### Working Paper PKWP1003

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

March 2010

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: Collective Works: General B10: History of Economic Thought through 1925: General B20: History of Economic Thought since 1925: General B50: Current Heterodox Approaches: General C02: Mathematical Methods C60: Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: General E10: General Aggregative Models: General E20: Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy: General (includes Measurement and Data)

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