Need for Fiscal Deficits and Government Debt: Using an Infinite Duration Growth Model with Government Debt Holdings

Abstract

Using a model in which people (consumers) derive utility from their consumption of goods and their holdings of government debt for liquidity and other purposes and live for an infinite period of time, we examine the necessity of budget deficits and government debt in a growing economy and will prove the following results: 1) A budget deficit is necessary to achieve full employment with stable prices in a growing economy, and its value is equal to the increase in government debt holdings of consumers. 2) If a certain condition regarding the growth rate, the propensity to consume, and the discount rate holds, then the ratio of debt to GDP required to maintain full employment at constant prices (debt-GDP ratio) will converge to a finite value over time. 3) However, even if the condition in 2) is not satisfied and the debt-GDP ratio diverges, there is no problem because full employment without inflation is assumed.