Need help with Question 2 and Question 3

Tom Hanks and Wilson consume two types of goods: a private good X (coconut) and a public good F (fireworks). The preferences of Tom and Wilson are given by: UTH (XTH , F) = In(XT ) + In( F) UW (XW , F ) = In(X" ) + In(F) where F = F" + FW. The price of both coconuts and firewords is $1. Both Tom and Wilson have $120 of income each. 1. How many fireworks are consumed when the government does not intervene? (a) Solve for the demand functions of Tom and Wilson as a function for each other. e.g. Solve for the optimal Fr as a function of FW . (5 pts) (b) What happens to the purchase/provision of fireworks of Tom Hanks F as Wilson increases his FW? What phenomenon does this demonstrate? (5 pts) (c) Use the Nash Equilibrium framework to find the total private provision of fireworks. Hint: The answer is algebra from part 1(a). (5 pts) 2. Solving the social planner's problem, find the socially optimal amount of fireworks. What can you say about the outcome in the private provision of a public good and the outcome of a socially optimal provision? What is the intuition behind the optimality condition for the provision of public goods? (5 points) 3. This question will demonstrate the crowding-out effect. (a) What is the shortfall/deficit when fireworks provision is done privately? The shortfall/deficit between the private and public provision is given by Fdeficit = Fpublic - Fprivate. (5 pts) (b) Now suppose the government decides to supply the deficit Fdeficit. The government funds this initiative by a lump-sum tax on both Tom and Wilson of Edchee. Set-up the problem of Tom Hanks and Wilson. (5 pts) (c) Solve the problem of Tom Hanks and Wilson. (5pts) (d) Is there crowding out? Why do you say so? (5 pts)