1. A natural monopolist has a cost structure C(g) 400+25q and faces market deman
ID: 1137060 • Letter: 1
Question
1. A natural monopolist has a cost structure C(g) 400+25q and faces market demand D(p) 200-2p Solve for monopolist's profit, output and consumer surplus when: a. Price is set to marginal cost. b. Price is set to average cost c. What are the pros and cons of regulating the monopolist according to (a) vs. (b)? 2. Production of certain good is discrete and has a cost structure characterized as follows: q100 200 300 400 500 600 240 220 200 190 188 187 Cla Assume inverse demand is p)500 0.50 a. Find the optimal monopoly output. b. Assume an incumbent monopoly operates according to (a). Show that it is profitable for a second firm to enter c. Find the monopoly output level that would deter entry.Explanation / Answer
(1)
D(p) = Q = 200 - 2p
2p = 200 - Q
p = 100 - 0.5Q
When Q = 0, p = 100 (Reservation price)
(a) Marginal cost (MC) = dC(q)/dq = 25
Setting P = MC,
100 - 0.5Q = 25
0.5Q = 75
Q = 150
P = MC = 25
Profit = Revenue (TR) - Cost (C) = (p x q) - 400 - 25q = (25 x 150) - 400 - (25 x 150)
= 3750 - 400 - 3750 = - 400
Consumer surplus (CS) = Area between demand curve and market price
= (1/2) x (100 - 25) x 150 = 75 x 75 = 5625
(b) Average cost (AC) = C(q)/q = (400/q) + 25
Equating P with AC,
(400/q) + 25 = 100 - 0.5q
(400/q) + 0.5q = 75
400 + 0.5q2 = 75q
0.5q2 - 75q + 400 = 0
q2 - 150q + 800 = 0
Solving this quadratic equation using online solver,
q = 144 or q = 6 (Taking integer values for output)
When q = 144, p = 100 - (0.5 x 144) = 100 - 72 = 28
Profit = 0 (When price equals AC, revenue equals costs and profit equals zero).
CS = (1/2) x (100 - 28) x 144 = 72 x 72 = 5184
When q = 6, p = 100 - (0.5 x 6) = 100 - 3 = 97
Profit = 0
CS = (1/2) x (100 - 97) x 6 = 3 x 3 = 9
(c) When marginal cost pricing is used, there is a loss since profit is negative, so producers lose compared to average pricing model, but consumer surplus is higher, therefore producers gain compared to average pricing model.
NOTE: As per Answering Policy, first question has been answered.
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