The government of Catalina Island is currently inviting investors to bid for the

Question

The government of Catalina Island is currently inviting investors to bid for the exclusive right to provide cable television service to its resident. The market demand for this service is P=55-0.01Q, where Q is the number of households that would subscrie to the cable service and P is the monthly fee charged to teh 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 were to be awarded the excluse right to provide cable, how many households would it service? what price would it charge per household per month?

b. if they were to be awarded, how much profit would it earn?

c. what is the most universal entertainment would bid for the franchise?

d. at what level of output (numer of households) is uniersal entertainment's total revenue maximized?--- this is the one I really need help with. I think I have figured out the rest where Q=2,000 P= $35, profit= $40,000, and would bid $40,000... I can't figure out how to do this one part. Is it MR=MC and solve for Q? because that just gets me back to 2,000 or am I missing something more. Thank you for any assistance.

Explanation / Answer

Answering part (d) as required.

P = 55 - 0.01Q

Total revenue, TR = P x Q = 55Q - 0.01Q2

TR is maximized when dTR / dQ = 0 (In other words, when MR = 0)

55 - 0.02Q = 0

0.02Q = 55

Q = 55 / 0.02 = 2,750

You got confused because, MR = MC rule is followed when firm wants to maximize profits. But when it wants to maximize revenue, MC or cost structure is totally irrelevant. The only relevant factor is Total revenue or Marginal revenue, and the revenue maximization rule is MR = 0.

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