2. Consider the following model economy; consisting of an innite number of innitely lived agents indexed by j = U; 1; 2; 00. There is an innite number of timedated goods; c[t) ;t 3 1. A typej = [I person values only good (5(1). A typej = 1 person values goods c(1) and C(2); and; in general; a type j 2 1 values goods c(j) ; c(j + 1) according to a utility function u {c (j) ; c (j + 1))- Each type of agent has an endowment of goods; y(t) ;t 3 1. A typej = U person has no endowment; i.e.; y (t) = [I for all t- A typej = 1 person has an endowment y{1) = y :21 [I and y[t) = D for all t I} 1. A type j = 2 person has an endowment y(1] = ULy (2) = y :5 U and y (t) = U for all t 2} 2; and so on. The endowment is nonstorable. (a) Explain why this economy displays a complete lack of doublecoincidence of wants. (b) What is the autarlcy allocation? (c) Consider any stationary allocation [c (j) ; C(j | 1)} = (Cy; c") for all j 23 1; with c (D) = c\". Characterize the Golden Rule allocation; i-e.; the Firstbest allocation- (d) Assume that agents lack a commitment technology. There is; however; a publicly accessible and costless recordkeeping technology. Explain how it is possible to implement any feasible (stationary) allocation (that dominates autarky) as an equilibrium without money. (e) Assume now that agents are completely anonymous (so that no recordkeeping technology is available]. Demonstrate that there are now only two stationary equilibria; i.e.; one in which at money is valued; and one in which it is not- Be sure to dene a monetary equilibrium. (f) Show that the (stationary) monetary equilibrium implements the Golden Rule allocation