| 1. |
- Puu, Tönu, 1936-, et al.
(författare)
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Can Bertrand and Cournot oligopolies be combined?
- 2019
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 125, s. 97-107
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Tidskriftsartikel (refereegranskat)abstract
- There have been some recent attempts to combine Cournot and Bertrand duopolies in one single model. Unfortunately, these attempts do not work. A commodity cannot be homogenous and non-homogenous at the same time. It is always the consumers, who decide whether they perceive competing products as identical or as different brands for which they are willing to pay different prices. There is, of course, nothing that forbids the coexistence of both such consumer groups. Neither is there any obstacle for the competing sellers to sell to both markets. Then we only need an old idea from economic theory, i.e., price discrimination, to rectify the logic. By this the challenging combination idea comes on a stable footing. The model also results in some interesting mathematical facts, such as mulistability and coexistence of attractors.
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| 2. |
- Panchuk, A., et al.
(författare)
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Dynamics of a durable commodity market involving trade at disequilibrium
- 2018
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Ingår i: Communications in nonlinear science & numerical simulation. - : ELSEVIER SCIENCE BV. - 1007-5704 .- 1878-7274. ; 58, s. 2-14
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Puu, Tönu, 1936-
(författare)
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Disequilibrium economics : oligopoly, trade, and macrodynamics
- 2018
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Bok (refereegranskat)abstract
- This book discusses mathematical models for various applications in economics, with a focus on non-linear dynamics. Based on the author's over 50 years of active work in the field, the book has been inspired by models from the period between 1920 and 1950. Following a brief introduction to economics for mathematicians and other modelers, it assembles a repository of useful specific functions for global dynamic modeling. Furthermore, twelve "research stubs" - outlined research agendas that have not yet been fully worked on - are suggested for further study and could even be expanded to entire research projects. The book is a valuable resource, particularly for young scientists who are skilled in mathematical and computational techniques and are looking for applications in economics.
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| 4. |
- Puu, Tönu, 1936-
(författare)
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Hotelling duopoly revisited
- 2016
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Ingår i: Essays in economic dynamics. - Singapore : Springer. - 9789811015212 - 9789811015205 - 9789811093746 ; , s. 35-55
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Bokkapitel (refereegranskat)abstract
- Many articles have been written about Harold Hotelling’s model of two competitors on a fixed line segment, competing by choosing mill price and location. Most of them have focused on the paradoxical case of crowding in the middle when demand is totally inelastic. Yet Hotelling conjectured that this would not happen if the consumers not only chose the least expensive supplier, but their demand were dependent on the price charged. However, surprisingly little has been written about the case with elastic demand. Even less has been attempted to put the problem in a dynamic format.
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| 5. |
- Puu, Tönu, 1936-
(författare)
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Arts, sciences, and economics : a historical safari, second edition
- 2015. - 2
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Bok (refereegranskat)abstract
- 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. The second edition is extended and updated especially as regards the illustration material.
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| 6. |
- Puu, Tönu, 1936-
(författare)
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Diffusion of Growth and Cycles in Continuous Time and Space
- 2015
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Ingår i: Complexity and Geographical Economics. - Cham : Springer Science+Business Media B.V.. - 9783319128054 ; , s. 99-112
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Bokkapitel (refereegranskat)abstract
- Spatial economics can be formatted in two different ways. One can see geographical space as a set of locations connected by arcs. Or one can see it as a continuous plane in two dimensions. Activities, such as production and consumption can be represented in both, and so can flows, of trade or migrants. When space is the continuous plane such flows are represented by continuous fields as in physics. The continuous outlook was the traditional both in economics and geography. However, it does not so easily lend itself to computations and fitting to actual data as in the discrete representation. The disadvantage of seeing space as a matrix of locations and connecting arcs is that space, in the sense of geometric shape and size slips out. In the twentieth century there were presented two ingenious economic models using continuous space, Hotelling (A mathematical theory of migration, MA Thesis, University of Washington, reprinted in Environment and Planning A, 10, 1223–1239) who dealt with migration, and Beckmann (1952) who dealt with trade and pricing in a spatially dispersed market. Here we take a simpler case dealing with the diffusion of growth and business cycles in continuous geographical space.
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| 7. |
- Puu, Tönu, 1936-
(författare)
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Pattern formation in economic geography
- 2012
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Ingår i: Global analysis of dynamic models in economics and finance. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642295034 - 3642295029 - 9783642295027 ; , s. 133-158
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Bokkapitel (refereegranskat)abstract
- Classical spatial economics as formulated by Johann Heinrich von Thünen and Wilhelm Launhardt in the nineteenth century dealt with economic geographical phenomena in the continuous two-dimensional plane. The present chapter explores to what extent their equilibrium outlook can be extended to deal with dynamic phenomena. Issues, such as spatial distributions of prices, land rents, and populations, along with flows - of traded commodities, migrants, and diffusion of non-material influences, such as economic growth or business cycles, definitely seem to call for such a dynamic perspective. In particular, it is argued that, even in motivating persistent equilibrium patterns, focus should be shifted from optimality to structural stability. Implicit is then that one considers topological properties rather than strictly geometrical ones. This in itself is a move towards more realism, as the extreme regularity inherent in the classical geometric models is so unconvincingly abstract. This reasoning is applied to two much discussed cases; the emergence of shapes of market areas, and the shapes of structurally stable flows of trade.
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| 8. |
- Cánovas, J.S., et al.
(författare)
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On the dynamics of a piecewise linear oligopoly model with capacity limits and reinvestment periods
- 2011
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Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885 ; , s. 237-257
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Bokkapitel (refereegranskat)abstract
- In this chapter we study the stability problem for an oligopoly market when the number of competitors grows. It has been pointed out that Cournot oligopoly is destabilized when the number of competitors grows beyond a very small number. However, all such studies concerned models with firms facing constant marginal costs. If one is interested in the question whether a Cournot equilibrium smoothly transforms into a perfect competition equilibrium when the number of competitors grows, the instability pointed out is neither surprising nor very relevant. In the competitive market we assume many small firms, whereas in the oligopoly there are few big firms. A firm with constant marginal costs is potentially infinitely large. So, to take this in consideration, we introduce capacity limits due to fixed amounts of capital which only occasionally are changed due to replacements of worn out capital. We find that the Cournot equilibrium destabilizes depending on the number of firms, but also on the way they choose the investment periods. Anyway, the oligopoly market becomes more complex when the number of firms increases.
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| 9. |
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Nonlinear economic dynamics
- 2011
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Samlingsverk (redaktörskap) (refereegranskat)abstract
- his new book focuses on recent advances made in the field of non-linear dynamic modeling in economics. Mathematically, linearity is a very special kind of relation between variables chosen to the purpose of simplification. Even in physics linear modeling of dynamical systems was a first choice for quite some time, due to convenience in analysis, as exemplified by the acceleration law, the harmonic oscillator, the wave equation, and the like. The methods of analysis were simply developed to the ease of dealing with such systems. These methods are found under the heading of infinitesimal calculus; at early stages dynamical processes were formulated as differential equations in continuous time.
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| 10. |
- Panchuk, Anastesiia, et al.
(författare)
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Industry dynamics, stability of cournot equilibrium, and renewal of capital
- 2011
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Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885 ; , s. 259-275
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Bokkapitel (refereegranskat)abstract
- This chapter focuses industrial dynamics of an oligopoly market with increasing competition where the firms enter one by one. At the moment of entry each firm chooses capital stock of a size corresponding to current market conditions. According to the assumed production technology (a CES function with constant returns and substitution elasticity equal to 0.5), at the moments of investment the firms access a constant returns technology, whereas in between they produce with decreasing returns - even with capacity bounds due to the fixed capital stock. Once capital has worn out, it is renewed, again under constant returns. This puts up a mixed dynamics of short and long run adjustment, with some firms constrained by fixed capital stocks, others entering or reinvesting. Two scenarios under these assumptions are focused; one where the durability of capital is very long compared to the ultimate number of competitors; another where capital just lasts two periods so that the firms fall in two categories which take turns in reinvesting.
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