umu.sePublikationer
Ändra sökning
Avgränsa sökresultatet
123 1 - 50 av 107
RefereraExporteraLänk till träfflistan
Permanent länk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Träffar per sida
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sortering
  • Standard (Relevans)
  • Författare A-Ö
  • Författare Ö-A
  • Titel A-Ö
  • Titel Ö-A
  • Publikationstyp A-Ö
  • Publikationstyp Ö-A
  • Äldst först
  • Nyast först
  • Skapad (Äldst först)
  • Skapad (Nyast först)
  • Senast uppdaterad (Äldst först)
  • Senast uppdaterad (Nyast först)
  • Disputationsdatum (tidigaste först)
  • Disputationsdatum (senaste först)
  • Standard (Relevans)
  • Författare A-Ö
  • Författare Ö-A
  • Titel A-Ö
  • Titel Ö-A
  • Publikationstyp A-Ö
  • Publikationstyp Ö-A
  • Äldst först
  • Nyast först
  • Skapad (Äldst först)
  • Skapad (Nyast först)
  • Senast uppdaterad (Äldst först)
  • Senast uppdaterad (Nyast först)
  • Disputationsdatum (tidigaste först)
  • Disputationsdatum (senaste först)
Markera
Maxantalet träffar du kan exportera från sökgränssnittet är 250. Vid större uttag använd dig av utsökningar.
  • 1.
    Agliari, Anna
    et al.
    Catholic University of Milano, Italy.
    Gardini, Laura
    University of Urbino, Italy.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Global Bifurcations in Duopoly when the Cournot Point is Destabilized through a Subcritical Neimark Bifurcation2003Rapport (Övrigt vetenskapligt)
    Abstract [en]

    An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive Cournot fixed point.

  • 2.
    Agliari, Anna
    et al.
    Dip. Scienze Economiche e Sociali, Catholic University.
    Gardini, Laura
    Dip. Scienze Economiche, University of Urbino .
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi. Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Global bifurcations in duopoly when the Cournot Point is destabilized through a subcritical Neimark bifurcation2006Ingår i: International Game Theory Review, ISSN 0219-1989, Vol. 8, nr 1, s. 1-20Artikel i tidskrift (Refereegranskat)
  • 3.
    Agliari, Anna
    et al.
    Univ Cattolica Sacro Cuore, Ist Econometria & Matematica, Italy.
    Gardini, Laura
    University of Urbino, Dept of Economics, Italy.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM). Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Global bifurcations of basins in a triopoly game2002Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 12, nr 10, s. 2175-2207Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 4.
    Agliari, Anna
    et al.
    Dipartimento di Scienze Economiche e Sociali, Catholic University.
    Gardini, Laura
    Dept. Scienze Economiche, University of Urbino.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi. Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Some global bifurcations related to the apperance of closed invariant curves2005Ingår i: Mathematics and Computers in Simulations, ISSN 0378-4754, Vol. 68, nr 3, s. 201-219Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we consider a two-dimensional map (a duopoly game) in which the fixed point is destabilized via a subcritical Neimark–Hopf (N–H) bifurcation. Our aim is to investigate, via numerical examples, some global bifurcations associated with the appearance of repelling closed invariant curves involved in the Neimark–Hopf bifurcations. We shall see that the mechanism is not unique, and that it may be related to homoclinic connections of a saddle cycle, that is to a closed invariant curve formed by the merging of a branch of the stable set of the saddle with a branch of the unstable set of the same saddle. This will be shown by analyzing the bifurcations arising inside a periodicity tongue, i.e., a region of the parameter space in which an attracting cycle exists.

  • 5.
    Agliari, Anna
    et al.
    Catholic University in Milan, Italy/University of Parma, Italy.
    Gardini, Laura
    University of Parma, Italy/Istituto di Scienze Economiche, University of Urbino, Italy.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    The dynamics of a triopoly Cournot game2000Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 11, nr 15, s. 2531-2560Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper reconsiders the Cournot oligopoly (noncooperative) game with iso-elastic demand and constant marginal costs, one of the rare cases where the reaction functions can be derived in closed form. It focuses the case of three competitors, and so also extends the critical line method for non-invertible maps to the study of critical surfaces in 3D. By this method the various bifurcations of the attractors and their basins are studied. As a special case the restriction of the map to an invariant plane when two of the three firms are identical is focused.

  • 6.
    Agliari, Anna
    et al.
    Catholic University, Faculty of Economics, Milan, Italy.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    A Cournot duopoly model with bounded demand2002Bok (Övrigt vetenskapligt)
  • 7.
    Agliari, Anna
    et al.
    Univ Sacred Heart, Ist Econometria & Matemat, Milan.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    A Cournot duopoly with bounded inverse demand function2002Ingår i: OLIGOPOLY DYNAMICS: MODELS AND TOOLS, BERLIN: SPRINGER-VERLAG BERLIN , 2002, s. 171-194Konferensbidrag (Övrigt vetenskapligt)
  • 8.
    Ahmed, E
    et al.
    Department of Mathematics, Faculty of Science, Mansoura University, Egypt.
    Elsadany, AA
    Department of Basic Science, Faculty of Computers and Informatics, Ismailia, Suez Canal University, Egypt; Department of Mathematics, Shanghai University, Shanghai 200444, China.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    On Bertrand duopoly game with differentiated goods2015Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 251, s. 169-179Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The paper investigates a dynamic Bertrand duopoly with differentiated goods in which boundedly rational firms apply a gradient adjustment mechanism to update their price in each period. The demand functions are derived from an underlying CES utility function. We investigate numerically the dynamical properties of the model. We consider two specific parameterizations for the CES function and study the Nash equilibrium and its local stability in the models. The general finding is that the Nash equilibrium becomes unstable as the speed of adjustment increases. The Nash equilibrium loses stability through a period-doubling bifurcation and the system eventually becomes chaotic either through a series of period-doubling bifurcations or after a Neimark–Sacker bifurcation.

  • 9. Canovas, Jose S.
    et al.
    Panchuk, Anastasiia
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Asymptotic dynamics of a piecewise smooth map modelling a competitive market2015Ingår i: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 117, s. 20-38Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the present work we study asymptotic dynamics of a multi-dimensional piecewise smooth map which models an oligopoly market where competitors use adaptive scheme for reaction choice. Each competitor also defines the moment for renewing the capital equipment depending on how intensively the latter is used. Namely, the larger output is produced, the quicker the capital exhausts. It is shown then that the asymptotic dynamics of the map allows coexistence of different metric attractors in which case it is sensitive to initial conditions. We also investigate stability of trajectories representing Cournot equilibria which are here not fixed but periodic points. In particular, it is shown that several such Cournot equilibria, belonging to different invariant manifolds, may coexist some of them being locally asymptotically stable and some being unstable. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS).

  • 10.
    Canovas, Jose S
    et al.
    Univ Politecn Cartagena, Dpto Matemat Aplicada Estadist, Spain.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Marin, Manuel Ruiz
    Univ Politecn Cartagena, Dpto Metodos Cuantitat Informat, Spain.
    Detecting Chaos in a Duopoly Model via Symbolic Dynamics2010Ingår i: Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, E-ISSN 1553-524X, Vol. 13, nr 2, s. 269-278Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper considers a Cournot duopoly model assuming isoelastic demand and smooth cost functions with built-in capacity limits. When the firms cannot obtain positive profits they are assumed to choose small "stand-by" outputs rather than closing down, in order to avoid substantial fitting up costs when market conditions turnout more favorable. It is shown that the model provides chaotic behavior. In particular, the system has positive topological entropy and hence the map is chaotic in the Li-Yorke sense. Moreover, chaos is not only topological but also physically observable.

  • 11.
    Cánovas, José S
    et al.
    Dpto. Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Ruiz Marín, Manuel
    Dpto. Métodos Cuantitativos e Informáticos, Universidad Politécnica de Cartagena.
    A Method for Studying Non-Autonomous Affine Maps: An Application to a Two-Region Business Cycle Model2007Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, Vol. 34, nr 4, s. 1285-1298Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper is devoted to the study of the dynamics of a non-autonomous affine system. We apply the results to a two-region business cycle model of the Samuelson [Interactions between the multiplier analysis and the principle of acceleration. Rev Econ Statist 1939;21:75-8] multiplier-accelerator type.

  • 12.
    Cánovas, José S
    et al.
    Departamento Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM). Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Ruíz, Manuel
    Departamento Métodos Cuantitativos e Informáticos, Universidad Politécnica de Cartagena.
    The Cournot-Theocharis Problem Reconsidered2008Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, Vol. 37, nr 4, s. 1025-1039Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In 1959 Theocharis [Theocharis RD. On the stability of the Cournot solution on the oligopoly problem. Review of economic Studies 1959;27:133–4] showed that with linear demand and constant marginal costs Cournot equilibrium is destabilized when the competitors become more than three. With three competitors the Cournot equilibrium point becomes neutrally stable, so, even then, any perturbation throws the system into an endless oscillation. Theocharis’s argument was in fact proposed already in 1939 by Palander [Palander T. Konkurrens och marknadsjämvikt vid duopol och oligopol. Ekonomisk Tidskrift 1939;41:124–45, 222–50]. None of these authors considered the global dynamics of the system, which necessarily becomes nonlinear when consideration is taken of the facts that prices, supply quantities, and profits of active firms cannot be negative. In the present paper, we address the global dynamics.

  • 13.
    Gallegati, Mauro
    et al.
    Department of Economics, Universita Politecnica delle Marche, Italy.
    Gardini, Laura
    Department of Economics, University of Urbino, Italy.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Sushko, Irina
    Institute of Mathematics, National Academy of Sciences of Ukraine, Ukraine.
    Hicks’ trade cycle revisited: cycles and bifurcations2003Ingår i: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 63, nr 6, s. 505-527Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a piecewise-linear model. This paper shows the need for a reinterpretation of Hicks’ contribution in the light of a more careful mathematical investigation. In particular, it will be shown that only one bound is needed to have non explosive outcome if the equilibrium point is an unstable focus. It will also be shown that when the fixed point is unstable the attracting set has a particular structure: It is a one-dimensional closed invariant curve, made up of a finite number of linear pieces, on which the dynamics are either periodic or quasi-periodic. The conditions under which the model produces periodic or quasi-periodic trajectories and the related bifurcations as a function of the main economic parameters are determined.

  • 14. Gardini, Laura
    et al.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Sushko, Irina
    A Goodwin-Type Model with Piecewise Linear Investment Function2006Ingår i: Business Cycle Dynamics: Models and Tools, Springer-Verlag , 2006Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 15. Gardini, Laura
    et al.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Sushko, Irina
    The Hicksian Model with Investment Floor and Income Ceiling2006Ingår i: Business Cycle Dynamics: Models and Tools, Springer-Verlag , 2006Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 16. Panchuk, A.
    et al.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Dynamics of a durable commodity market involving trade at disequilibrium2018Ingår i: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 58, s. 2-14Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The present work considers a simple model of a durable commodity market involving two agents who trade stocks of two different types. Stock commodities, in contrast to flow commodities, remain on the market from period to period and, consequently, there is neither unique demand function nor unique supply function exists. We also set up exact conditions for trade at disequilibrium, the issue being usually neglected, though a fact of reality. The induced iterative system has infinite number of fixed points and path dependent dynamics. We show that a typical orbit is either attracted to one of the fixed points or eventually sticks at a no-trade point. For the latter the stock distribution always remains the same while the price displays periodic or chaotic oscillations. (C) 2017 Elsevier B.V. All rights reserved.

  • 17. Panchuk, A.
    et al.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Oligopoly model with recurrent renewal of capital revisited2015Ingår i: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 108, s. 119-128Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of the present paper is to investigate an oligopoly market, modelled by using CES production function in combination with the isoelastic demand function. It is supposed that the competitors act not under constant, but eventually decaying returns, and thus, from time to time they need to renew their capital equipment, choosing its optimal amount according to the current market situation. It is shown that the asymptotic trajectories depend essentially on the value of the global capital durability, and are also sensitive to the initial choice of individual inactivity times. In particular, the firms may merge into different groups renewing their capitals simultaneously, which lead to distinct dynamical patterns. It is also studied how the capital wearing out rate influences the system behaviour.

  • 18. Panchuk, Anastasiia
    et al.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Cournot equilibrium stability in a non-autonomous system modeling the oligopoly market2009Ingår i: Iteration Theory (ECIT 08): proceedings of the European Conference on Iteration Theory, Yalta, Crimea, Ukraine, September 7 - 13, 2008 / [ed] Alexandr Sharkovsky, Irina Sushko, Graz: Karl-Franzens-Universität Graz , 2009, in printKapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 19.
    Panchuk, Anastasiia
    et al.
    Institute of Mathematics, National Academy of Sciences, Ukraine.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Stability in a non-autonomous iterative system: an application to oligopoly2009Ingår i: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 58, nr 10, s. 2022-2034Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper reconsiders the relation between oligopoly and perfect competition, more specifically the problem of emergent instability when the number of competitors increases, as pointed out by several authors. A process of mixed short and long run dynamics is set up. In the short run the competitors are subject to capacity limits due to fixed capital stocks, in the long run they may renew these stocks and so in the moments of reinvestment have access to a constant returns technology. The evolution of the system depends on the number of competitors, the interval between their entry on the market, and the durability of capital. The main result is a theorem showing that if capital has a durability of more periods than the spacing of reinvestment times among the firms, multiplied with their total number, then the system always contracts to the Cournot equilibrium state.

  • 20.
    Puu, Tonu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Good Old Economic Geography2016Ingår i: COMPLEX NETWORKS AND DYNAMICS: SOCIAL AND ECONOMIC INTERACTIONS / [ed] Commendatore, P.; MatillaGarcia, M.; Varela, L.M.; Canovas, J.S., Springer, 2016, s. 329-359Konferensbidrag (Refereegranskat)
    Abstract [en]

    This chapter discusses classical economic modelling in continuous two-dimensional geographical space, focusing some ingenious models due to Harold Hotelling and Martin Beckmann concerning population growth and migration, and spatial market equilibrium, respectively. It also adds some modelling of business cycles, and discusses the issue the shape of market areas. Focus is on transversality and stability of structure.

  • 21.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    A century of oligopoly theory 1838-19412002Ingår i: OLIGOPOLY DYNAMICS: MODELS AND TOOLS, BERLIN: SPRINGER-VERLAG BERLIN , 2002, s. 1-14Konferensbidrag (Övrigt vetenskapligt)
  • 22.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    A CHAOTIC PROCESS WITH SLOW FEED BACK - THE CASE OF BUSINESS CYCLES1992Ingår i: ECONOMIC EVOLUTION AND DEMOGRAPHIC CHANGE: FORMAL MODELS IN SOCIAL SCIENCES, BERLIN: SPRINGER-VERLAG BERLIN , 1992, s. 3-34Konferensbidrag (Övrigt vetenskapligt)
  • 23.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    A chaotic process with slow feedback: the case of business cycles1992Ingår i: Lecture notes in economics and mathematical systems, ISSN 0075-8442, E-ISSN 2196-9957, Vol. 395, s. 3-34Artikel i tidskrift (Refereegranskat)
  • 24.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    A mathematics refresher for students of economics2004Bok (Övrigt vetenskapligt)
  • 25.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    A New Approach to Modeling Bertrand Duopoly2017Ingår i: Review of Behavioral Economics, ISSN 2326-6198, E-ISSN 2326-6201, Vol. 4, nr 1, s. 51-67Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Bertrand oligopoly needs global demand functions which apply to close substitutes. This is a problem, because economic theory never supplied anything but local definitions for substitutes. Lancaster's "new theory of demand" is therefore invoked to supply one. In its format one can also quantify closeness of substitutes and incorporate optimisation of design. The present study focuses the pure price dynamics for Bertrand oligopoly when the design of the competing products is given, though quantified through Lancaster's approach. Resulting is some complex dynamics, including high periodicity and chaos.

  • 26.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    A simplified model of spatiotemporal population dynamics.1985Ingår i: Environment and planning A, ISSN 0308-518X, E-ISSN 1472-3409, Vol. 17, nr 9, s. 263-269Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper is an extension of the model of population growth and migration originally developed by H. Hotelling in 1921. This model consists of two ingredients, a logistic growth function and a linear spatial diffusion term. The author notes that the saturation population can be affected by the development of new technology and that improvements in transportation have increased the possibilities for migration. "Basic nonlinearities are introduced by use of a production technology with increasing-decreasing returns to scale. It is demonstrated how industrial takeoffs, population transitions, and agglomerative spatial patterns can emerge by changing the model parameters.

  • 27.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Arts, Sciences, and Economics: A Historical Safari2006Bok (Övrigt vetenskapligt)
    Abstract [en]

    This book deals with the economic aspects of changing attitudes in arts and sciences. The effects of the public good character of culture, along with the very long production period and lifetime for its products, are emphasized, since both contribute to the failure of normal market solutions. Embodiment of ideas, and the consequences of modern reproduction technology for protection of property rights are closely examined. The evolution within arts and sciences, which often seems to return to previously scrapped ideals, is illustrated by detailed case studies, in which the importance of changing tastes, rather than progress proper, is emphasized. The author attempts an understanding for this using Darwinian evolution in combination with modern mathematical complexity theory, expressed in terms accessible to the general reader.

  • 28.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Attractors, Bifurcations, & Chaos: Nonlinear Phenomena in Economics2003 (uppl. 2)Bok (Övrigt vetenskapligt)
  • 29.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Bertrand oligopoly revisited2001Ingår i: Discrete dynamics in nature and society, ISSN 1026-0226, E-ISSN 1607-887X, ISSN 1026-0226, Vol. 6, nr 1, s. 1-10Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper reconsiders Bertrand duopoly and oligopoly in the spatial formulation due to Hotelling, 1929. The equilibrium configurations of price and location structure are considered, given elastic demand, and a full dynamics is formulated in order to check for stability of equilibrium and the possibilities of complex dynamics, such as occurs easily with Cournot oligopoly. The main discussion concerns Hotelling's original case of two sellers on a given interval, though results for different cases, such as three firms on a circle, and lattices in 2D are indicated.

  • 30.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Capacity Limits2011Ingår i: Oligopol: Old Ends - New Mean / [ed] Tönu Puu, Berlin: Springer Berlin/Heidelberg, 2011, s. 101-125Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    In Chap. 2 the Cournot–Theocharis stability issue, which will be called so, though it was raised 20 years earlier by Palander, was discussed. The problem was that in certain model families increasing competition through adding new competitors destabilised Cournot equilibrium. Accordingly, the idea of a straight path leading from monopoly, over oligopoly, to perfect competition, where profits were eliminated and marginal cost pricing was used, became subject to doubt. What interest do the properties of an equilibrium have, after all, if it becomes unstable?

  • 31.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Catastrophe theory applied to the refraction of traffic1988Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 22, nr 2-3, s. 315-318Artikel i tidskrift (Refereegranskat)
  • 32.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM). Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Catastrophic structural change in a continuous regional model2004Ingår i: Complexity in Economics, Edward Elgar Publishing , 2004Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 33.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Chaos in business cycles1991Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 1, nr 5, s. 457-473Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The business cycle is studied in terms of the mapping

    Zt = λZt−1 − (λ+1)Z3t−1 − σYt−1

    Yt = Zt−1 + Y−1

    where the variables Y, Z denote income and rate of income change respectively, and λ, σ are two structural parameters. The model produces chaotic or periodic output for income differences. For small σ income acts as a slow feed back causing bifurcations between periodic and chaotic behaviour over the cycle. Typically, transitions between prosperity and depression set in with chaos after which there follows a period halving route to order.

  • 34.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM). Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Chaos in duopoly pricing2004Ingår i: Complexity in Economics, Edward Elgar Publishing , 2004Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 35.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Chaos in duopoly pricing1991Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 1, nr 6, s. 573-581Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The dynamics of two competing firms in a market is studied in terms of Cournot's duopoly theory. Assuming iso-elastic demand and constant unit production costs the iterative mapping

    for the outputs of the two firms ensues. The two constants are the unit production costs. The fixed point, the Cournot equilibrium, has earlier been assumed to be the only interesting feature of this model. It is, however, shown that the model can produce persistent motion, periodic or chaotic. 

  • 36.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Complex dynamics in economic and social systems: Introduction1996Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 7, nr 12, s. R7-R7Artikel i tidskrift (Övrigt vetenskapligt)
  • 37.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Complex dynamics with three oligopolists1996Ingår i: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 7, nr 12, s. 2075-2081Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The adjustment process by three Cournot oligopolists is studied. An iso-elastic demand function and constant marginal costs are assumed. The system can easily result in chaotic behaviour, and a much richer variety of bifurcations will occur than in the case of duopoly with two agents, discussed before under the same assumptions.

  • 38.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM). Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Complex oligopoly dynamics2005Ingår i: Nonlinear Dynamical Systems in Economics, Springer , 2005Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 39.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Continuous economic space modelling: Draft of a survey2009Ingår i: The annals of regional science, ISSN 0570-1864, E-ISSN 1432-0592, Vol. 43, nr 1, s. 5-25Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper attempts a survey of continuous modelling in spatial economics. The classics of spatial economics, from von Thünen on, like geographers always did, considered phenomena in the two dimensional plane, though later development was in favour of modelling discrete location point sets connected by communication arcs. The models discussed here are strongly focused around Beckmann’s continuous space market model from the early 1950s.

  • 40.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Cournot Oligopoly2011Ingår i: Oligopoly: Old Ends - New Means / [ed] Tönu Puu, Berlin: Springer Berlin/Heidelberg, 2011, s. 17-41Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    As mentioned in Chap. 1, Cournot’s oligopoly model was one of the first mathematical models proposed in the field of economics. It addresses the functioning of a market with numerous atomistic demanders versus few relatively large suppliers. This implies that all the suppliers influence market price appreciably, and hence, like monopolists, take account of the demand function of the consumers on the market in order to calculate their best moves. As a rule, demand is a decreasing function of price. In equilibrium demand equals supply, and one can also speak of the inverse demand function which states how market price depends on supply.

  • 41.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Disequilibrium trade and the dynamics of stock markets2014Ingår i: Complexity in economics: cutting edge research / [ed] Marisa Faggini, Anna Parziale, Springer-Verlag New York, 2014, s. 225-245Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The present work considers pricing and trade dynamics for stock commodity markets, which, unlike flow commodity markets have been little studied, if at all. Concepts and tools in economics are shaped to deal with flow markets, where commodities disappear in each period and then reemerge. This allows one to define unique demand and supply functions and their equilibria. A durable commodity, a stock, in contrast, remains on the market to the next period and may just change owner through exchange. This, however, changes demand and supply functions, and hence the equilibrium state to which a dynamic process may be heading. Dynamic processes are provided with memory of the actual exchange history. We also need to state how disequilibrium trade in stock markets takes place. This is another neglected issue, though a fact of reality. Using a case with only two traders of two stock commodities, and focusing pure trade, it is possible to specify the exact conditions for disequilibrium trade in each step of the dynamic process. In the end any of an infinity of equilibria can be reached, or trade can stick in some disequilibrium point while complex, even chaotic, price dynamics goes on.

  • 42.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Duopoly and Complex Dynamics2011Ingår i: Oligopoly: Old Ends - New Means / [ed] Tönu Puu, Berlin: Springer Berlin/Heidelberg, 2011, s. 43-67Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    As mentioned in Chap. 1, Rand (1978) conjectured that with suitable shapes of the reaction functions the outcome of dynamic duopoly would be chaotic. His purely mathematical treatment does not, however, include any substantial economic assumptions under which this becomes true. In what follows a very simple duopoly model, already encountered in Chap. 2, based on traditional microeconomis, will be discussed.

  • 43.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Economic Development in the Arts, Crafts, and Sciences2001Ingår i: Evolutionary Controversy in Economics, Tokyo: Springer-Verlag , 2001, s. 59-72Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 44.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    From catastrophe to chaos- a general theory of discontinuities- J B Rosser1994Ingår i: Environment and Planning, B: Planning and Design, ISSN 0265-8135, E-ISSN 1472-3417, Vol. 21, nr 3, s. 379-380Artikel, recension (Övrigt vetenskapligt)
  • 45.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Hotelling's "ice cream dealers" with elastic demand2002Ingår i: The annals of regional science, ISSN 0570-1864, E-ISSN 1432-0592, Vol. 36, nr 1, s. 1-17Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This article reconsiders the Hotelling duopoly model of 1929, but under elastic demand, more precisely a linear demand function. The equilibrium state for identical firms is fully described, and the intervals of different regimes: independent monopolies, genuine duopoly competition, and price cutting wars, are specified in terms of one single compound parameter (maximum price, minus marginal production cost, divided by transportation cost).

  • 46.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Nationalekonomi.
    Hotelling's migration model revisited1991Ingår i: Environment and planning A, ISSN 0308-518X, E-ISSN 1472-3409, Vol. 23, nr 8, s. 1209-1216Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the present article Hotelling's model of population growth and migration of 1921 is 'revisited'. After a discussion of the stationary solutions and their stability the main point is made. The model itself is structurally unstable, but can be easily stabilized by adding a simple autonomous migration component. By this, the solution curves, in the shape of constant amplitude population waves over space for the original model, either become damped in one direction and explosive in another or are replaced by just one single spatial limit cycle.

  • 47.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
    Introduction2011Ingår i: Oligopoly: Old Ends - New Means / [ed] Tönu Puu, Berlin: Springer Berlin/Heidelberg, 2011, s. 1-16Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    According to Joseph Schumpeter’s “History of Economic Analysis” from 1954 - the still unsurpassed source book for economics, mathematical modelling in the field had two roots. The first was Johann Heinrich von Thünen’s theory of land use dating from 1827, implicitly containing the most general theory of the emergence of specialization and trade ever presented up to now, as it was based on the mathematical principle of transversality alone; much more general than the Ricardian comparative advantages or the later Heckscher–Ohlin theory which also was based on immobile resources. As a historical irony the theory has not to this day been recognized as anything more than a theory in agricultural economics.

  • 48.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Introduction to Mathematical Economics2007Ingår i: Mathematical Models in Economics: UNESCO Encyclopedia of Life Support Systems, Oxford: EOLSS Publishers , 2007Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 49.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Layout of a New Industry: From Oligopoly to Competition2005Ingår i: Pure Mathematics and Applications, ISSN 1218-4586, Vol. 16, nr 4, s. 475-492Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Oligopoly models with constant marginal costs for the competitors tend to produce destabilization of the Cournot equilibrium point when the number of competitors increases. It therefore becomes difficult to explain how an oligopoly can evolve into perfect competition through an increase in the number of competitors. In the present study it is explored how cost functions with built in capacity limits can eliminate this problem. It is also shown how such cost functions can be derived from CES functions when the input of capital is fixed through an act of investment. It turns out that the durability of capital equipment is what is needed to stabilize the system, and so make it possible for an oligopoly to seamlessly transform into a competitive equilibrium.

  • 50.
    Puu, Tönu
    Umeå universitet, Samhällsvetenskaplig fakultet, Centrum för regionalvetenskap (CERUM).
    Mathematical Location and Land Use Theory: An Introduction2003 (uppl. 2)Bok (Övrigt vetenskapligt)
123 1 - 50 av 107
RefereraExporteraLänk till träfflistan
Permanent länk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf