Fixed Deficit Per Head

Abstract

Let us begin with capital dynamics. From Y = K^αN^β, r = αY/K and N₊₁ = (1+ n)N one can deduce that K₊₁ = (1 + n)K. Now regard the dynamics of public debt. The government spends a given sum per head on goods and services G = gN with g = const. In addition the government borrows a certain amount per head B = bN with b = const. Public debt and the budget deficit this period add up to public debt next period D₊₁ = D + B. Moreover the government collects a lumpsum tax T = tN with t = const. The government budget constraint is B + T = G + rD. Pay attention to the behavioural functions to arrive at bN + tN = gN + rD. Properly speaking, the government presets its purchases per head and the deficit per head, while it accommodates the lumpsum tax.