The Cambridge controversies in the theory of capital: a solution to the reswitching puzzle

When two production techniques are compared, reswitching occurs when a technique begins by being cheapest at a low interest rate, switches to being more expensive at a higher rate, and then reswitches to being cheapest at yet higher rates. Some believe the inconsistency undermines the foundations of neoclassical economics. The time-value-of-money (TVM) equation is at the core of the puzzle. The equation is an nth order polynomial having n roots (interest rates). In most economic analyses only one root is used. The remaining (n-1) roots, mostly complex or negative, are usually ignored. In this article, all roots are employed in an expression relating differences in the dependent variable to differences in interest rates. When multiple-interest-rate analysis is applied to the Sraffa-Pasinetti example of reswitching, the phenomenon disappears. The solution has contemporary significance because reswitching is one problem in a class of similar problems having the TVM equation at their core.