Consider the following model economy, consisting of an infinite number of infinitely lived agents indexed by j = 0, 1, 2, ..., ∞. There is an infinite number of time-dated goods, c (t), t ≥ 1. A type j = 0 person values only good c (1). A type j = 1 person values goods c (1) and c (2); and, in general, a type j ≥ 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 ≥ 1. A type j = 0 person has no endowment; i.e., y (t) = 0 for all t. A type j = 1 person has an endowment y (1) = y > 0 and y (t) = 0 for all t > 1. A type j = 2 person has an endowment y (1) = 0, y (2) = y > 0 and y (t) = 0 for all t > 2; and so on. The endowment is non-storable. 

(a) Explain why this economy displays a complete lack of double-coincidence of wants. 

(b) What is the autarky allocation? 

(c) Consider any stationary allocation (c (j), c (j + 1)) = (c y , co ) for all j ≥ 1, with c (0) = c o . Characterize the Golden Rule allocation, i.e., the First-best allocation. 

(d) Assume that agents lack a commitment technology. There is, however, a publicly accessible and costless record-keeping technology. Explain how it is possible to implement any feasible (stationary) allocation (that dominates Autarky) as an equilibrium without money.