Question

The demand for tickets to the Katy Perry concert​ (Q) is given as​ follows: Q​ = ​120,000minus−​2,000P The marginal revenue is given​ as: MR​ = 60minus−.001Q The stadium at which the concert is planned holds​ 60,000 people. The marginal cost of each additional concert goer is essentially zero up to​ 60,000 fans, but becomes infinite beyond that point. Refer to Scenario 4. Given the information​ above, what are the​ profit-maximizing number of tickets sold and the price of​ tickets?

Answer 1

Answer:

Q = 60,000

P = 30

Explanation:

Given:

Q​ = ​120,000 - ​2,000P

MR​ = 60 - 0.001Q

Number of people can hold = 60,000

Computation:

Q​ = ​120,000 - ​2,000P

2,000P = 120,000 - Q

P = [120,000 - Q]2,000

P = 60 - 0.0005Q

Total revenue(TR) = PQ

Total revenue(TR) = [60 - 0.0005Q]Q

So,

​ Profit-maximizing number

MR = MC , MC = 0

60 - 0.001Q = 0

Q = 60,000

P = 60 - 0.0005Q

P = 60 - 0.0005(60,000)

P = 60 - 30

P = 30