
.
Hence with 10,000
f
rms supply is 10
,
000
∗
24 = 240
,
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View Full Document•
We know that the price must be higher than the minimum level of the average
variable cost for
f
rms to be willing to produce in the SR. The AVC is given by
VC
(
q
i
)
/q
i
=0
.
5
q
i
−
4
.
The minimum level of the AVC is hence
−
4(BTW
,wha
t
would this mean?). Thus
P
=
q
i
−
4 applies for all prices
P
≥
0 because even at
P
=0the
f
rm would like to stay in business in the short run.
(c) (4 marks) [In this question you need to derive the market supply curve if you have not
yet in (b)]. Immediately after the coop student’s proposal gets implemented supply and
demand determine the price. Supply is given by
Q
=10
,
000
P
+40
,
000
,
demand is given
by
Q
=
−
10
,
000
P
+400
,
000
.
Hence the equilibrium price is given by 10
,
000
P
+40
,
000 =
−
10
,
000
P
+400
,
000
⇒
20
,
000
P
=360
,
000
⇒
P
=18
.
[Each
f
rm now o
f
ers
q
i
=22
BTW]
(d)(6marks)Inthelongrun
f
rmscanenterorex
itthemarket
.Inth
iscase
f
rms enter
entry because they are pro
f
table in the SR with
P
=18
.
Entry or exit will take place
until
f
rms operate at the quantity for which the average total cost (ATC) is minimal. The
prevailing market price will be equal to the ATC at its minimum level (e.g. Figure 1115)
There are two ways to
f
ndthepo
intwheretheATCism
in
ima
l
:(1)F
indthepo
intwhere
MC=ATC. (2) Directly
f
nd the point where ATC is minimal. I like the second way better.
ATC
(
q
i
)=
C
(
q
i
)
/q
i
=0
.
5
q
i
−
4+200
/q
i
.
At the minimum the derivative is 0 so we get
the FOC 0
.
5
−
200
/q
2
i
=0
.
This gives
q
i
= 20 and hence in the LR equilibrium we have
P
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 Fall '12
 Danvo
 Microeconomics, Government, Supply And Demand, ........., Elizabeth, Paul Schure, Y. Let Arnold

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