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

To find the profit-maximizing price and quantity for New York, we need to calculate the total demand and cost functions. The demand function for New York is QNY = 60 - 0.25PNY, and the cost function is C = 1000 + 40Q. We can substitute QNY into Q in the cost function to get the total cost function: C = 1000 + 40(QNY + QLA). Now we can find the profit function by subtracting the cost function from the revenue function, which is PNY * QNY. We want to maximize profit, so we take the derivative of the profit function with respect to PNY and set it equal to zero. Solving this equation will give us the profit-maximizing price for New York. To find the corresponding quantity, we plug the price into the demand function for New York.

Step-by-step explanation:

To find the profit-maximizing price and quantity for New York, we need to calculate the total demand and cost functions. The demand function for New York is QNY = 60 - 0.25PNY, and the cost function is C = 1000 + 40Q. We can substitute QNY into Q in the cost function to get the total cost function: C = 1000 + 40(QNY + QLA). Now we can find the profit function by subtracting the cost function from the revenue function, which is PNY * QNY. We want to maximize profit, so we take the derivative of the profit function with respect to PNY and set it equal to zero. Solving this equation will give us the profit-maximizing price for New York. To find the corresponding quantity, we plug the price into the demand function for New York.

Answer 2

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

Step-by-step 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.