Consider the following variant of the economy in Section 9.1. The utility of the individual indexed i = j is
where β ∈ (0, 1), and each individual has one unit of the good with the same index as his own.
(a) Define a competitive equilibrium for this economy.
(b) Characterize the set of competitive equilibria in this economy.
(c) Characterize the set of Pareto optima in this economy.
(d) Can all Pareto optima be decentralized without changing endowments? Can they be decentralized by redistributing endowments?