1
EXCERCISES 1B:
MONOPOLIES
Here are the solutions to the second exercise.
1.
Optimal outcome.
The optimal is found by maximizing total surplus with respect to Q and setting it equal to
zero.
Total surplus is given by the area under the demand curve above the cost curve, or:
TS =
∫
P(Q)dQ – TC
= 120Q½Q
2
½Q
2
=
120Q  Q
2
dTS/dQ =
120 – 2Q = 0
Q = 60
Price is given by 120 – Q = 120 – 60
= 60
Profit or producer surplus is P*Q – Cost:
Π
=
120Q  Q
2 
½Q
2
=
120Q – 1½Q
2
=
120(60) –
1½(60)
2
Π
=
1800
Consumer surplus is the area under the demand curve, above price, or:
CS =
∫
P(Q)dQ – P*Q
=
120Q½Q
2
120Q+Q
2
=
½Q
2
CS =
1800
Total surplus can be found by plugging Q into the equation above:
TS =
120Q  Q
2
=
120(60) – (60)
2
TS =
3600
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Table 1 summarizes the answers.
2.
Monopoly outcome.
The monopolist maximizes profit, so maximize the equation for profit
Π
=
120Q – 1½Q
2
d
Π
/dQ = 120 –3Q = 0
Q = 40
Plug Q into each equation above to find price, consumer, producer, and total surplus.
See
table 1.
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 Fall '07
 SandraBlack
 Economics, Monopoly, Supply And Demand, producer, total surplus

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