Money holding and budget deficit in a growing economy with consumers living forever

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.