The Economic-implications of An Incomplete Asset Market - Polemarchakis, Heraklis (American Economic Review, 1990)
When the asset market is incomplete, the role of prices extends beyond conveying the aggregate scarcity of commodities. In conjunction with the asset structure, they determine the attainable reallocations of revenue. This affects nontrivially the existence, optimality, and determinacy of competitive equilibrium allocations, as well as the revelation of information by prices. Further, it accounts for diverse phenomena, among them the preservation of memory in macroeconomics aggregates. A simple exchange economy extends over two periods. Uncertainty, indexed by finitely many states of nature, s = 1,..., S, is resolved in the second period. Commodities, 1 = 1, .. ., L, are traded in spot markets in the second period after the uncertainty has been resolved and assets have paid off. A commodity bundle is x = ( . . ., x(s), . . . ) = (...,x1(s) ...). Commodity prices are p = (-,P(s) ....) (. (—, Pi(s), -.). Assets, a= 19 . . ., A, are traded in the first period and pay off in the second. A portfolio is y = (..., Ya. ). Assets are real: the payoff of an asset is a commodity bundle ra = (..., ra(s), .. .). At commodity prices p, the payoff of an asset, more precisely the payoff of an asset in terms of revenue, is