Question

Suppose there are three types of consumers who attend concerts at Marshall university's performing arts center: students, staff, and faculty. Each of these groups has a different willingness to pay for tickets; within each group, willingness to pay is identical. There is a fixed cost of $1,000 to put on a concert, but there are essentially no variable costs.

For each concert:
i. There are 140 students willing to pay $20.
ii. There are 200 staff members willing to pay $35.
iii. There are 100 faculty members willing to pay $50.
If the performing arts center can charge only one price, what price should it charge? What are profits at this price?

Answer 1

The performing arts center should charge a price close to $19.55 to maximize total revenue and profits. At this price, the profits would amount to $7,600.

Step-by-step explanation:

To determine the price that the performing arts center should charge, we need to find the price that maximizes total revenue and profits. In this case, since there are no variable costs, total revenue is equal to the number of tickets sold multiplied by the ticket price.

Thus, we need to find the price that maximizes the product of the number of tickets sold and the ticket price.

To find this price, we can first calculate the total willingness to pay for each group: students (140 x $20), staff (200 x $35), and faculty (100 x $50). Adding these together gives us a total willingness to pay of $8,600.

Since there are three types of consumers, we can divide the total willingness to pay by the total number of consumers (440) to find the average willingness to pay per consumer, which is approximately $19.55. Therefore, the performing arts center should charge a price close to $19.55 to maximize total revenue and profits.

The profits at this price can be calculated by subtracting the fixed cost of $1,000 from the total revenue. Assuming all 440 consumers purchase tickets at the average price of $19.55, the total revenue would be $8,600. Subtracting the fixed cost, the profits would be $7,600.