| Popis: |
In this paper, we propose and analyze an IS-LM macroeconomic model with delay-dependent coefficients. The model assumes that the tax revenues have two complementary components, one based on the current income and the other on a past income where the fixed discrete time delay arises. Moreover, we assume that the tax share on each component depends on the time delay, and thus the resulting model is a system of delay differential equations with delay-dependent coefficients. Previously, De Cesare and Sportelli (2005) studied a similar model but the tax shares that they used were fixed constants. They showed that the equilibrium point may undergo a sequence of alternated stability switches. This can be observed for example in the case with low tax rate and low share of delayed tax revenue where loci of Hopf bifurcation points form closed curves with some of these curves overlap, and the equilibrium is unstable inside these loci. Our proposed model introduces a new parameter μ in the tax share terms, and the case where μ = 0 captures the previously studied model with constant tax shares. We showed that increasing this new parameter results to decoupling and shrinking of the ‘islands of instability’, and eventually results to the absolute stability of the equilibrium. |
