On periodic solutions of Goodwin's business cycle model with only floor in induced investment

We present here an analytical solution of Goodwin's business cycle model in the form of delay differential equation with fixed delay θ and piecewise linear accelerator with only the floor (or the ceiling). We conclude that in this model the time behavior of the solution similar to Goodwin's limit cycle is not possible. These solution looks similar to the oscillation with a period θ, the amplitude of the oscillation growing exponentially to infinity as t →∞. The conditions for existence of the periodic solution in Goodwin's model with fixed delay for the nonlinear accelerator are also discussed.