Abstract

This paper contains a model designed to serve two purposes, to examine long-run competitive equilibrium in a growth model and then to explore the effects on this equilibrium of government debt. Samuelson [8] has examined the determination of interest rates in a singlecommodity world without durable goods. In such an economy, interest rates are determined by consumption loans between individuals of different ages. By introducing production employing a durable capital good into this model, one can examine the case where individuals provide for their retirement years by lending to entrepreneurs. After describing alternative long-run equilibria available to a centrally planned economy, the competitive solution is described. In this economy, which has an infinitely long life, it is seen that, despite the absence of all the usual sources of inefficiency, the competitive solution can be inefficient. Modigliani [4] has explored the effects of the existence of government debt in an aggregate growth model. By introducing a government which issues debt and levies taxes to finance interest payments into the model described in the first part, it is possible to re-examine his conclusions in a model where consumption decisions are made individually, where taxes to finance the debt are included in the analysis, and where the changes in output arising from changes in the capital stock are explicitly acknowledged. It is seen that in the "normal" case external debt reduces the utility of an individual living in long-run equilibrium. Surprisingly, internal debt is seen to cause an even larger decline in this utility level. External debt has two effects in the long run, both arising from the taxes needed to finance the interest payments. The taxes directly reduce available lifetime consumption of the individual taxpayer. Further, by reducing his disposable income, taxes reduce his savings and thus the capital stock. Internal debt has both of these effects as well as a further reduction in the capital stock arising from the substitution of government debt for physical capital in individual portfolios.