1. The demand function for football tickets for a typical game at a large Midwes
ID: 1134770 • Letter: 1
Question
1. The demand function for football tickets for a typical game at a large Midwestern university is D(p) 200 000 10 000p. The university has a clever and avaricious athletic director who sets ticket prices so as to maximize revenue. The university's football stadium holds 100 000 spectators. a. Write down the inverse demand function b. Write expression for total revenue and marginal revenue as a function of the number of tickets sold. c. Graph the demand function and the marginal revenue function. Show the capacity of the stadium on your diagram. d. What price will generate the maximum revenue? What quantity will be sold at this price? e. At this quantity what is the marginal revenue? At this quantity what is the price elasticity of demand? Will the stadium be full? f. A series of winning seasons caused the demand curve for football tickets to shift upwards. The new demand curve is q(p) 300 000-10 000p. Ignoring the capacity constraint what price would generate maximum revenue? What quantity would be sold at this price? g. Now considering the capacity constraint faced by the directo, how many tickets should he sell and what is the price? i. If he does this, what are the MR and the price elasticity of demand?Explanation / Answer
SOLUTION:
d) Quantity: 20-Q/5000 = 0
Q= 100,000
Marginal price = 10
e) Marginal revenue: 0
EOD: -10,000 * 10/100,000 = -1
Yes, stadium will be full
f) 30-Q/10,000
g) MR = 30-Q/5000 = 0; It gives Q=150,000
Price generating maximum revenue: $15
Quantity sold at this price: 150,000
h) Number of tickets to be sold is by setting it to maximum capacity i.e. 100,000
Price at which tickets should be sold: 20
i) Marginal revenue: 30 - 100,000/5,000 = 10
EOD: -10,000 * 20/100,000 = -2
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