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. 2. The market for full fare tickets (F) f) Calculate the inverse demand, write the profit maximizing condition, compute the profit maximizing price ?'"and the number of concession tickets ?'" that Rugby AU will choose to sell, as well as its profit π'". g) Use a diagram to illustrate the producer surplus PSF that Rugby AU enjoys, the marginal revenue MR, the consumer surplus for concession tickets customers CSF, and the deadweight loss DWLF in this market. Then, compute CSF and DWLF. h) Tax per unit (TU): The government wants to tax Rugby AU at $1 per ticket sold. Find the new optimal price PMTU and quantity QMTU that Rugby AU chooses and calculate its profit πMTU. Compute the government's tax revenue TRTU. i) Lump sum tax (LS): Instead of TU, the government imposes a lump tax of $75 on Rugby AU. Calculate the new optimal price PMTU and quantity QMTU that Rugby AU chooses and compute its profit πMLS in this scenario. j) The government wants to tax Rugby AU to build a new health center for children and pensioners and needs your help on deciding which one of the taxes above, a tax per unit or lump sum - to implement. Which would you recommend? Explain why please.
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.
2. The market for full fare tickets (F)
f) Calculate the inverse demand, write the profit maximizing condition, compute the
profit maximizing price ?'"and the number of concession tickets ?'" that Rugby AU
will choose to sell, as well as its profit π'".
g) Use a diagram to illustrate the
consumer surplus for concession tickets customers CSF, and the deadweight loss
DWLF in this market. Then, compute CSF and DWLF.
h) Tax per unit (TU): The government wants to tax Rugby AU at $1 per ticket sold. Find the new optimal price PMTU and quantity QMTU that Rugby AU chooses and calculate its profit πMTU. Compute the government's tax revenue TRTU.
i) Lump sum tax (LS): Instead of TU, the government imposes a lump tax of $75 on Rugby AU. Calculate the new optimal price PMTU and quantity QMTU that Rugby AU chooses and compute its profit πMLS in this scenario.
j) The government wants to tax Rugby AU to build a new health center for children and pensioners and needs your help on deciding which one of the taxes above, a tax per unit or lump sum - to implement. Which would you recommend? Explain why please.
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