You are contracted by the city of Quebec to resolve longstanding issues of transportation infrastructure in Quebec. The government is considering two mutually exclusive public good options: 1. Tramway (Tr) 2. Tunnel (Tu) There are n=3 representative individuals in society: 1. A social democrat: u1={2ln(Tu)+y11.5ln(Tr)+y1ifTunnelifTramway 2. An undecided: u2={2ln(Tu)+y2ln(Tr)+y2ifTunnelifTramway 3. A car dealership owner: u3{3ln(Tu)+y32ln(Tr)+y3ifTunnelifTramway As usual, it is assumed that quantities of the private good yi can be converted to quantities of either public goods with a 1:1 technology. Endowments of each individuals is as follows: wi=3i=1,2,3 a) Find the socially optimal level of Tr and Tu using Wicksell-Lindahl taxes for both goods. Hint: use i=13tiu=1 to find Tu, and likewise for Tr b) Show that the proposed allocation in a) is not an allocation, e.g. it is not feasible to finance both goods with those taxes. c) Since the Wicksell-Lindahl taxes are not feasible, the government of Quebec decides that it will only finance one of the two public goods. To do so, it will use Fixed Tax Shares and majority voting tiu=n1=tir to allocate each public good, and then choose the public good that yields the highest sum of utilities i=13ui. i. Derive the allocation under the Tramway. Is it pareto optimal? ii. Derive the allocation under the Tunnel. Is it pareto optimal? iii. Derive the sum of utilities under both public goods. What is the final choice of the government? You are contracted by the city of Quebec to resolve longstanding issues of transportation infrastructure in Quebec. The government is considering two mutually exclusive public good options: 1. Tramway (Tr) 2. Tunnel (Tu) There are n=3 representative individuals in society: 1. A social democrat: u1={2ln(Tu)+y11.5ln(Tr)+y1ifTunnelifTramway 2. An undecided: u2={2ln(Tu)+y2ln(Tr)+y2ifTunnelifTramway 3. A car dealership owner: u3{3ln(Tu)+y32ln(Tr)+y3ifTunnelifTramway As usual, it is assumed that quantities of the private good yi can be converted to quantities of either public goods with a 1:1 technology. Endowments of each individuals is as follows: wi=3i=1,2,3 a) Find the socially optimal level of Tr and Tu using Wicksell-Lindahl taxes for both goods. Hint: use i=13tiu=1 to find Tu, and likewise for Tr b) Show that the proposed allocation in a) is not an allocation, e.g. it is not feasible to finance both goods with those taxes. c) Since the Wicksell-Lindahl taxes are not feasible, the government of Quebec decides that it will only finance one of the two public goods. To do so, it will use Fixed Tax Shares and majority voting tiu=n1=tir to allocate each public good, and then choose the public good that yields the highest sum of utilities i=13ui. i. Derive the allocation under the Tramway. Is it pareto optimal? ii. Derive the allocation under the Tunnel. Is it pareto optimal? iii. Derive the sum of utilities under both public goods. What is the final choice of the government