A Dynamic Model of a Small Open Economy Under Flexible Exchange Rates

In the paper a three dimensional dynamic model of a small open economy, describing the development of net real national income, real physical capital stock and the expected exchange rate of the near future, which was introduced by T. Asada in [1], is analysed under flexible exchange rates. We study the question of the existence of business cycles. Sufficient conditions for the existence of a pair of purely imaginary eigenvalues with the third one negative in the linear approximation matrix of the model are found. For the existence of business cycles and their properties the structure of the bifurcation equation of the model is very important. Formulae for the calculation of the bifurcation coefficients in the bifurcation equation of the model are derived. Theorem on the existence of business cycles in a small neighbourhood of the equilibrium point is presented.