Question: A consulting firm estimates the demand by local businesses for attendance at a pro sports team's games:
PB = $140 - 4AB
where PB is the ticket price paid by businesses, measured in dollars, and AB is their attendance measured in thousands of fans.
a. Draw this attendance demand function with the traditional P on the vertical axis, and Q/A on the horizontal axis.
b. Using this demand function, find the total revenue function. What is the shape of the total revenue function? What is the highest possible total revenue that the team can hope to collect? At what level of attendance? At what price?
c. Using this demand function and your answer to part (b), what is the elasticity of demand at the revenue maximizing attendance level (hint: if your calculations are correct, there is only one answer you should get for this0?
d. Using your answers to a-c, if capacity at the team's stadium is 25,000 seats, should the team owner fill the stands with business buyers? Why or why not?
The same consulting firm also estimates that the demand by families for attendance at the same games and the same seat-types is as follows:
PF = $80 - (2/3)AF
where PF is the price of a ticket for individual family members, measured in dollars, and AF is the attendance by individual family members, measured in thousands.
Explain, comparing the elasticity of demand found in 1C with that found using the above equation, why individual family members will be charged a different price than business buyers for the same game and seat-type. What is the ratio of business buyer to family member price (PB/PF) if the team owner cares about the bottom line (you will need to calculate PF in much the same way as you calculated PB in question 1. Is this price discrimination?
Calculate both the business buyers consumer surplus and family members consumer surplus given your answers to questions 1 and 2a. What does this number represent?