On Paying-As-You-Go In An Explicit Overlapping Generations Model

In this application of an overlapping generations model the effects of a pay-as-you-go retirement scheme on the optimal savings rate, magnitude and stability of the equilibrium capital per capita level are established through the assumptions of explicit, well-behaved utility and production functions. The expected results regarding the partial effects of the population growth rate and discount rate on the optimal savings rate are obtained. In addition the optimal savings rate is seen to be inversely related to the proportion of wages collected as social security taxes. Under the assumed hypotheses a higher interest rate induces agents to save more. Existence of a positive equilibrium point is demonstrated and the partial effects of parameters are explored through numerical simulations. These results suggest an inverse relation between the magnitude of the equilibrium value and the population growth rate, tax rate and discount rate. The exponent of the Cobb-Douglas production function also has a negative effect on the equilibrium capital (per capita) level. The accumulation path can be written explicitly only in the backward dynamics form. On the basis of numerical calculations it is demonstrated that the relation between future and current capital values is one-to-one. Using the latter result it can be shown that the unique, positive equilibrium is in fact stable and the forward dynamics can be identified.