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Sal’s satellite company broadcasts TV to subscribers in Los Angeles and New York. The demand functions...

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 + 40Q where Q = QNY + QLA

What are the profit-maximizing price and quantity for Los Angeles?

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Answer #1

Since there is only one broadcaster, he will maximize the joint profit

profit = PNY*QNY + PLA*QLA - C

to maximize the profit, we will partially differentiate profit first w.r.t QNY and then w.r.t QLA

and set it equal to zero.

the calculation below:---

Hence the profit-maximizing QLA = 35 &

profit-maximizing PLA = $180

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