1. Take an economy with 2 consumers, 1 private good and 1 public good. Let each consumer have an income of M. The prices of public and private goods are both 1. Let the consumers have utility functions U4 =log(x?) + log(G) UB =log(x?) + log(G) . Assume that the public good is privately provided so that G = g* + g. Eliminating A from the utility function using the budget constraint, show that E1l0 T e T i (o (o WRubi gy o V| 1 1 B - - Gl e R s R and hence: R P . Consider A choosing g# to maximize utility. Show that the optimal choice PNy 7 g = . Repeat part b for B, and calculate the level of private provision od the public i eTe R . Calculate the optimal level of provision for the welfare function R Contrast this with the private provision level. M g8 F A