Abstract for: A Transformation of the Growth Cycle into the Industrial Cycle in a Four-Dimensional Goodwinian Model with Leontiev Technology
A three-dimensional Goodwinian model L-1, containing the greed feedback loops, reflects destabilizing cooperation and stabilizing competition of investors. The growth rate of output per worker directly depends on growth rate of fixed capital whereas the capital-output ratio is constant. Oscillations imitating growth cycles are endogenous. A 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 one with a period of about 7.5 years reflects business cycle except reduced net output in a recession. 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 status (phase variable) in four-dimensional L-2. L-2 includes new 11 intensive feedback loops. This model implements proportional and derivative control over the capital-output ratio by owners of fixed capital. A pair of supercritical Andronov – Hopf bifurcations cause 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 output in the outright crisis.