Introduction

The foundations of the mathematical theory of business cycles were laid down in the 1930s in the same intellectual atmosphere in which Keynes published his General Theory. Indeed, most of the analyses of the cycle developed in those years and subsequently were interpreted as dynamic extensions of the Keynesian static theory of income.

In an attempt to rectify somewhat this bias in the literature on business cycles, we shall present a formal analysis of a competing approach to the problem of the cycle, which we have decided to call “classical,” with many apologies to the historians of economic thought. This use of the term classical may be defended on two grounds. First, the appellative neatly contrasts our model with the demand-oriented models of Keynesian (or Kaleckian) inspiration. Second, the model contains some basic ideas that can be traced back to such classical writers as Adam Smith, Ricardo, and especially Marx (Steindl, 1952, pp. 237 ff.). Whichever terminology is used, the important thing is to clearly specify the concepts which are being employed.

The cornerstones of the classical approach, as we take it here, are the assumptions regarding the behaviour of capitalists and the role of the labor market. As concerns the former, it is assumed that, owing to the economic and social conditions within which they operate, capitalists tend to save and invest as much profit as they can, without regard to the overall effect of accumulation on the rate of profit. This means that a divergence between individual optimization and collective optimization may ensue, and that the outcome of the capitalists' collective behaviour may be quite different from that intended by the individual capitalists.