Please show your work.

USC is organizing a big concert at Bovard Auditorium that only holds 1100 seats. Based on the data so far this season, USC estimates that if they set the ticket price to be $150 then they will sell 825 tickets, whereas if they set the price to be $50 then they will sell 1075 tickets.

a) Assuming demand is a linear function of the price, what must be the demand function D(p)? Remember, two points determine a line: the slope (m) and intercept (b) of a linear function (y= m*x + b) can be found from just two pairs of x and y.

Answer is D(p) = 1200 - 2.5*p

b) Using the demand function you calculated in (a):

What is the revenue maximizing price for the concert tickets?

Under the revenue maximizing price, will USC fill all 1100 seats?

[NOTE: Your answers will be graded relative to the demand function you found in (a), i.e. errors in (a) will not be carried forward in the grading of the rest of the problem. If you are not satisfied with your answer to (a), you can use D(p) = 1500 - 5*p.]

Answer: p* = 240; No, USC will not fill all the seats.

c) To get fans in seats, USC will offer two prices: a higher price for better seats and a lower price for farther seats. Using the demand function you calculated in (a), if the better seat price is $150, what should the farther seat price be in order to sell all the tickets? Assume that anyone willing to pay for a high price ticket will always buy the better seat.

Answer: $40

d) Using what you have calculated, what makes more money: the single revenue maximizing price from (b) or the seat-filling two price strategy from (c)

Answer: $144,000 for (b), $134,750 for (c)

Therefore, single price makes more money.