Fixed Deficit Per Head

Abstract

In section 1, we postulated that the government fixes the deficit ratio. In section 3, instead, we shall suppose that the government fixes the deficit per head. Let us begin with the dynamics of public debt. The government buys a certain volume of goods and services per head G = gN with g = const. In addition the government borrows a given amount per capita B = bN with b = const. The budget deficit in turn augments public debt $\dot{D}=B$. Apparently b denotes the deficit per head. Moreover the government collects a lumpsum tax T = tN with t = const. The government pays the interest rate r on public debt D, so public interest equals rD. The government budget constraint is B + T = G + rD. Taking account of the functional relationships, the identity can be expressed as bN + tN = gN + rD. Here the government presets purchases per head and the deficit per head, while it adjusts the lumpsum tax.