Keynesian systems with rigidity and flexibility of prices and inflation–deflation expectations

• We present generalized nonlinear disequilibrium Keynesian systems for rigid-price and flexible-price situations.
• The existence of a limit cycle and the global asymptotic stability of the unique equilibrium is rigorously examined.
• The strength of the effect of income on income adjustment affects the dynamic properties of the rigid-price system.
• The stability of the equilibrium is more easily violated in the flexible-price system than in the rigid-price one.
• Expectations on inflation and deflation, as well as flexibility of prices, are destabilizing factors.

In this paper, by utilizing the Poincaré–Bendixson theory and the Hopf bifurcation theory, we analyze both rigid-price and flexible-price nonlinear disequilibrium Keynesian macroeconomic systems, prove the existence of a persistent business cycle and derive the conditions for global asymptotic stability of the equilibrium. Consequently, we find that a Hopf bifurcation occurs for a lower value of the quantity adjustment parameter in the flexible-price system than in the rigid-price one and that inflation expectation effects may easily destabilize the economic system. Furthermore, we reveal that global asymptotic stability of the flexible-price system is unlikely to be achieved.