Existence of equilibrium in an overlapping‐generations model with government debt

Abstract

The Diamond overlapping generations (OLG) model with government debt has been widely utilized in economics, but the existence of the steady-state equilibrium is either assumed or illustrated numerically. This paper provides easily checkable conditions for the existence and uniqueness of steady-state equilibrium in this model. By checking the first derivatives of the production and utility functions and their interactions, we can determine whether the model has a nontrivial equilibrium or not. We show that the level of government debt, production technology, individual preference, and the growth rate are important for the existence of equilibrium. If government debt exceeds a certain level, equilibrium will not exist. Given technology, preference, and the growth rate, the upperbounds of the government debt-output ratio in equilibrium can be determined based on our results.

Climate policy and optimal public debt

“…However, the aim of our analysis is to provide a stylized theoretical framework for identifying the basic mechanism at work. A more sophisticated and empirically calibrated model, based on overlapping-generations models similar to Chiroleu-Assouline and Fodha (2006) or Li and Lin (2021) or an extended DICE simulation model employed by van der Ploeg and Rezai (2019), for instance, is beyond the scope of our paper and left for future research.…”