Notes on Keynesian models of recession and depression

In this paper we have developed a "minimalist" Keynesian model (simplified version of Tobin's model, 1975) aiming at demonstrating the existence of endogenous cycles. We have shown that the Tobin's interpretation of the forces governing the stability can be misleading, in that 1) the speculative effect on demand is not necessary for instability, 2) this latter depends on the relative strength of the speeds of quantity adjustment and of price expectations to experience, given the "propensity to spend", in contrast with the condition claimed by Tobin, requiring that the "speculative" effects are prevailing on the "price" effects on aggregate demand. Moreover, we have shown that 1) on the one side a stable business cycle can emerge, despite of the almost linear assumptions; 2) on the other side the Tobin's belief that the economy might be stable for small deviations from its equilibrium but unstable for large shocks, has been confirmed in consequence of a local subcritical bifurcation in some parametric cases; 3) both price flexibility and price effects (i.e. Keynes and Pigou effects) does not play any role in restoring full employment equilibrium, in contrast with a common macroeconomic belief; 4) the business cycle not only is endogenous, but, as a matter of fact, it is the result of a traditional Walras-Keynes-Phillips macroeconomic model even with linear behavioural functions.