AEM 331
Suggested Answers to Problem Set #5
1.
For both firms, solve for the lowest price where the average cost curve intersects
demand.
For firm 2, this is straightforward – average cost always equals 12, so
this is the lowest price they could bid.
For firm 1, we must find where:
100/
1 102
Q
Q
+ =

.
Multiplying both sides by Q and rearranging, we have:
2
101*
100
0
Q
Q

+
=
.
The solutions are Q = 1 and Q = 100.
At Q = 1, AC =
101, and at Q = 100, AC = 2; therefore, firm 1 can bid all the way down to 2.
So,
firm 1’s lowest bid is 2 while firm 2’s lowest bid is 12; therefore, firm 1 will win
with a bid just under 12.
2.
Now, solve for the monopoly profits each firm would make if they had control of
the industry.
For both firms, marginal revenue is 102 – 2Q.
For firm 1, marginal
cost is 1, so it will set 102 – 2Q = 1, to get Q = 50.5 and P = 51.5.
This means
total profits will be 51.5*50.5 – 100 – 50.5 = 2450.25.
For firm 2, marginal cost
is 12, so it will set 102 – 2Q = 12, to get Q = 45 and P = 57.
This means total
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 Winter '08
 PRINCE,J.
 Economics, Firm, Average cost, MCI, Cournot equilibrium price

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