The budget deficit in an endogenous growth model with bequest and money holdings

By an endogenous growth model with a two-period overlapping generations structure, I examine the existence of a budget deficit in an economy that endogenously grows by investments of firms. The consumers leave bequests to their descendants and hold money as a part of their savings. I use a Barro-type utility function, where people include the utility of their children in their own utility. The main results are as follows. 1) A 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, a balanced budget cannot achieve full employment under constant prices. I do not assume that the budget deficit must later be made up by a budget surplus. I use a Barro-type utility function to prove the necessity (or inevitability) of a budget deficit instead of the neutrality of government debt. In the appendix of this paper, I show that if money, as well as goods, are produced by capital and labor, a budget deficit is not necessary for full employment under constant prices.