1 The demand equations for airplane trips for business travelers and vacationers are P = 600 â?" 0.2QB and P = 200 â?" 0.05QV, respectively. Assume that the airline can serve an extra passenger with no extra cost.
(a) If the airline company has to charge a single price to all passengers, what are the profitmaximizing price, the number of tickets sold to each type of travelers, and the total profit for the airline company?
(b) If the airline company can price-discriminate and charge different prices to different types of customers, what are the price it will charge to business travelers and vacation travelers? What is the airlineâ??s profit with price discrimination?
2 Times and Newsweek are two competing news magazines. Suppose that each company charges the same $5.00 price for their magazines. Each wants to maximize its sales given the $5.00 price. Each week, there are two potential cover stories. One in on politics, and the other is on the economy. Sales of both companies are affected by the decision on which story to place on the covers. The two magazines make their decision independently and at the same time. The resulting sales for the two companies are given in the following table:
Time Cover Newsweek Cover Time Sales ($000â??s) Newsweek Sales ($000â??s)
Politics Politics 400 150
Politics Economy 700 200
Economy Politics 300 700
Economy Economy 200 150
a. Construct a payoff matrix of this game.
b. What is the Nash equilibrium in this game?
c. Does either or both of the magazines have a dominant strategy?
d. Suppose that both magazines are owned by the same publishing company that maximizes the combined profits of the magazines. Will the company make the same choice as in the noncooperative game (i.e., owned by different publishing companies)?
a) if the company charges the same price, we know that P = 600 â?" 0.2QB and P = 200 â?" 0.05QV (P is the same)
so 600 â?" 0.2Qb = 200 â?" 0.05Qv or 0.2Qb = 400 + 0.05Qv => Qb = 2000 + Qv/4
so revenue = revenue from business + revenue from vacationer (MC is 0 so we can forget about cost)
revenue = price X (Qb + Qv) = (200 â?" 0.05Qv)(2000 + Qv/4 + Qv) = -0.0625Qv^2+150Qv+400000
take derivative with resp. to Qv and set it to 0 to maximize
150 - 0.125Qv = 0 and we get Qv = 1200
substitute back into P = 200 â?" 0.05QV and get P = 140. P = 600 â?" 0.2QB and we get Qb = 2300
revenue from business is 2300 X 140 = 322000 and ...