Federal Reserve and Monetary Policy: “A Watched Pot Never Boils”

I want to begin this entry by proving the existence of elasticity of labor with respect to capital. In previous entries I proved the existence of the “value added chain” as a topological lift between K(capital) vector(co-vector) space and L(labor) co-vector(vector) space. The K-L spaces are linear which implies there exists a Cartesian product of this multi-linear space:

This is a handy tensor because one can raise and lower indexes by the use of the metric tensor and a contraction (convert capital into labor and visa versa).

I’m going to use scalars to show the concept of the time evolution of the arc elasticity of labor with respect to capital (% change of labor with respect to the % change of capital).




The time evolution is the direct product of the arc elasticity of labor with respect to capital and the arc elasticity of time (its inverse; which implies none of the matrixes are singular).

It is realistic to simplify this time evolution to a set of average times. As time evolves in steps those shocks, that have a short period, affect the evolution before those with longer periods. In other words, the time evolution is a superposition of average periods.