The Cambridge controversies in the theory of capital: Revisiting the reswitching puzzle

By Michael Osborne

PKES Working Paper 1003

March 2010
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When two techniques of production are compared, reswitching is the possibility that one technique can be cheapest at a low interest rate, switch to being more expensive at a higher rate, then reswitch to being cheapest at yet higher rates. Some think 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, including reswitching analysis, it is normal to use only one root. The remaining (n-1) roots are mostly complex or negative and they are usually ignored. The new approach in this paper employs all n possible solutions for the interest rate to produce a new equation for the cost of production in which reswitching does not occur.

Keywords: Capital theory, complex plane, interest rate, reswitching

JEL classification: A30 B10 B20 B50 C02 C60 E10 E20