Increasing returns and business cycles in a family of Goodwinian models with Leontiev technology

The main purpose of this paper is to build a family of tutorial Goodwinian (essentially Marxist) models of capital accumulation through industrial cycles that are less complicated than the author's models of the extended capitalist reproduction in the USA already published. The subordinate purpose is to advance refinement of these models from the standard "neoclassical" assumptions that distort the generic structures determining perpetual disequilibrium in the reproduction of the aggregate social capital. The ascending from abstract to concrete applies the notion of twofold nature of capitalist production as creation of use value and labour value (prioritizing surplus value). This approach reveals substantial facets of endogenous increasing returns and technological progress induced by capitalist production relations. A three-dimensional Goodwinian model L-1, containing the greed feedback loops, reflects destabilizing cooperation and stabilizing competition of investors. Monopoly capital implements proportional and derivative control over the capital accumulation rate. The growth rate of output per worker directly depends on the growth rates of capital intensity and employment ratio in a technical progress function, whereas the capital-output ratio is constant. Oscillations imitating growth cycles are endogenous. A recession (mild crisis) is a manifestation of relative and absolute over-accumulation of capital. A knife-edge limit cycle maintains a growth cycle with the Kondratiev duration; a more solid limit cycle with a period of about 7.5 years upholds a business cycle with a recession without reduced net output. These limit cycles result from the subsequent supercritical Andronov-Hopf bifurcations. The transformation of the growth cycle into industrial cycle gives credit to raising status of capital-output ratio from auxiliary in L-1 to the level (phase) variable in four-dimensional L-2. A mechanization (automation) function mirrors induced technical progress. L-2 embraces new 11 intensive feedback loops involving capital-output ratio. Proportional and derivative control over this ratio by monopoly capital is taken into account. Pair of supercritical Andronov-Hopf bifurcations gives birth to two limit cycles. The second is a remote analogue for Kuznets cycle with the period of about 18 years; the first upholds the industrial cycle with period of about 7 years and declining net output in the outright crisis. Besides relative and absolute over-accumulation of capital, the specific positive and negative feedback loops containing capital-output ratio are required for crises in industrial cycles. Long-term enhancement of monopoly profit through lowering a targeted domestic capital accumulation rate and diminishing a targeted output-capital ratio is substantiated analytically and validated by computer simulations. The gained insights highlight caveats for hastily policy recommendations.