The Dynamic Nonsubstitution Theorem. Generalization of the Elasticity of Substitution.

Abstract

In part I we have proved the nonsubstitution theorem. The proof rested on the uniqueness of the solution of the system of the price equations

$$p = \phi \left( {\bar w,p} \right)$$

for any given w, where φ was the unit cost function as a function of input prices. In the model where time enters into the production process the unit cost function changes to φ ($\bar w$, r, p). But otherwise it keeps all relevant properties. For given r φ_i remains homogeneous of degree one in $\bar w$ and p, and φ_i remains a strictly increasing function of $\bar w$, if a_oi is positive.