Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in 4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following 4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.