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Winter 2008
QUIZ 5
Section B
Question 1 [5 marks] A monopolist has an inverse demand function P  700  10Q , and
initially faces a constant marginal cost MC  100 .
a)
[3 marks] Calculate the profit-maximizing monopoly quantity and price and compute the
monopolist’s total revenue at the optimal price.
With inverse demand function P  700  10Q , MR  700  20Q . The monopolist
will produce an output where MR  MC .
700-20Q=100
600=20Q
Q=30
We find price by plugging the optimal value of Q into the demand curve.
P  700  10Q
P  700  300
P  400
Total revenue equals price times quantity.
b)
TR=400*30=12,000.
[2 marks] Suppose that a tax T=100 is imposed on each unit of the output of monopolist.
Derive the total revenue at the optimal price.
Following the process described in part a),
700-20Q = 200
20Q = 500
Q = 25
P = 700-10Q
=700-250
=450
TR = PQ
=450 * 25
=11250
Question 2 [5 marks] In a certain market in the long-run, each firm and potential entrant has a
long-run average cost curve AC=10Q2-5Q+20 and long-run marginal cost curve
MC=30Q2-10Q+20 where Q is thousands of units per year. Market demand is given by
D(P)=39,000-2,000P.
a)
[2 marks] In equilibrium, how many units will each firm produce?
P=AC=MC
10Q2-5Q+20=30Q2-10Q+20
20Q2-5Q=0
20Q-5=0
Q=0.25
b)
[2 marks] What is the market equilibrium price?
P=30Q2-10Q+20
P=30(0.25)2-10(0.25)+20
P=19.375
c)
[1 mark] What is the equilibrium number of firms in the long-run?
Since total market demand is 250 and each firm is producing 0.25 units, the total number of
firms in the market in equilibrium will be
N=250/0.25=1,000