6. Sal\'s satellite company broadcasts TV to subscribers in Los Angeles and New

Question

6. Sal's satellite company broadcasts TV to subscribers in Los Angeles and New York The demand functions for each of these two groups are:QNY 50-(1/3)P and QLA 80-(23)PLA, where Q is in thousands of subscriptions per year, and P is the subscription price per year. The cost of providing Q units of service is given by C(Q) = 1000 + 30Q, where Q = QNy4QLA. If the company is a monopoly and can engage in third-degree price discrimination, then (a) What is the profit-maximizing price and quantity in the New York market? (b) What is the profit-maximizing price and quantity in the Los Angeles market? (c) What is the total deadweight loss in the 2 markets? (d) Suppose Sal can only charge a single price. What price should he charge, and what is the total quantity sold? (e)What is the deadweight loss now?

Explanation / Answer

a) demand in new york market = 50 - (1/3)Pn

P = 151.51 - 3.03Q

TR = 151.51Q - 3.03Q2

MR = 151.51 - 6.06Q
MC = 30

A monopoly firm produce the quantity where MR = MC and charge the price.

151.51-6.06Q = 30

Q = 20

P = 151.51 -3.03*20

P =$91

B ) Demand in Los angles market = 80 -(2/3)Pl

P = 119.4 - 1.5Q

TR = 119.4Q - 1.5Q2

MR = 119.4 - 3Q

MC = 30

119.4-3Q = 30

Q = 30

P = 119.4 - 1.5*30

P = $74

C) Total deadwieght loss in two market = deadweight loss in new york market + deadweigh loss in los angles market

we need to find socially optimal quantity in both market. By equating ->> P =MC

SO in new market = 151.51-3.03Q =30

Q = 40

S.O in loss angles market = 119.4-1.5Q = 30

Q = 60

DL in new york market = 1/2 ( 91-30) * ( 40 -20)

DL = $610

DL in los angles market = 1/2 *(74-30) *( 60 - 30)

DL = $660

Total DL = 610 +660 = $1270

D)

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