Improving Coalitions in a Monetary Economy
The competitive or Walrasian equilibrium has a well-known stability property-every Walras allocation belongs to the core of the economy. In an earlier paper (Gale, 1978) analogous results were shown to hold in a sequence economy with money. One of the limitations of that paper was the assumption of a complete set of securities. The extension of these results to an economy with only one asset (money) and several states of nature turns out to be frought with difficulty. The equilibrium in this case is highly unstable. Unless some quite unacceptable restrictions are imposed, there will always exist a group of consumers who can make themselves better off than they would be in equilibrium. The intractability of the problem casts doubt on the whole Edgeworthian programme of modelling market equilibrium as the outcome of a cooperative game. Consider a pure exchange economy in which there are two dates, indexed t = 0, 1, but no uncertainty. At each date a single consumption good is available. The economy comprises two consumers, A and B, who have identical tastes but different endowments. Their preferences are described by the utility function u(x) = [x ]2+[x']2 (X E R+) where xt denotes consumption at date t. Their endowments are described by the ordered pairs