Regular Demand with Several, General Budget Constraints

The past several years have witnessed burgeoning interest in models of competitive equilibrium with incomplete financial markets. Unlike the earlier development of the now standard Walrasian theory, this later development has passed very quickly from concern with the fundamental properties of existence and optimality to more general concern with the structure of the equilibrium set from the differentiable viewpoint.1 There are a number of plausible explanations for this rapid shift of emphasis. The presence of a large literature on smooth Walrasian models (see, for instance, the extensive references in Balasko, 1988) is surely by itself quite important. However, two substantive considerations stand out: first, in some formulations of the model with incomplete markets (e.g., where nominal yields on financial instruments are taken to depend linearly on spot prices for physical commodities), perhaps the most basic question about equilibrium — existence — is best answered in generic terms. Second, in other formulations of the model (e.g., where nominal yields are taken to be exogenous to the markets under consideration), perhaps the most critical property of equilibrium, multiplicity (or indeterminacy), is best characterised in dimensional terms.