Question 12
(a) TRUE [See e.g. Figure 11.15]
(b) TRUE [See e.g. Figures 11.6 + 11.7]
(c) TRUE [See defn equilibriums in the SR and LR]
Question 21
(a1) (3 marks) max
Q
Π
(
Q
) = (60
−
Q
)
Q
−
0
.
5
Q
2
−
275
.
[Alternatively:
max
P
Π
(
P
) =
P
(60
−
P
)
−
0
.
5(60
−
P
)
2
−
275
.
]
(a2) (3 marks) The FOC is 60
−
2
Q
−
Q
= 0
.
This yields
Q
M
= 20
,
so that
P
M
= 60
−
20 =
40
.
(a3) (4 marks) See the picture. CS in yellow (light) and PS in blue (dark)
(b1) (total:7 marks)
STEP 1: (3 marks) You can depart from the monopolists problem, or do things directly.
There are two paths you can follow: (1) formulate the monopolists problem as to maximize
pro
fi
ts by choosing prices optimally, (2) formulate the monopolists problem as to maximize
pro
fi
ts by choosing quantities optimally. The last is the easiest. Reward students that write
up the monopolist’s problem correctly by 3 points because they have got a very good start.
If students skip this step but arrive at the next, that is
fi
ne too.
STEP 2. (2 marks) Going the quantity way is the easiest and you arrive at the following
two conditions:
MR
A
(
Q
A
) =
MC
(
Q
)
MR
B
(
Q
B
) =
MC
(
Q
)
where
Q
=
Q
A
+
Q
B
.
In this case the equations are:
55
−
2
Q
A
=
Q
A
+
Q
B
1
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Figure 1: The consumer and producer surplus
35
−
Q
B
=
Q
A
+
Q
B
STEP 3 (3 marks) Figure out the total quantity that the monopolist produces. That is solve
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
= 20 per
bushel (That is, do not interbene in the market by o
ff
ering
P
= 20
.
Market forces will
determine the price); (2). Allow farmers to start growing wheat (i.e. allow entry).
(b) (6 marks) with a price of
P
= 20 individual
fi
rms o
ff
er
q
i
such that
P
=
MC
(
q
i
) =
q
i
−
4
.
Since the supply of an individual
fi
rm is given by
P
=
q
i
−
4 or
q
i
=
P
+4 = 24 the market
supply is given by
Q
= 10
,
000
P
+ 40
,
000
.
With
P
= 20 we get
Q
= 240
,
000
.
Two remarks [not needed in your answer]
•
Another way: individual supply determined by
P
=
q
i
−
4 so
q
i
= 24 if
P
= 20
.
Hence with 10,000
fi
rms supply is 10
,
000
∗
24 = 240
,
000
2
•
We know that the price must be higher than the minimum level of the average
variable cost for
fi
rms to be willing to produce in the SR. The AVC is given by
V C
(
q
i
)
/q
i
= 0
.
5
q
i
−
4
.
The minimum level of the AVC is hence
−
4 (BTW, what
would this mean?). Thus
P
=
q
i
−
4 applies for all prices
P
≥
0 because even at
P
= 0 the
fi
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
fi
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 Fall '12
 Danvo
 Microeconomics, Government, Supply And Demand, ........., Elizabeth, Paul Schure, Y. Let Arnold

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