Limit cycles in a model of supply-side liquidity/profit-rate in the presence of a Phillips curve

In the present paper, we study how the dynamics of Foley's model may be affected by the introduction of a money wage Phillips curve with a perfect spill-over of price inflation on wage inflation. The upshot is a model with endogenous price and wage dynamics with unstable equilibrium, meaning that the integration of the Foley liquidity/profit rate cycle with the Goodwin cycle requires state intervention to stabilize the economy. With this approach, we show that Foley's initial insight is consistent with flexible prices and wages only in the presence of a rule for money supply. The stable equilibrium, in this case, may degenerate into a limit cycle if the growth rate of liquidity increases to a sufficient degree. To illustrate this result, we carry out the analysis both regarding general functions as well as in terms of a particular example.