I examine the problem of budget deficit in a growing economy in which consumers hold money as a part of their savings in the case where consumers live forever. For simplicity and tractability I use a discrete time dynamic model and Lagrange multiplier method. In the appendix I briefly explain the solution using a discrete time version of the Hamiltonian method. I will show the following results. 1) Budget deficit is necessary for full employment under constant prices. 2) Inflation is induced if the actual budget deficit is greater than the value at which full employment is achieved under constant prices. 3) If the actual budget deficit is smaller than the value which is necessary and sufficient for full employment under constant prices, a recession occurs. Therefore, balanced budget cannot achieve full employment under constant prices. I do not assume that budget deficit must later be made up by budget surplus.

In his "The World’s smallest macroeconomic model” (Krugman (1999)), Paul Krugman argued that under the assumption of price rigidity, a shortage of money supply leads to underemployment or recession, so increasing money supply can eliminate underemployment and restore full employment. But, how do we increase the money supply? I will show that we need a government deficit to increase the money supply in order to restore full employment from recession. Also, I will show that in a growing economy, if people hold money, a government deficit is necessary to maintain full employment under constant price or inflation. A government deficit is not only effective in pulling the economy out of recession, it is even necessary for continued growth without inviting either recession or inflation. The government deficit in this paper represents the difference between government expenditures and government revenues. When the difference is positive, we say that the government has a deficit. This paper seeks to explore theoretically and normatively the role of government deficits in achieving and maintaining full employment in a growing economy without causing inflation, using a very simple model by Krugman.