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Puu, Tönu
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Publications (10 of 107) Show all publications
Panchuk, A. & Puu, T. (2018). Dynamics of a durable commodity market involving trade at disequilibrium. Paper presented at International Workshops on Dynamic Models in Economics and Finance (MDEF), JUN 23-25, 2016, Urbino, ITALY. Communications in nonlinear science & numerical simulation, 58, 2-14
Open this publication in new window or tab >>Dynamics of a durable commodity market involving trade at disequilibrium
2018 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 58, p. 2-14Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2018
Keywords
Durable commodity markets, Disequilibrium trade, Path dependence, Piecewise smooth systems
National Category
Economics
Identifiers
urn:nbn:se:umu:diva-150719 (URN)10.1016/j.cnsns.2017.08.003 (DOI)000416034300002 ()2-s2.0-85028330597 (Scopus ID)
Conference
International Workshops on Dynamic Models in Economics and Finance (MDEF), JUN 23-25, 2016, Urbino, ITALY
Available from: 2018-08-16 Created: 2018-08-16 Last updated: 2018-08-16Bibliographically approved
Puu, T. (2017). A New Approach to Modeling Bertrand Duopoly. Review of Behavioral Economics, 4(1), 51-67
Open this publication in new window or tab >>A New Approach to Modeling Bertrand Duopoly
2017 (English)In: Review of Behavioral Economics, ISSN 2326-6198, E-ISSN 2326-6201, Vol. 4, no 1, p. 51-67Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
NOW PUBLISHERS INC, 2017
Keywords
Bertrand oligopoly, Lancaster's new demand, Product design, Complex dynamics
National Category
Economics and Business
Identifiers
urn:nbn:se:umu:diva-145821 (URN)10.1561/105.00000058 (DOI)000426000900003 ()
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-06-09Bibliographically approved
Puu, T. (2016). Good Old Economic Geography. In: Commendatore, P.; MatillaGarcia, M.; Varela, L.M.; Canovas, J.S. (Ed.), COMPLEX NETWORKS AND DYNAMICS: SOCIAL AND ECONOMIC INTERACTIONS. Paper presented at Training School on Complex Networks and Dynamics, Natl Distance Educ Univ, Fac Econ, Madrid, SPAIN, FEB 12-14, 2014 (pp. 329-359). Springer
Open this publication in new window or tab >>Good Old Economic Geography
2016 (English)In: COMPLEX NETWORKS AND DYNAMICS: SOCIAL AND ECONOMIC INTERACTIONS / [ed] Commendatore, P.; MatillaGarcia, M.; Varela, L.M.; Canovas, J.S., Springer, 2016, p. 329-359Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Springer, 2016
Series
Lecture Notes in Economics and Mathematical Systems, ISSN 0075-8442 ; 683
Keywords
Business cycle diffusion, Continuous geographical space, Interregional trade, Migration, Structural stability
National Category
Social and Economic Geography
Identifiers
urn:nbn:se:umu:diva-131677 (URN)10.1007/978-3-319-40803-3_13 (DOI)000392194600014 ()978-3-319-40803-3 (ISBN)
Conference
Training School on Complex Networks and Dynamics, Natl Distance Educ Univ, Fac Econ, Madrid, SPAIN, FEB 12-14, 2014
Available from: 2017-02-21 Created: 2017-02-21 Last updated: 2018-06-09Bibliographically approved
Canovas, J. S., Panchuk, A. & Puu, T. (2015). Asymptotic dynamics of a piecewise smooth map modelling a competitive market. Mathematics and Computers in Simulation, 117, 20-38
Open this publication in new window or tab >>Asymptotic dynamics of a piecewise smooth map modelling a competitive market
2015 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 117, p. 20-38Article in journal (Refereed) Published
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).

Keywords
Multidimensional piecewise smooth map, Coexisting metric attractors, Oligopoly market model, urnot equilibrium stability
National Category
Computer Sciences Mathematics
Identifiers
urn:nbn:se:umu:diva-107844 (URN)10.1016/j.matcom.2015.05.004 (DOI)000358972900003 ()
Available from: 2015-10-13 Created: 2015-08-28 Last updated: 2018-06-07Bibliographically approved
Panchuk, A. & Puu, T. (2015). Oligopoly model with recurrent renewal of capital revisited. Paper presented at International Workshop on Dynamic Models in Economics and Finance (MDEF), SEP 20-22, 2012, Urbino, ITALY. Mathematics and Computers in Simulation, 108, 119-128
Open this publication in new window or tab >>Oligopoly model with recurrent renewal of capital revisited
2015 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 108, p. 119-128Article in journal (Refereed) Published
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.

Keywords
Oligopoly market, Isoelastic demand function, Non-constant returns
National Category
Business Administration
Identifiers
urn:nbn:se:umu:diva-99352 (URN)10.1016/j.matcom.2013.09.007 (DOI)000347021900008 ()
Conference
International Workshop on Dynamic Models in Economics and Finance (MDEF), SEP 20-22, 2012, Urbino, ITALY
Available from: 2015-03-09 Created: 2015-02-07 Last updated: 2018-06-07Bibliographically approved
Ahmed, E., Elsadany, A. & Puu, T. (2015). On Bertrand duopoly game with differentiated goods. Applied Mathematics and Computation, 251, 169-179
Open this publication in new window or tab >>On Bertrand duopoly game with differentiated goods
2015 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 251, p. 169-179Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2015
Keywords
Bertrand game, CES utility function, Nash equilibrium point, Bifurcation, Chaos
National Category
Economics
Identifiers
urn:nbn:se:umu:diva-100237 (URN)10.1016/j.amc.2014.11.051 (DOI)000347405500016 ()
Available from: 2015-02-26 Created: 2015-02-26 Last updated: 2018-06-07Bibliographically approved
Puu, T. (2014). Disequilibrium trade and the dynamics of stock markets. In: Marisa Faggini, Anna Parziale (Ed.), Complexity in economics: cutting edge research (pp. 225-245). Springer-Verlag New York
Open this publication in new window or tab >>Disequilibrium trade and the dynamics of stock markets
2014 (English)In: Complexity in economics: cutting edge research / [ed] Marisa Faggini, Anna Parziale, Springer-Verlag New York, 2014, p. 225-245Chapter in book (Refereed)
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.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2014
Series
New economic windows, ISSN 2039-411X
Keywords
disequilibrium trade, durable commodity markets, complex dynamics, multiple equilibria, path dependence
National Category
Business Administration
Identifiers
urn:nbn:se:umu:diva-96522 (URN)10.1007/978-3-319-05185-7_12 (DOI)000343052900013 ()978-3-319-05185-7 (ISBN)978-3-319-05184-0 (ISBN)
Available from: 2014-11-23 Created: 2014-11-21 Last updated: 2018-06-07Bibliographically approved
Puu, T. (2011). Capacity Limits. In: Tönu Puu (Ed.), Oligopol: Old Ends - New Mean (pp. 101-125). Berlin: Springer Berlin/Heidelberg
Open this publication in new window or tab >>Capacity Limits
2011 (English)In: Oligopol: Old Ends - New Mean / [ed] Tönu Puu, Berlin: Springer Berlin/Heidelberg, 2011, p. 101-125Chapter in book (Other academic)
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?

Place, publisher, year, edition, pages
Berlin: Springer Berlin/Heidelberg, 2011
National Category
Social Sciences Interdisciplinary
Identifiers
urn:nbn:se:umu:diva-74550 (URN)10.1007/978-3-642-15964-0_5 (DOI)000285558400005 ()978-3-642-15963-3 (ISBN)978-3-642-15964-0 (ISBN)
Available from: 2013-07-02 Created: 2013-07-01 Last updated: 2018-06-08Bibliographically approved
Puu, T. (2011). Cournot Oligopoly. In: Tönu Puu (Ed.), Oligopoly: Old Ends - New Means (pp. 17-41). Berlin: Springer Berlin/Heidelberg
Open this publication in new window or tab >>Cournot Oligopoly
2011 (English)In: Oligopoly: Old Ends - New Means / [ed] Tönu Puu, Berlin: Springer Berlin/Heidelberg, 2011, p. 17-41Chapter in book (Other academic)
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.

Place, publisher, year, edition, pages
Berlin: Springer Berlin/Heidelberg, 2011
National Category
Social Sciences Interdisciplinary
Identifiers
urn:nbn:se:umu:diva-74547 (URN)10.1007/978-3-642-15964-0_2 (DOI)000285558400002 ()978-3-642-15963-3 (ISBN)978-3-642-15964-0 (ISBN)
Available from: 2013-07-02 Created: 2013-07-01 Last updated: 2018-06-08Bibliographically approved
Puu, T. (2011). Duopoly and Complex Dynamics. In: Tönu Puu (Ed.), Oligopoly: Old Ends - New Means (pp. 43-67). Berlin: Springer Berlin/Heidelberg
Open this publication in new window or tab >>Duopoly and Complex Dynamics
2011 (English)In: Oligopoly: Old Ends - New Means / [ed] Tönu Puu, Berlin: Springer Berlin/Heidelberg, 2011, p. 43-67Chapter in book (Refereed)
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.

Place, publisher, year, edition, pages
Berlin: Springer Berlin/Heidelberg, 2011
National Category
Social Sciences Interdisciplinary
Identifiers
urn:nbn:se:umu:diva-74548 (URN)10.1007/978-3-642-15964-0_3 (DOI)000285558400003 ()978-3-642-15963-3 (ISBN)978-3-642-15964-0 (ISBN)
Available from: 2013-07-02 Created: 2013-07-01 Last updated: 2018-06-08Bibliographically approved
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