Consider the following simplied scenario. Imagine that the Australian national rugby union (for short, Rugby AU) has exclusive rights to organize the games played by the national team. Rugby AU decides that the next match, between the Wallabies and the All Blacks (i.e., the Australian and the New Zeeland national rugby teams), will be hosted at the Marvel Stadium in Melbourne. Rugby AU has no xed costs for organizing the game, but it must pay a marginal cost MC of $20 per seat to the owners of the Marvel Stadium. Two types of tickets will be sold for the game: concession and full fare. Based on any ofcial document that attests to their age, children and pensioners qualify to purchase concession tickets that offer a discounted price; everyone else pays the lll fare. The demand for full-fare tickets is QF(P) = 120 2P. The demand for concession tickets is Qc(P) = 80 2P. 1. The market or all are tickets F (40 points) a) b) d) Calculate the inverse demand, write the prot maximizing condition, compute the prot maximizing price PIE-'4 and the number of tickets Q}? that Rugby A U will choose to sell at full fare, as well as its prot g. (10 points) Use a diagram to illustrate the producer surplus PSF that Rugby A U enjoys, the consumer surplus of the full fare paying customers CSF, and the deadweight loss DWLF in this market. Then, compute CSF and DWLF. (6 points) Tax per unit (TU): The government decides to tax Rugby AU at $10 per ticket sold. Find the new optimal price P115!\" and quantity Q?!\" that Rugby A U chooses and compute its prot 2%,. Compute the government's tax revenue T Rm. (9 points) Lump sum tux (LS): Instead of a tax per unit, the government imposes a lump tax of $400 on Rugby A U. Find the new optimal price PE; and quantity Qfg that Rugby AU chooses and compute its prot 11:5; in this case. (9 points) Suppose that the government is looking to tax Rugby AU to raise revenue for building new sport facilities for kids and hires you to advise which one of the taxes above a tax per unit or a lump sum to implement. Which one of the two taxes would you recommend? Justify and explain why. (6 points) 2. The market [or concession tickets [C2 (30 points) f) Calculate the inverse demand, write the prot maximizing condition, compute the prot maximizing price PS' and the number of concession tickets (2%\" that Rugby AU will choose to sell, as well as its prot 1T3iv . (10 points) g) Use a diagram to illustrate the producer surplus PSC that Rugby AU enjoys, the consumer surplus for concession tickets customers CSC, and the deadweight loss DWLC in this market. Then, compute CS: and DWLC. (6 points) h) The government wants to encourage children and pensioners to attend sport events. To do so, it is willing to give Rugby A U a subsidy of 5 per concession ticket sold, but the government wishes to calibrate this subsidy such that Rugby AU will sell the same number of concession tickets as in perfect competition. Assuming that the government knows the demand and the costs that Rugby AU has, compute how much the subsidy s should be. (8 points) Cross subsidz'zatz'on: Suppose the government wishes to nance the total cost of the subsidy given in h) for concession tickets by taxing the tickets sold at full fare. Can you nd the minimum amount of tax per unit I that the government would have to charge Rugby AU for the tickets sold at full fare in order to cover the total subsidy needed for the concession tickets? Justify your answer. (6 points) 3. Combined/met\" ed market M (30 points) i) k) 1) Suppose that Rugby AU becomes unable to verify the age of its customers; thus, the formerly distinct full fare and concessional ticket markets must be combined/merged in one single market. First, write the equation of the merged demand and show it using a diagram. Then show and calculate the prot maximizing price Pf; and number of tickets Q that Rugby A U will choose to sell, as well its prot 1:3}. (15 points) How is each category of customers (i.e., full fare vs. concessional ticket customers) affected by the market merger? Do customers in each category benet or are they harmed by the merger? Justify and explain your answer. (6 points) Given the choice, would a prot maximizing Rugby AU prefer to operate distinct full fare and concession ticket markets, or just one single merged market? Justify your answer. (4 points) 111) If the government (seeking to maximize social welfare) could mandate which type of market Rugby A U should operate, should it opt for requiring distinct full fare and concession ticket markets, or just one single merged market? Justify your answer. (5 points)