Question

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) = ln(XT) + ln(F) UW (XW, F) = ln(XW)+ln(F) where F = FT + 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 FT as a function of FW. (5 pts) (b) What happens to the purchase/provision of fireworks of Tom Hanks FT 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)

Answer 1

Answer - Page No - 1 The preference of Tom and wilson are given by UTH (XTH F = dn (XTH ) thn (F) UW (XW, F = ln (XW)+ ln (F) Point (a) - using the eam condition is MRS - PX /pf 1 for the tom is mm3 - mux/mut - cyx)/1784 ++- (644th x) (ft + In 1x D=1 ft tfn = x Using the budget constraint PX.X +Pt. F=m XE+ (Ft + h) = 120 X= 120 2020.02.19 19:28

Page No - 2 Xt = 60 = Sttfw Go ft ton fit= 60-tw point (6) As the fit and fw are negatively related to the each other so as wilson increases his the consumption / demand, tom's consumption fall. I