Consider the following simplified 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 fixed 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 official document that attests to their age, children and pensioners qualify to purchase concession tickets that offer a discounted price; everyone else pays the full fare. The demand for full-fare tickets is QF(P)=1202P. The demand for concession tickets is QC(P)=802P. 1. The market for full fare tickets (F) (40 points) a) Calculate the inverse demand, write the profit maximizing condition, compute the profit maximizing price PFM and the number of tickets QFM that Rugby AU will choose to sell at full fare, as well as its profit FM. (10 points) b) Use a diagram to illustrate the producer surplus PSF that RugbyAU 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) c) Tax per unit (TU): The government decides to tax Rugby AU at $10 per ticket sold. Find the new optimal price PTUM and quantity QTUM that RugbyAU chooses and compute its profit TUM. Compute the government's tax revenue TRTU. (9 points) d) Lump sum tax (LS): Instead of a tax per unit, the government imposes a lump tax of $400 on Rugby AU. Find the new optimal price PLSM and quantity QLSM that RugbyAU chooses and compute its profit LSM in this case. (9 points) e) 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)