The Cambridge controversies in the theory of capital: contributions from the complex plane

A controversy in capital theory concerns reswitching. When two production techniques are compared, reswitching occurs when one technique is cheapest at low interest rates, switches to being more expensive at higher rates, and then reswitches to being cheapest at yet higher rates. Some believe this inconsistency undermines neoclassical economics. The time-value-of-money (TVM) equation is at the core of the puzzle. The equation is a polynomial having n roots, implying n interest rates. In most analyses, including reswitching, one interest rate is used and the remaining rates are ignored. This analysis demonstrates that every TVM equation has a ‘dual’ form employing all interest rates. The dual of the reswitching equation explains the puzzle.