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?
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Ответ:
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.
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