Two Steady States and Two Movement Patterns under the Balanced Budget Rule: An Economy with Divisible Labor

Authors: Fujio Takata

Abstract:

When governments levy taxes on labor income on the basis of a balanced budget rule, two steady states in an economy exist, of which one can cause two movement patterns, namely, indeterminacy paths and a saddle path. However, in this paper, we assume an economy with divisible labor, in which labor adjustment is made by an intensive margin. We demonstrate that there indeed exist the two paths in the economy and that there exists a critical condition dividing them. This is proved by establishing the relationship between a finite elasticity of labor with regard to real wages and the share of capital in output. Consequently, we deduce the existence of an upper limit in the share of capital in output for indeterminacy to occur. The largest possible value of that share is less than 0.5698.

Keywords: balanced budget rule, divisible labor, labor income taxation, two movement patterns