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 = 60 - 0.25PNY QLA = 100 - 0.50PLA 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 +40Q where Q=QNY +QLA What are the profit-maximizing price and quantity for the New York?

Answer 1

Answer:

For New York, the profit-maximizing price is $100 and the profit-maximizing quantity is 25.

Explanation:

For both Los Angeles and New York, we have:

C = 1000 + 40Q where Q=QNY +QLA

MC = dC/dQ = 40 ………………………. (1)

For New York, we have:

QNY = 60 - 0.25PNY ……………… (2)

Solving for PNY, we have:

0.25PNY = 60 - QNY

PNY = (60 / 0.25) - (1/0.25)QNy

PNY = 240 - 4QNY ………………. (3)

RNY = Revenue in New York = PNY * QNY = (240 - 4QNY)QNY = 240QNY – 4QNY^2 ………. (5)

MRNY = dRNY/dQNY = 240 - 8QNY ……….. (5)

Since profit is maximized when MC = MR, we therefore equate equations (1) and (5) and solve for QNY as follows:

40 = 240 - 8QNY

8QNY = 240 - 40

8QNY = 200

QNY = 200 / 8 = 25

Substituting QNY = 25 into equation (3), we have:

PNY = 240 - (4 * 25) = 240 - 100 = 100

Therefore, the profit-maximizing price is $100 and the profit-maximizing quantity is 25 for the New York.