Question

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 =150−0.75PNY QLA=80−0.25PLA 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 = 1000 + 80Q where Q = QNY + QLA What are the profit-maximizing price and quantity for Los Angeles?

A. $140, 45

B. $190, 32.5

C. $180, 35

D. $120, 60

Answer 1

PLA = 200 and QLA = 30
(Given options are not correct. Or there might be some error in the given equations.)

(MC = dC/dQ = 80

QLA = 80−0.25PLA
So, 0.25PLA = 80 - QLA
So, PLA = 80/0.25 - QLA/0.25
So, PLA = 320 - 4QLA
TR = PLA*QLA = (320 - 4QLA)*QLA = 320QLA - 4QLA²
MR = d(TR)/dLA = 320 - 2(4QLA) = 320 - 8QLA

Profit is maximized when MR = MC.
Thus, 320 - 8QLA = 80
So, 8QLA = 320 - 80 = 240
So, QLA = 240/8 = 30
PLA = 320 - 4QLA = 320 - 4(30) = 320 - 120 = 200)