My Understanding of Marx Part Six–The Mathematics Shows Up — Robert Paul Wolf

In order to reduce the complexity of real economic activity to equations, economists must in effect choose between supposing that there is one dominant technique for the production of each distinct commodity and supposing that there are an infinite number of techniques for the production of each distinct commodity. To put this point as simply and formulaically as I can, they have to decide whether they are going to use linear algebra or calculus. The neoclassical assumption of an infinity of alternative ways of combining inputs to produce an output lends itself to analysis using calculus and the classical assumption of a single dominant technique of production for each commodity finds its most natural expression in systems of linear equations.

Linear algebra makes it possible to handle formally any finite number of commodities, each one represented by a single vector of inputs per unit of output. One can then manipulate what is called the unit input matrix to derive a variety of powerful conclusions. Since I may have lost many of you at this point, let me give a very simple example which will serve quite adequately to illustrate what I want to say. All this is laid out precisely and at length in my book, Understanding Marx....

The Philosopher's Stone
PART SIX THE MATHEMATICS SHOWS UP
Robert Paul Wolff | Professor Emeritus, University of Massachusetts Amherst