Rudolf Zimka

The Stability of Normal Equilibrium Point and the Existence of Limit Cycles in a Simple Keynesian Macrodynamic Model of Monetary Policy

In this chapter, a simple Keynesian macroeconomic model of monetary policy describing the development of nominal rate of interest, expected rate of inflation, and nominal money supply in the period of deflationary depression, which was introduced by Asada (2011) is investigated rigorously. The normal equilibrium point of the model is derived and its dynamic stability is investigated. Questions concerning the existence of limit cycles are studied analytically. The bifurcation equation is found. The formulae for the calculation of its coefficients are gained. A numerical example is presented by means of numerical simulations.

On stability in generalized Schinasi’s macroeconomic model under fixed exchange rates

Abstract A nonlinear dynamic macroeconomic model of a small open economy is constructed. The model is based on the IS-LM structure and generalizes the Schinasi’s model of a closed economy. Sufficient conditions for the existence of the equilibrium of the model are found and the question of its stability is analyzed.

On dynamics in a Keynesian model of monetary and fiscal stabilization policy mix with twin debt accumulation

In this paper, a six‐dimensional model of flexible prices with the monetary and fiscal policy mix, describing the development of the firms’ private debt, the output, the expected rate of inflation, the rate of interest, government expenditure, and government bonds are analyzed. The stress put on the “twin debt accumulation” means that in our model both private debt accumulation and the public debt (government bond) accumulation are explicitly introduced. Questions concerning the existence of limit cycles around its normal equilibrium point are investigated. The bifurcation equation is found. The formulae for the calculation of its coefficients are gained. Numerical example illustrating the results attained is presented by means of numerical simulations.

On Liu´s Criterion in Asada´s Model of Monetary and Fiscal Policy

It is known that a simple Hopf bifurcation in a dynamic model can arise if the Jacobian matrix of the model has a pair of purely imaginary eigenvalues and others have negative real parts. Liu ́s criterion gives conditions under which the eigenvalues have required properties. In this paper, a six-dimensional dynamic model of Asada (2014), describing the development of the firms ́ private debt, the output, the expected rate of inflation, the rate of interest, the government expenditures, and the government bond is introduced. There are found conditions on the parameters of the model under which Liu ́s criterion is satisfied. A numerical example illustrates the reached result.

On the bifurcation of a torus in a small open economy model

Abstract A four-dimensional macroeconomic model of a small open economy under fixed exchange rates is investigated. The model describes the development of national income, capital stock, interest rate and money stock. Sufficient conditions for the existence of an invariant torus are given. A numerical example illustrating the gained results is presented.

Can business cycles arise in a two-regional model with fixed exchange rates?

Abstract The two-regional five dimensional model describing the development of income, capital stock and money stock, which was introduced by T. Asada in [A Two-regional Model of Business Cycles with Fixed ExchangeRates: A Kaldorian Approach, Discuss. Paper Ser., No. 44, Chuo University, Tokyo, Japan, 2003] is analysed. Sufficient conditions for the existence of one pair of purely imaginary eigenvalues and three eigenvalues with negative real parts in the linear approximation matrix of the model are found. Theorem on the existence of business cycles is presented.