An endogenous profit rate cycle

Endogenous business cycles can be generated using second-order linear equation systems. A generally accepted criticism of linear models is that only one value of the control parameter produces self-sustaining stable cycles. The problem therefore remains of accounting for the most salient observed features of a market economy, namely the persistence of business cycles and the lack of a stable equilibrium. Models developed by Goodwin and his co-workers established that persistent cycles arise only if there are nonlinear terms in the equations of motion. But in most such models, the rate of profit as a determinant of investment behaviour has been either incidental or absent, and attention is focussed either on the interaction between investment and consumption or output, or on the interaction between employment and wage levels. Neither neoclassical nor Marxist thinkers have constructed formal models in which the rate of profit itself exercises the predominant influence on investment behaviour, notwithstanding the importance of the rate of profit assumes in Marxist and classical theory, nor the significant empirical evidence of profit rate variations during the course of the cycle. I devised this equation system to test whether stable cycles could be generated purely on the basis of changes in the rate of profit. The system therefore abstracts from all variations of investment behaviour which might be influenced or determined by changes in the labour market, the price level or by variations in quantities consumed or produced. For this reason S, the share of the money surplus available either for investment or private capitalist consumption, is held constant and only capital stock and investment may vary; investment itself is affected only by the rate of profit. The model generates stable persistent cycles for all values of the input parameters. Hence, it cannot be assumed without further investigation that either Goodwin models (based on interaction between wage and employment) or multiplier-accelerator models (based on interaction between investment and consumption or output) exhaust the range of possible causal explanations of the business cycle