On dynamics in a four-dimensional model of a small open economy

Abstract

In the paper, a four-dimensional nonlinear macroeconomic model of a small open economy describing the development of net real national income, real physical capital stock, nominal interest rate and nominal money stock is analysed. The functions of investment, savings, real income tax, liquidity preference and net exports that are included in the model are set up in accordance with economic theories. Therefore, the dependence of investments on net real national income is captured through an S-shaped curve, and the dependence of investments on nominal interest rate is modelled by an inverse of S-shaped curve. The Hopf bifurcation is applied to determine the bifurcation parameter of the model, to formulate the bifurcation equation, and to make a statement on the existence of business cycles.