Stability and bifurcations in IS-LM economic models

In this note, we analyze the local dynamics of a general non-linear fixed-price disequilibrium IS-LM model. We assume investment behavior as a general non-linear function avoiding any Kaldor type assumptions. By proving the existence of a family of periodic solutions bifurcating from a steady state, we confirm and extend some results in the literature for IS-LM models reducible to Leinard’s equation. We use bifurcation theory and study the effect of a change of the adjustment parameter in the money market upon the solutions of the model as the steady state loses stability. We establish analytically that the values of the adjustment parameter in the money market may affect the equilibrium relative to the product market and the government budget constraint