Suppose there are two individuals, i = 1,2. Each person has wealth w (w > ,) and consumes both a public and a private good. The public good is provided by contributions from each individual. If persons 1 contributes gi and person 2 contributes ga, then total public good provision is G =g1 + 92. If person i contributes gi, i's remaining wealth, w - 9, is i's private consumption. Each person's utility depends on the amount of the public good, G, and private consump- tion, wi - g; for person i = 1,2. Preferences are: Also, note that with Gan+2. "=G+w-gi+ (m-g)Gutg, + ( -g)G. (a) Find the (symmetric) Nash equilibrium levels of g, and gr. (b) Show that total utility / = wj + up depends only on G and W= w + w. (c) Find the socially optimal level of the public good - the value of g + 92 that maximizes total utility U = us + up. (d) Show that the Nash equilibrium level of the public good is less than the socially optimal level