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AEM 331
Practice Problems
1.
Consider a market with demand: Q = 100 – P.
Let marginal costs be 20 if there is
perfect competition.
However, if there is a monopolist, assume it must pay an
additional $10 per unit of output to reimburse lobbyists for their efforts in
persuading legislators to keep the monopoly insulated from competition.
a.
Calculate the prices and quantities under monopoly and competition.
b.
Calculate total economic surplus under monopoly and competition.
The
difference is the social cost of monopoly.
c.
The social cost of monopoly can be disaggregated into two distinct types
of cost: the resources cost of rent seeking and the usual deadweight loss of
output restriction.
What are their respective magnitudes?
2.
The inverse market demand for mineral water is P = 200 – 10*Q, where Q is total
market output and P is the market price.
Two firms, A and B, have complete
control of the supply of mineral water and both have zero costs.
a.
Find the Cournot solution.
b.
Find an identical output for each firm that maximizes joint profits.
3.
Continuing with problem 2, assume that each firm can choose only two outputs –
the ones from parts a and b in question 2.
Denote those outputs
a
q
and
b
q
.
a.
Compute the payoff/profit matrix showing the four possible outcomes
(this is just a table similar to the ones we’ve used to solve for equilibria of
games).
b.
Show that each firm’s optimal output is independent of what the other firm
produces.
Now consider firms playing an infinitely repeated version of
this game and consider the following strategy for each firm: (i) produce
b
q
in period 1, (ii) produce
b
q
in period t if both firms produced
b
q
in all
preceding periods, and (iii) produce
a
q
in period t if one or more firms did
not produce
b
q
in some past period.
Assume each firm acts to maximize
its sum of discounted profits where the discount rate is r.
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 Spring '08
 PRINCE,J.

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