TY - JOUR

T1 - Increasing returns and business cycles in a family of Goodwinian models with Leontiev technology

AU - Ryzhenkov, Alexander V.

N1 - Funding Information: This study was funded by Research Project no. 5.6.6.4. (0260-2021-0008) of the IEIE SB RAS. Funding Information: The author is grateful for the reviewers of the submitted manuscript for their critical remarks and appreciates generous efforts of the Journal editors. This cooperative interaction has helped successive vital improvements to the initial manuscript. This study has been carried out with the plan of research work of IEIE SB RAS, base project “Methods and models for substantiating the strategy for the development of the Russian economy in the context of a changing macroeconomic reality”, no. 5.6.6.4. (0260-2021-0008). Publisher Copyright: © 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

KW - Andronov–Hopf bifurcation

KW - Capital accumulation

KW - Feedback sequence

KW - Industrial cycle

KW - Limit cycle

KW - Long-term trend

KW - Monopoly power

KW - Primary income distribution

KW - Surplus value

UR - http://www.scopus.com/inward/record.url?scp=85142451256&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/42a531f5-afc1-386b-ba0b-850cf88c6e9a/

U2 - 10.1186/s40008-022-00280-w

DO - 10.1186/s40008-022-00280-w

M3 - Article

AN - SCOPUS:85142451256

VL - 11

JO - Journal of Economic Structures

JF - Journal of Economic Structures

SN - 2193-2409

IS - 1

M1 - 26

ER -