Abstract:
This talk gives a brief introduction to macroeconomic theory with a focus on how a balanced-budget restriction on government policy may affect the macroeconomy. Standard macro models have the property of a unique equilibrium converging to a steady state (saddle path). However, under a balanced-budget rule it is possible for the steady state to be locally indeterminate (sink) implying muliple equilibria. I find that there are two bifurcation points in the model. The one with the higher tax rate is a fold bifurcation, the lower tax rate is a flip bifurcation implying the existence of two cycles. Furthermore, I show analytically using local bifurcation techniques that this flip bifurcation is supercritical so the two cycles are stable. In addition, global analysis reveals Euler equations "branching" allowing for regime switching equilibria with cycles and complex behavior