1. Plot the reaction function and find the Nash equilibrium
2. What is the utility of each agent at the equilibrium
3. Show that the equilibrium is inefficient: there is an action pair that gives both individuals higher utility

Question 2. This question concerns contributing to a public good. The extra mntribution by one person benets all so there is a positive externality. However, this is not taken into account whll an individual makes a contribution. Denote person i's wealth by mg, and the amount the person contributes to the public good by Cg [Cl 5 c, g mg]. The person's remaining wealth, w,- - c, is spent on \"private goods\" [like clothes and food, whose consumption by one person precludes consumption by anyone else). The amount of the public good is equal to the sum of the contributions. Each person cares both about the amount of the public good and their consumption of private goods. Let the utility of person '3, u,{c1, :22], be the sum of three parts: the amount c1 + cg of the public good provided, the amount w, Cg person i spends on private goods, and a term (w,- oi] [c1 + c2] that reects an interaction between the amount of the public good and private consumptionthe greater the amount of the public good, the more private consumption is valued. In summary, suppose that person i's payoff is: its =01 +52 +111; _C-i+ [111i -Bi)[31+zl =w+cj+ (we: -1J|:E51 +132] where j is the other person. Specically: 1151 = 1111+ E32 + [W1 - CHEF-1 + C2] 1151 = we + 1 + [we - Cent11 + C2] Assume that w] = 1112 = w, and that each player 11's contribution Cg may be any number [positive or negative, possibly larger than to]