INFINITE-HORIZON INCOMPLETE MARKETS

The model of general equilibrium with incomplete markets is a generali zation of the Arrow-Debreu model which provides a rich framework for s tudying problems of macroeconomics. This paper shows how the model, wh ich has so far been restricted to economies with a finite horizon, can be extended to the more natural setting of an open-ended future, ther eby providing an extension of the finite horizon representative agent models of modem macroeconomics to economies with heterogeneous agents and incomplete markets. There are two natural concepts of equilibrium over an infinite horizon which prevent agents from entering into Ponzi schemes, that is, from indefinitely postponing the repayment of their debts. The first is based on debt constraints which place bounds on d ebt at each date-event; the second is based on transversality conditio ns which limit the asymptotic rate of growth of debt. The concept of a n equilibrium with debt constraint is a natural concept of equilibrium for macroeconomic analysis; however the concept of an equilibrium wit h transversality condition is more amenable to theoretical analysis si nce it permits the powerful techniques of Arrow-Debreu theory to be ca rried over to the setting of incomplete markets. In an economy in whic h agents are impatient (expressed by the Mackey continuity of their pr eference orderings) and have a degree of impatience at each date-event which is bounded below (a concept defined in the paper), we show that the equilibria of an economy with transversality condition coincide w ith the equilibria with debt constraints. An equilibrium with transver sality condition is shown to exist: it follows that for each economy t here is an explicit bound M such that an equilibrium with explicit deb t constraint M exists, in which the constraint is never binding-this l atter property ensuring that the debt constraint, whose objective is t o prevent Ponzi schemes, does not in itself introduce a new imperfecti on into the model over and above the incompleteness of the markets.