3. Suppose there are two individuals, 2' = 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 91 and person 2 contributes gg, then total public good provision is G = 91 + 9'2. If person i contributes 9,, i's remaining wealth, w g,- is i's private consumption. Each person's utility depends on the amount of the public good, G, and private consump- tion, w,- g, for person i = 1, 2. Preferences are: 91 = 91 +92 +101 "-91 +001 -91)(91 +92) = "101 +92 + (\")1 '91)(91 +92) U2 = 91 +92 + 102 92 + (W2 - 92)(91 +92) = 102 +91 +0112 92)(91 +92) Also, note that with G = 91 + 92, 1a,: G + w, g,- + (w,- 9,)G = w, + gj + (w, 9,)G. (3.) Find the (symmetric) Nash equilibrium levels of 91 and 92. (b) Show that total utility U = m + 71.2 depends only on G and W = w + w. (c) Find the socially optimal level of the public good the value of 91 + 92 that maximizes total utility U 2 ul + 'UBQ. (d) Show that the Nash equilibrium level of the public good is less than the socially optimal level