- Puu, Tönu, 1936-, et al.
A Hicksian Multiplier-Accelerator Model with Floor Determined by Capital Stock and Tongues of Periodicity in a Family of Two-dimensional Discontinuous Maps of Real Möbius Type
Rapport (övrigt vetenskapligt)abstract
- A Hicksian Multiplier-Accelerator ModelThis article reconsiders the Hicksian multiplier-accelerator model with the "floor" related to the depreciation on actual capital stock. Through the introduction of the capital variable a growth trend is created endogenously by the model itself, along with growth rate oscillations around it. The "ceiling" can be dispensed with altogether. As everything is growing in such a model, a variable transformation is introduced to the end of focusing relative dynamics of the income growth rate and the actual capital output ratio.Tongues of Periodicity in a Family of Two-dimensional Discontinuous Maps of Real Möbius TypeIn this paper we consider a two-dimensional piecewise-smooth discontinuous map representing the so-called "relative dynmics" of an Hicksian business cycle model. The main features of the dynamics occur in the parameter region in which no fixed points at finite distance exist, but we may have attracting cycles of any periods. The bifurcations associated with the periodicity tongues of the map are studied making use of the first return map on a suitable segment of the phase plane. The bifurcation curves bounding the periodicity tongues in the parameter plane are related with saddle-node and border-collision bifurcations of the first-return map. Moreover, the particular "sausages structure" of the bifurcation tongues is also explained.