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?
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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