Fixed Tax Per Head

Abstract

In full analogy to the preceding sections, the short-run equilibrium can be represented by a system of eleven equations:

$$Y=K_{i}^{\alpha }N_{i}^{\beta }$$

(1)

$$r={\alpha {{Y}_{i}}}/{{{K}_{i}}}\;$$

(2)

$${{\dot{D}}_{i}}+{{\dot{F}}_{i}}+{{\dot{K}}_{i}}=s({{Y}_{i}}+r{{D}_{i}}+r{{F}_{i}}-{{t}_{i}}{{N}_{i}})$$

(3)

$$\dot{D}={{g}_{i}}{{N}_{i}}+r{{D}_{i}}+r{{F}_{i}}+r{{F}_{i}}-{{t}_{i}}{{N}_{i}}$$

(4)

$${{\dot{N}}_{i}}=n{{N}_{i}}$$

(5)

$${{F}_{1}}=-{{F}_{2}}$$

(6)

Here α, β, g_i, n, s, t_i, F_i, K_i and N_i are exogenous, whereas r, ${{\dot{D}}_{i}},{{\dot{F}}_{i}},{{\dot{K}}_{i}},{{\dot{N}}_{i}}$ and Y_i are endogenous.