tutorial_5ans - price elasticity of demand Will the stadium...

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ECOS 2001 Tutorial 5 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 p(q) = 20 – q/10000 b. Write expression for total revenue and marginal revenue as a function of the number of tickets sold. R(q) = 20q – q2/10000 MR = 20 – q/5000 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? $10 100 000 seats e. At this quantity what is the marginal revenue? At this quantity what is the
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Unformatted text preview: price elasticity of demand? Will the stadium be full? MR = 0 e = – 1 yes 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? $15 150 000 seats g. Now considering the capacity constraint faced by the director, how many tickets should he sell and what is the price? 100 000 seats at $20 i. If he does this, what are the MR and the price elasticity of demand? MR = 10 and e = – 2 2. Write revenue as a function of quantity sold, and derive the marginal revenue. Analyse the relationship between marginal revenue and the elasticity of demand. See Varian pp. 278-79 or lecture 4 pp 14-16....
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