Suppose that the Telecommunications minister of a small country is considering a
ID: 1150995 • Letter: S
Question
Suppose that the Telecommunications minister of a small country is considering a proposal to award an exclusive contract (monopoly) to Clear Vision Inc., a cable television carrier. The relevant demand and cost functions for the market are as follows: P-280-0.08Q and TC 120,000 service. 2Q, where Q the number of cable subscribers and P the price of monthly cable (a) at price and quantity would be expected if the firm is not regulated? What price would you recommend if the minister asks for a socially efficient price? Explain (b) Calculate the consumer surplus under unregulated monopoly and at the socially efficient price (c) Suppose that this firm can practice perfect first degree price discrimination. What is the lowest price it will charge? Explain.Explanation / Answer
P = 280 - 0.08Q
TR = PQ = (280-0.08Q)Q = 280Q - 0.08Q2
MR = 280 - 0.16Q
TC = 120000 + 2Q
MC = 2
a. Monopolist sets price where MR = MC
280 - 0.16Q = 2
0.16Q = 280 - 2 = 278
Q* = 278/0.16 = 1737.5 units
P* = 280 - 0.08 Q* = 280 - 0.08 × 1737.5
= 280 - 139
P* = $141 / unit
In unregulated market Price = $ 141 per unit and Quantity = 1737.5 units.
socially efficient price will be in perfect competition where P = MC
280 - 0.08 Q = 2
0.08Q = 278
Q = 278/0.08 = 3475 units
Socially Efficient Price = $2 / unit (=280 - 0.08×3475)
b. Consumer Surplus (Monopoly) = 0.5 × (280 - 141)×(1737.5 - 0)
= 0.5 × 139 × 1737.5
= $ 120756.25
Consumer Surplus (Socially Efficient Price)= 0.5×(280-2)(3475-0)
CS = 0.5 × 278 × 3475 = $ 483025
c. When first degree price discrimination is practiced then seller charges different prices from different customers. Under this the monopolist will charge a price from a range of $280 per unit (Maximum) and $2 per unit (Minimum)
Here all the Consumer Surplus will be lost to Perfect Price Discrimination.
Lowest Price = $ 2 per unit.
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