You are the chief economist of the County Regulatory Commission. The local cable
ID: 1218327 • Letter: Y
Question
You are the chief economist of the County Regulatory Commission. The local cable TV monopoly franchise is regulated. The consulting firm provides the long run total cost and demand function estimates for the franchise:
LTC = Q3 – 8Q2 + 50Q and P = 140 - 50Q
Where Q represents thousands of monthly subscribers and P is monthly price.
a) If the franchise were not regulated what price-quantity combination would maximize profit?
b) Now find the price-quantity combination if a regulatory policy of average cost pricing is imposed.
c) Given your answers to a and b, calculate the change in consumers’ surplus.
Explanation / Answer
(a) Without regulation, profit is maximized by equating MR with MC.
Marginal cost, MC = dLTC / dQ = 3Q2 - 16Q + 50
Total revenue, TR = P x Q = 140Q - 50Q2
Marginal revenue, MR = dTR / dQ = 140 - 100Q
Equating MR and MC,
140 - 100Q = 3Q2 - 16Q + 50
3Q2 + 84Q - 90 = 0
Q2 + 28Q - 30 = 0
Solving this quadratic equation using online solver tool, we get
Q = 1.03 or Q = - 29.03, which is inadmissible (as Q cannot be negative).
When Q = 1.03, P = 140 - (50 x 1.03) = 140 - 51.5 = 88.5
(b) Under average cost pricing rule, Price = Average cost (AC)
AC = LTC / Q = Q2 - 8Q + 50
Equating with demand (P),
Q2 - 8Q + 50 = 140 - 50Q
Q2 + 42Q - 90 = 0
Solving this quadratic equating using online solver tool, we get
Q = 2.04 or Q = - 44.04, which is inadmissible (Q > 0).
When Q = 2.04, P = 140 - (50 x 2.04) = 140 - 102 = 38
(c) Consumer surplus (CS) = Area between demand curve & market price.
From demand curve, when Q = 0, P = 140 (Reservation price).
CS without regulation = (1/2) x (140 - 88.5) x 1.03 = (1/2) x 51.5 x 1.03 = 26.52
CS with average cost pricing = (1/2) x (140 - 38) x 2.04 = (1/2) x 102 x 2.04 = 104.04
Change in CS = 104.04 - 26.52 = 77.52 (increase)
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