Scenario 10.4:
The demand for tickets to the Katy Perry concert (Q) is given as follows:
Q = 120,000 - 2,000P
The marginal revenue is given as:
MR = 60 - .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 10.4. Given the information above, what are the profit maximizing number of tickets sold and the price of tickets?

Question

Quizplus · Accepted Answer

To maximize profit, we need to find the quantity where marginal revenue equals marginal cost. Since marginal cost is zero up to 60,000 fans and infinite beyond that point, we only need to consider quantities up to 60,000.

First, we can find the equation for marginal cost up to 60,000 fans:
MC = 0

Setting MR = MC: 
60 - .001Q = 0 
.001Q = 60 
Q = 60,000

Now we can find the price that corresponds to this quantity using the demand equation: 
Q = 120,000 - 2,000P 
60,000 = 120,000 - 2,000P 
2,000P = 60,000 
P = $30

Therefore, the profit maximizing number of tickets sold is 60,000 and the price of tickets is $30.

Scenario 10.4: The Demand for Tickets to the Katy Perry Concert (Q)