On the significance of Sraffa's reswitching: some long-standing financial puzzles and their joint resolution

A solution is proposed to the reswitching puzzle. When two techniques of production are compared reswitching can occur. Reswitching is 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 reswitching puzzle. The equation takes the form of an nth order polynomial having n roots (interest rates). In most economic and financial analyses only one root is used. The remaining (n-1) roots, mostly complex or negative, are usually ignored. The approach in this article employs all n solutions for the interest rate in an expression relating differences in the dependent variable to differences in interest rates. The resulting analysis is applied to the Sraffa-Pasinetti example of reswitching. The expression provides a fresh perspective on the TVM equation. From this perspective, reswitching does not occur. The 'multiple-interest-rate' approach provides insights into issues other than reswitching. The issues include the NPV versus IRR debate in capital budgeting, and the quest for an accurate equation for duration in bond mathematics. Reswitching is only one example of a problem in a class of similar problems having the TVM equation at its core.