The Cambridge capital controversies: contributions from the complex plane

This article takes a fresh look at reswitching. When two production techniques are compared, reswitching occurs when one technique is more viable than the other at a high interest rate, switches to being less viable at a lower rate, and reswitches to being more viable again at even lower rates. For some, reswitching undermines the foundations of neoclassical economics because it belies the idea of a monotonic relationship between relative capital values and factor price. The reswitching equation is an nth degree polynomial having n roots, implying the existence of n interest rates. Conventional analysis uses one interest rate but ignores the others. We argue that the others should not be ignored because all rates are determined simultaneously, and when one rate shifts, all rates shift. We demonstrate that the Samuelson reswitching model possesses a ‘dual’ expression containing every interest rate, the rates being compressed into a composite, interest-rate variable, thereby establishing a role for interest rates previously thought lacking in use and meaning. The relationship between this composite interest rate and capital value does not exhibit reswitching. The notion of a composite interest rate has implications for economics beyond reswitching.