| 1. |
- Puu, Tönu, 1936-, et al.
(författare)
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A business cycle model with cubic nonlinearity
- 2004
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 19:3, s. 597-612
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with a simple multiplier-accelerator model of the business cycle, including a cubic nonlinearity. The corresponding two dimensional iterative map is represented in terms of its bifurcation diagram in parameter space. A number of bifurcation sequences for attractors and their basins are studied.
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| 2. |
- Puu, Tönu, 1936-, et al.
(författare)
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A Hicksian multiplier-accelerator model with floor determined by capital stock
- 2005
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Ingår i: Journal of Economic Behavior and Organization. - : Elsevier BV. - 0167-2681 .- 1879-1751. ; 56:3, s. 331-348
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Tidskriftsartikel (refereegranskat)abstract
- This 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 focus relative dynamics of the income growth rate and the actual capital output ratio.
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| 3. |
- Puu, Tönu, 1936-, et al.
(författare)
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Cournot duopoly when the competitors operate under capacity constraints
- 2003
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 18:3, s. 577-592
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Tidskriftsartikel (refereegranskat)abstract
- The paper considers Cournot duopoly where the competitors have capacity constraints. An isoelastic demand function, which always results when consumers maximise utility functions of the Cobb–Douglas type, is used. It has been demonstrated that isoelastic demand, combined with constant marginal costs, results in complex dynamics. The purpose of the present paper is to reconsider the case, using in stead cost functions with capacity limits. This is a point on which Edgeworth insisted as important. Comparisons between cases of few large and many small competitors cannot be made when firms have constant returns and hence are all infinitely large in potential.
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| 4. |
- Puu, Tönu, 1936-
(författare)
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On the Stability of Cournot Equilibrium when the Number of Competitors Increases
- 2008
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Ingår i: Journal of Economic Behavior and Organization. - : Elsevier BV. - 0167-2681 .- 1879-1751. ; 66:3-4, s. 445-456
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Tidskriftsartikel (refereegranskat)abstract
- This article reconsiders whether the Cournot equilibrium really becomes a perfect competition equilibrium when the number of competitors goes to infinity. It has been questioned whether the equilibrium remains stable with an increasing number of firms. Contraindications were given for linear and for isoelastic demand functions. However, marginal costs were then taken as constant, which means adding more potentially infinite-sized firms. As we want to compare cases with few large firms to cases with many small firms, the model is tuned so as to incorporate capacity limits, decreasing with an increasing number of firms. Then destabilization is avoided.
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| 5. |
- Puu, Tönu, 1936-, et al.
(författare)
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The dynamics of a triopoly Cournot game when the competitors operate under capacity constraints
- 2006
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 28:2, s. 403-413
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Tidskriftsartikel (refereegranskat)abstract
- This article considers Cournot oligopoly with three competitors, given an iso-elastic demand function, and cost functions that asymptotically go to infinity when capacity limits are approached. It is shown that for some parameter values (capacity limits) the Cournot equilibrium point loses stability through a Neimark-Sacker bifurcation. In addition global bifurcation scenarios are simulated numerically, and some are illustrated through Arnol'd tongues in the parameter plane.
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| 6. |
- Puu, Tönu, 1936-
(författare)
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The Hicksian Trade Cycle with Floor and Ceiling Dependent on Capital Stock
- 2007
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Ingår i: Journal of Economic Dynamics and Control. - : Elsevier BV. - 0165-1889 .- 1879-1743. ; 31:2, s. 575-592
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Tidskriftsartikel (refereegranskat)abstract
- This article reconsiders the Hicksian multiplier-accelerator model with 'floor' and 'ceiling'. The new thrust is that these constraints are tied to the actual stock of capital, the floor to the depreciation on this stock, the ceiling to capital as a limiting production factor according to the fixed proportions technology that also underlies the principle of acceleration. For capital formation just the Hicksian investment theory is used. The result is one unified model creating economic growth and growth rate cycles.
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| 7. |
- Sushko, Irina, et al.
(författare)
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Tongues of periodicity in a family of two-dimensional discontinuous maps of real Mobius type
- 2004
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 21:2, s. 403-412
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider a two-dimensional piecewise-smooth discontinuous map representing the so-called "relative dynamics" 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.
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| 8. |
- Tramontana, Fabio, et al.
(författare)
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Cournot duopoly when the competitors operate multiple production plants
- 2009
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Ingår i: Journal of Economic Dynamics and Control. - : Elsevier BV. - 0165-1889 .- 1879-1743. ; 33:1, s. 250-265
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Tidskriftsartikel (refereegranskat)abstract
- This article considers a Cournot duopoly under an isoelastic demand function and cost functions with built-in capacity limits. The special feature is that each firm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so each has three cost options, the third being to run both plants, dividing the load according to the principle of equal marginal costs. As a consequence, the marginal cost functions come in three disjoint pieces, so the reaction functions, derived on basis of global profit maximization, may also consist of disjoint pieces. This is reflected in a particular bifurcation structure, due to border-collision bifurcations and to particular basin boundaries, related to the discontinuities. It is shown that stable cycles may coexist, and the non-existence of unstable cycles constitutes a new property. We also compare the coexistent short periodic solutions in terms of the resulting real profits.
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| 9. |
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| 10. |
- Agliari, Anna, et al.
(författare)
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Global bifurcations of basins in a triopoly game
- 2002
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 12:10, s. 2175-2207
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Tidskriftsartikel (refereegranskat)abstract
- A Cournot model based on bounded inverse demand function and constant marginal production costs is studied. The case of three producers is considered and the adjustment process reduces to a three-dimensional noninvertible map in the output of competitors. The analysis of the dynamical behavior of the map is performed by the "critical curve method", extended to the critical surfaces in 3D. By this method, we explain the different bifurcations in the basins of attraction and in the attracting sets. In particular, given the economic application, feasible trajectories are focused, starting from the simple situation of two identical producers and extending the results to the generic case.
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