AEM 331
Practice Problems Answers
1.
a.
For the monopolist, MR = MC means that 100 – 2Q = 30 (marginal cost of
production plus marginal cost of lobbying).
Therefore, Q = 35 and P = 65.
Under competition, P = MC, so 100 – Q = 20, Q = 80, P = 20.
b.
Total surplus under competition is 80*80/2 = 3200 = consumer surplus
(note that producer surplus is zero).
Under monopoly, producer surplus is
(65 – 30)*35 = 1225.
Consumer surplus is 35*35/2 = 612.5.
So, total
surplus is 1837.5.
The difference, 32001837.5 = 1362.5 is the social cost
of monopoly.
c.
The resources cost of rent seeking is 10*35 = 350.
The deadweight loss
is (45*45)/2 = 1012.5.
2.
a.
Profit maximizing conditions yield:
200
20
10
0
A
B
q
q


=
.
So,
10
2
B
A
q
q
=

.
Recognizing that this will be the same for firm B, we solve
for each quantity to get both firms producing 20/3 units.
This means price
is 200 – 400/3 = 200/3.
b.
Simply find the monopoly output and then divide by two to have both
firms producing it (this is because each firm is identical, so they’ll each
get half of monopoly profit).
In monopoly, MR = MC, so we have 200 –
20Q = 0.
This means Q = 10, and price is 100.
Therefore, each firm
should produce 5 units.
3.
a.
We have the following table:
5
20/3
5
20/3
b.
To do this, look at each firm one at a time.
Firm 1: If firm 2 is producing
5, the optimal output is 20/3.
If firm 2 is producing 20/3, the optimal
output is 20/3.
The analysis carries through the same way for firm 2.
Therefore, each should produce 20/3 regardless of what the other is doing.
c.
This “titfortat” is an equilibrium if the payoff from doing it is higher
than the payoff from cheating in one period.
The payoff from titfortat is:
500*(1+r)/r.
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 Winter '08
 PRINCE,J.
 Consumer Surplus, Producer Surplus, Supply And Demand, producer, economic surplus

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