Question

Diamond Lanes is the only bowling alley in town. The demand for bowling is given by the function Q = 300 − 20P, where Q is the number of games demanded per day when the price of a game is P. The marginal cost of bowling is $5 per game. How much should the owners of Diamond Lanes charge per game?

Answer 1

Answer: Price=$14.5

Solution: Given that the Diamond lanes is the only bowling alley in the town which means Diamond lanes is a monopoly. Under monopoly, the pricing conditions are as follows :

P>MC = MR

Calculate marginal revenue (MR) from the given demand function:

Q=300-20P

P=(300-Q)/20

P=15-Q/20. ......(1)

Total revenue,TR function will be:

TR=PQ= 15Q-Q²/2

Differentiate TR with respect to Q to obtain Marginal revenue,MR:

MR= 15-Q

Also, given the value of marginal cost as:-

MC= $5

Equate MC=MR

5=15-Q

Q=10

Put the value of Q in equation (1):

P=15-10/20

P=15-0.5

P=$14.5