Answer to Question #258672 in Microeconomics for Josh

Question

The government of Beach Island is inviting investors to bid for the exclusive right to provide satellite television broadcast 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 service and P is the monthly fee charged to the subscribers. The associated marginal revenue curve is MR=55-0.02Q. Funtime TV Company is interested in bidding for the right to provide this service on Beach Island. It has a constant average and marginal cost of R5 for providing the service to each household.

(A) If Funtime TV Company were to be awarded the exclusive right to provide cable service on Beach Island, how many households would it service? 

(B). If Funtime TV Company were to be awarded the exclusive right to provide cable service on Beach Island, what price would it charge per household per month? 

(C). If Funtime TV Company were to be awarded the exclusive right to provide cable service on Beach Island, how much profit would it earn?  

Answer 1

A.The firm will produce output upto the level where the marginal cost and marginal revenue are equal.

$MR=MC\\55−0.02=5\\50=0.02Q\\Q=2500$

Therefore the firms will serve 2500 households.

B) The price charged by the firm can be calculated by substituting the quantity in the demand function.

$P=55−0.01Q\\=55−0.01×2500\\=30$

Therefore the price charged is R30.

C)The profit is the difference between total revenue and total cost. Total revenue is the product of price and quantity. Total revenue is the product of average total cost and quantity.

$Profit=Total\space revenue−Total\space cost\\=Price×Quantity−ATC×Quantity\\=(Price−ATC)Quantity\\=(30−5)2500\\=62500$

Therefore the profit is R62,500.