Debt to GDP Ratio from the Perspective of MMT

In this note we examine the debt to GDP ratio from the perspective of MMT (Modern Monetary Theory) by a simple macroeconomic model with savings by government bonds instead of money. Mainly we will show the following results. 1) In order to maintain full employment under economic growth, the budget deficit, including interest payments on government bonds, must be positive; and if the budget deficit is smaller than this value, there will be recession with involuntary unemployment. 2) Under full employment the debt to GDP ratio approaches to a finite value over time. 3) In the underemployment case the national income is determined by the budget deficit. 4) The excessive budget deficit causes inflation. 6) In order to recover full employment from recession we need budget deficit larger than that when full employment is maintained. 5) The budget deficit, including interest payments on government bonds, equals the increase of the savings of consumers between periods (generations); and this result holds whether we have full employment or not, whether we have inflation or not. Then, the ratio of the national debt to GDP in a period is smaller than one, and even if one period constitutes of several years, the debt to GDP ratio in a year is finite