Continuous time debt dynamics and fiscal policy for full-employment: A Keynesian approach by mathematics and simulation

We present a continuous time version of a dynamic analysis of debt-to-GDP ratio, and examine the effects of a fiscal policy which realizes full-employment from a state of under-employment or with deflationary GDP gap. We show that the larger the extra growth rate of real GDP by a fiscal policy is, the smaller the debt-to-GDP ratio at the time when full-employment is realized is, and a fiscal policy for full-employment can reduce the debt-to-GDP ratio. Therefore, full-employment can be realized by an aggressive fiscal policy with smaller debt-to-GDP ratio than before the fiscal policy. An increase in the government expenditure may induce a rise of the interest rate. Since the higher the interest rate is, the larger the debt-to-GDP ratio is, we need an appropriate monetary policy which maintains the low interest rate. Also we show that even if the propensity to consume is very small, an aggressive fiscal policy can realize full-employment without increasing debt-to-GDP ratio