n/ 2. Consider that there are n consumers. Each consumer can contribute to finance a public good by giving an amount of

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N 2 Consider That There Are N Consumers Each Consumer Can Contribute To Finance A Public Good By Giving An Amount Of 1 (214.84 KiB) Viewed 41 times

n/ 2. Consider that there are n consumers. Each consumer can contribute to finance a public good by giving an amount of money Pi € [0,c]. We assume that each consumer i's utility function is given by Ui(PiEj+iP;) = g(Pi +P-i) – Pi where P-i = Ej+iPj. = = (a) Characterize the first-order and second-order conditions if we assume that each consumer i maximizes hís utility given the others' profile of contribution (pj)j+i. [6 marks] (b) What is the first-order condition characterizing a Nash equilibrium of this game? What if we have a symmetric (pure) Nash equilibrium? [8 marks] (c) Assume that a planner consider the maximization of the aggregate utility function, U(P1, ...,Pn) = , U:((P1, ...,Pn) = ng(P) – P. What are the first-order and ((pP second-order conditions for a total contribution P* maximizing this aggregate utility function? Show that the total sum of optimal contribution P* = $1=1 Pi is higher under the planification of a planner than in a Nash equilibrium [6 marks] = = a 1 i=