Solutions to Workouts on Assignment 3

# Solutions to Workouts on Assignment 3 - NAME 197 15.9 (0)...

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NAME 197 15.9 (0) The demand function for football tickets for a typical game at a large midwestern university is D ( p ) = 200 , 000 10 , 000 p . The university has a clever and avaricious athletic director who sets his 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 )=2 0 q/ 10 , 000 .

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198 MARKET DEMAND (Ch. 15) (b) Write expressions for total revenue R ( q )=20 q q 2 / 10 , 000 and marginal revenue MR =20 q/ 5 , 000 as a function of the number of tickets sold. (c) On the graph below, use blue ink to draw the inverse demand function and use red ink to draw the marginal revenue function. On your graph, also draw a vertical blue line representing the capacity of the stadium. 0 20 40 60 80 100 120 140 160 5 10 15 20 25 30 Price Quantity x 1000 Red line Red line Black line Blue line Stadium capacity (d) What price will generate the maximum revenue? \$10. What quantity will be sold at this price? 100,000. (e) At this quantity, what is marginal revenue? 0. At this quantity, what is the price elasticity of demand? 1 . Will the stadium be full? Yes. (f) A series of winning seasons caused the demand curve for football tickets to shift upward. The new demand function is q ( p ) = 300 , 000 10 , 000 p . What is the new inverse demand function? p ( q )=30 10 , 000 .
NAME 199 (g) Write an expression for marginal revenue as a function of output. MR ( q )= 30 q/ 5 , 000 . Use red ink to draw the new demand function and use black ink to draw the new marginal revenue function. (h) Ignoring stadium capacity, what price would generate maximum revenue? \$15. What quantity would be sold at this price? 150,000. (i) As you noticed above, the quantity that would maximize total revenue given the new higher demand curve is greater than the capacity of the stadium. Clever though the athletic director is, he cannot sell seats he hasn’t got. He notices that his marginal revenue is positive for any number of seats that he sells up to the capacity of the stadium. Therefore, in order to maximize his revenue, he should sell 100,000 tickets at a price of \$20. (j) When he does this, his marginal revenue from selling an extra seat is 10. The elasticity of demand for tickets at this price quantity combination is ± = 2 .

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212 EQUILIBRIUM (Ch. 16) 16.12 (1) On August 29, 2005, Hurricane Katrina caused severe damage to oil installations in the Gulf of Mexico. Although this damage could eventually be repaired, it resulted in a substantial reduction in the short run supply of gasoline in the United States. In many areas, retail gasoline prices quickly rose by about 30% to an average of \$3.06 per gallon.
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## This note was uploaded on 09/27/2009 for the course ECON 101 taught by Professor Dannicatambay during the Spring '08 term at UPenn.

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Solutions to Workouts on Assignment 3 - NAME 197 15.9 (0)...

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