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Sökning: swepub > Umeå universitet > Puu Tönu 1936 > Tidskriftsartikel

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41.
  • Puu, Tönu, 1936- (författare)
  • Pattern formation in spatial economics
  • 1993
  • Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 3:1, s. 99-129
  • Tidskriftsartikel (refereegranskat)abstract
    • A market economy, extended in continuous two-dimensional space, defined by the differential equations:   is studied, where φ denotes the vector field of traded commodities, λ the scalar field of commodity prices, q the scalar field of excess supply over demand, and k the cost of transportation. The generic theory of differential equations is used to topologically characterize those patterns that are structurally stable, and the transitions among them are then studied by the elliptic and hyperbolic umblic catastrophes.
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42.
  • Puu, Tönu, 1936- (författare)
  • Rational expectations and the Cournot-Theocharis problem
  • 2006
  • Ingår i: Discrete dynamics in nature and society. - 1026-0226 .- 1607-887X. ; :32103, s. 11-
  • Tidskriftsartikel (refereegranskat)abstract
    • In dynamic models in economics, often “rational expectations” are assumed. These are meant to show that the agents can correctly foresee the result of their own and the other agents' actions. In this paper, it is shown that this cannot happen in a simple oligopoly model with a linear demand function and constant marginal costs. “Naive expectations,” that is, where each agent assumes the other agents to retain their previous period action, are shown to result in a 2-period cycle. However, adapting to the observed periodicity always doubles the actual resulting periodicity. In general, it is impossible for the agents to learn any periodicity except the trivial case of a fixed point. This makes the whole idea of “rational expectations” untenable in Cournot oligopoly models.
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43.
  • Puu, Tönu, 1936- (författare)
  • The chaotic duopolists revisited
  • 1998
  • Ingår i: Journal of Economic Behavior and Organization. - 0167-2681 .- 1879-1751. ; 33:3-4, s. 385-394
  • Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
    • The adjustment process of three oligopolists is studied, under Cournot and Stackelberg action. It is demonstrated that with an iso-elastic demand function and constant marginal costs, the system can result in periodic or in chaotic behaviour. In particular, the case with two identical and one different oligopolists is focused, which turns into a virtual duopoly, though displaying a wider set of bifurcations than can occur in genuine duopoly.
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44.
  • Puu, Tönu, 1936- (författare)
  • The chaotic monopolist
  • 1995
  • Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 5:1, s. 35-44
  • Tidskriftsartikel (refereegranskat)abstract
    • The search of a profit maximum by a monopolistic firm is studied, given a demand function with variable elasticity of demand. The system has multiple optimal solutions, so the search algorithm may result in chaotic behaviour.
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45.
  • Puu, Tönu, 1936- (författare)
  • Tord Palander och Uppsalamiljön
  • 1992
  • Ingår i: Ekonomisk Debatt. - Stockholm : Nationalekonomiska Föreningen. - 0345-2646. ; :3, s. 221-228
  • Tidskriftsartikel (populärvet., debatt m.m.)
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46.
  • Puu, Tönu, 1936- (författare)
  • Towards a theory of optimal roads
  • 1978
  • Ingår i: Regional Science and Urban Economics. - : Elsevier BV. - 0166-0462 .- 1879-2308. ; 8:3, s. 225-248
  • Tidskriftsartikel (refereegranskat)abstract
    • The purpose is to find an allocation of a given total amount of road capital in two-dimensional space such that total transportation costs for a region are minimized. A continuous model in analogy to hydrodynamics is used. Transports are supposed to be generated by the gravity hypothesis. It is discussed how transportation paths are optimally adjusted to a given distribution of road capital, and how road capital should be distributed at a given traffic distribution. It is also discussed how the latter problem should be solved when it is taken into account that the distribution of roads affects the choice of paths.
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47.
  • Rosser, J. Barkley, et al. (författare)
  • Discontinuous change in multilevel hierarchical systems
  • 1994
  • Ingår i: Systems Research and Behavioral Science (Systems Research). - : John Wiley & Sons Ltd. - 1092-7026. - 9781840649895 ; 11:3, s. 77-93
  • Tidskriftsartikel (refereegranskat)abstract
    • We examine sources and dynamics of discontinuous changes in discrete multi-level hierarchical ecological-economic systems. We hypothesize the anagenetic moment, the creation of a new level of hierarchy, as arising from variable entrainment at some level. Bottom-up as well as top-down dynamics are studied and competing theories of the sources of such discontinuities are reviewed. Implications for the analysis of complex ecological-economic systems are considered depending on whether they are characterized by single hierarchy, bi-hierarchy, or matrix hierarchy relationships.
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48.
  • Sushko, Iryna, et al. (författare)
  • Regular and chaotic growth in a Hicksian Floor/ceiling model
  • 2010
  • Ingår i: Journal of Economic Behavior and Organization. - : Elsevier. - 0167-2681 .- 1879-1751. ; 75:1, s. 77-94
  • Tidskriftsartikel (refereegranskat)abstract
    • In some previous papers the present authors reassembled the Hicksian trade cycle model in a new way. The floor was tied to depreciation on capital, itself the cumulative sum of past net investments, for which the principle of acceleration provided an explanation. Hence no alien elements were needed to include capital, and so close the system. The resulting model created a growth trend along with growth rate cycles, which could be periodic or quasiperiodic. In the current paper, the ceiling, using capital stock as a capacity limit for production, is added. It then turns out that pure growth no longer exists, and chaos and multistability become possible, which they were not in the previous model. A variety of bifurcation scenarios is explored, and a full understanding of the working of the four-piece, originally three-dimensional, piecewise smooth map, is attained, using a reduction to a one-dimensional return map.
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49.
  • Tramontana, Fabio, et al. (författare)
  • Global bifurcations in a piecewise-smooth Cournot duopoly game
  • 2010
  • Ingår i: Chaos, Solitons & Fractals. - Oxford : Pergamon-Elsevier Science Ltd. - 0960-0779 .- 1873-2887. ; 43:1-2, s. 15-24
  • Tidskriftsartikel (refereegranskat)abstract
    • The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu [2]. The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Sacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist. (C) 2010 Elsevier Ltd. All rights reserved.
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50.
  • Tramontana, Fabio, et al. (författare)
  • Mathematical properties of a discontinuous Cournot-Stackelberg model
  • 2011
  • Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 44:1-3, s. 58-70
  • Tidskriftsartikel (refereegranskat)abstract
    • The object of this work is to perform the global analysis of a recent duopoly model which couples the two points of view of Cournot and Stackelberg [17,18]. The Cournot model is assumed with isoelastic demand function and unit costs. The coupling leads to discontinuous reaction functions, whose bifurcations, mainly border collision bifurcations, are investigated as well as the global structure of the basins of attraction. In particular, new properties are shown, associated with the introduction of horizontal branches, which differ significantly when the constant value is zero or positive and small. The good behavior of the model with positive constant is proved, leading to stable cycles of any period. 
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