The government of Catalina Island is currently inviting inve

The government of Catalina Island is currently inviting investors to bid for the exclusive right to provide cable television service to its residents. The market demand for this service is P = 55 - 0.01Q, where Q is the number of households that would subscribe to the cable service and P is the monthly fee charged to the subscribers. The associated marginal revenue curve is MR = 55 - 0.02Q. Universal Entertainment is interested in bidding for the right to provide cable service on Catalina Island. It has a constant average and marginal cost of $15 for providing cable service to each household

a. If Universal Entertainment were to be awarded the exclusive right to provide cable service on Catalina Island, how many households would it service? What price would it charge per household per month?

b. If Universal Entertainment were to be awarded the exclusive right to provide cable service on Catalina Island, how much profit would it earn?

c. What is the most Universal Entertainment would bid for the franchise?

d. At what level of output (number of households) is Universal Entertainment\'s total revenue maximized?

Solution

Universal will produce where MR=MC

MC is constant at $15; MC = 15

MR=55-0.02Q

Thus 55-0.02Q=15

Q = 2000

To find the price, plug in the quantity into the demand equation P = 55-0.01Q

P = 55-0.01(2000) = $35 per month

b. If Universal Entertainment were to be awarded the exclusive right to provide cable service on Catalina Island, how much profit would it earn?

Total cost = ATC x Q =$15 x 2000 =$30,000

Total revenue = P x Q = $35 x 2000 = $70,000

Profit = $70,000 - $30,000 = $40,000

c. What is the most Universal Entertainment would bid for the franchise?

$40,000

d. At what level of output (number of households) is Universal Entertainment\'s total revenue maximized?

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