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

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.