Question

2 Variable Game Pricing Consider that the Minnesota Vikings have two games left in their season. The first game is against the Chicago Bears and the game determines who wins the NFC North Division. The second game is against the lowly Green Bay Packers and their washed up quarterback. The game has no playoff or division implications. The aggregate inverse demand curve for the game against the Bears is P 300-2Q and the inverse demand for the game against the Packers is P = 240 - 20, where Q is in thousands. The marginal cost of supplying a seat is zero. 1. First, consider that the Vikings' front office is required to charge the same price for all tickets to both games. (a) Write down the Vikings' profit maximization problem. (b) What price maximizes profit? (c) What is total attendance for the two games? (d) What is total Profit (producer surplus) at the optimal price? (e) What is total Consumer Surplus at the optimal price? 2. Now consider that the Vikings can choose a different price for each game. (a) Write down the Vikings' profit maximization problem. (b) What prices maximizes profit? (c) What is total attendance for the two games? (d) What is total Profit (producer surplus) at the optimal prices? (e) What is total Consumer Surplus at the optimal price?

Answer 1

Answer Page : For Bears P=300- 20 B where 13: Number of seats for bears game 2003 = 300-P B = 300 - & B = 150 - 0.5P for viking P= 240-280 v where ev: Number of seats for viking game. 20 v= 240-P @ov 240 - SP - 120 - 0:5p @ With Single pricing model, Total demand (@) - XB4 @v. = 150 - 0.5P + 120-0.5P Q - 270-P P=270-

Profit (2) - Revenue - cost 19-2 = (Px) - (Mc x® - 0700-03-0(Sence HC is zego - 2700 - 2 the profit-maximization problem as: maximum = 2700 - 2 subged to 0 = 0 (6) Poolat as maximized when da 120=0 and dz/do²c0 dz Ide- 270-20 = 0 270 - 200 = 135 P 270-135 P = 135 21 do ² - a/do (270 - 20) - - 2 <0. So second order condation as salisfied E) Profit maximizing altandance () is 135 Seats.

d) Poolit = (210x135) - ( 135 x 135) Pg - 3) 36.450 -18,225 = 18, 225 Chion, e) from mosket demand function, when = 0, P= 270 (Reservation poice and vertical intercept of demand curve). Consumer sulplug- Area between demand curve and market price = (1/2) x (270-135) XB5 - 67.58135 - 9,112.5. Note: As per answering policy, 1st part with multiple sub-pasts as answered.