The market for full fare tickets (F) :

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) = 120 - 2P. The demand for concession tickets is QC(P) = 80 - 2P.

1. 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 P^M_LS and quantity Q^M_LS that Rugby AU chooses and compute its profit Phi^M_LS in this case.