The overlapping-generations model. III. The case of log-linear utility functions

Abstract

Existence of competitive equilibria in the overlapping-generations model has been studied in some detail; see [4-6,9]. We need to know more about the properties of these equilibria. How many are there? How do they depend on the basic parameters of the economy? We also need to compare the set of monetary competitive equilibria with the set of nonmonetary competitive equilibria. Are there “vastly more” monetary equilibria than nonmonetary equilibria? Analysis of the properties of competitive equilibria is for the overlappinggenerations model an important, but difficult, task. In his seminal article [8], Samuelson put it this way: “... if we take any finite stretch of time and write out the equilibrium conditions, we always find them containing discount rates from before the finite period and discount rates from afterward. We never seem to get enough equations; lengthening our time periods turns out always to add as many new unknowns as it supplies equations . ..” Samuelson suggested that, rather than facing this difficulty directly, “We can try to cut the Gordian knot by our special assumption of stationariness . ..”