A generalized business cycle model with delays in gross product and capital stock

In this work, we propose a delayed business cycle model with general investment function. The time delays are introduced into gross product and capital stock, respectively. We first prove that the model is mathematically and economically well posed. In addition, the stability of the economic equilibrium and the existence of Hopf bifurcation are investigated. Our main results show that both time delays can cause the macro-economic system to fluctuate and the economic equilibrium to lose or gain its stability. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the normal form method and center manifold theory. Furthermore, the models and results presented in many previous studies are improved and generalized.