On the debt to GDP ratio in monopolistic competition

Research background: Many people in Japan and other countries believe that national finances will not stand still and will go bankrupt if deficits continue at present level. It is like a religion. In this paper, however, we prove that this religion is wrong by using a simple mathematical model. Research methodology: This paper uses a macroeconomic model based on microeconomic foundations for consumers and firms with overlapping generations of consumers under monopolistic competition. Results: Although fiscal failure or collapse is generally defined as the government debt to GDP ratio going beyond a finite value to an infinite value, i.e., diverging, the following analysis theoretically proves that such a failure does not occur under stable prices or under a constant inflation rate. It is often said that the government debt to GDP ratio will continue to increase if the interest rate on government bonds exceeds the economic growth rate, but we prove that such a fiscal failure does not occur even when the interest rate of government bonds exceeds the growth rate. This paper shows that the debt to GDP ratio converges to or remains at a finite value over time and that the budget deficit over a given period is equal to the difference between the savings of the younger generation of consumers and the savings of the older generation of consumers. Novelty: There are few papers that analyze the fact that financial collapse does not occur using mathematical models, and it is worthwhile to do so.