| 21. |
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| 22. |
- Puu, Tönu, 1936-
(författare)
-
Chaos in business cycles
- 1991
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 1:5, s. 457-473
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 23. |
- Puu, Tönu, 1936-
(författare)
-
Chaos in duopoly pricing
- 1991
-
Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 1:6, s. 573-581
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 24. |
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| 25. |
- Puu, Tönu, 1936-
(författare)
-
Complex dynamics with three oligopolists
- 1996
-
Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 7:12, s. 2075-2081
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 26. |
- Puu, Tönu, 1936-
(författare)
-
Continuous economic space modelling : Draft of a survey
- 2009
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Ingår i: The annals of regional science. - : Springer Science and Business Media LLC. - 0570-1864 .- 1432-0592. ; 43:1, s. 5-25
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 27. |
- Puu, Tönu, 1936-
(författare)
-
Hotelling's "ice cream dealers" with elastic demand
- 2002
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Ingår i: The annals of regional science. - : Springer Science and Business Media LLC. - 0570-1864 .- 1432-0592. ; 36:1, s. 1-17
-
Tidskriftsartikel (refereegranskat)abstract
- 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).
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| 28. |
- Puu, Tönu, 1936-
(författare)
-
Hotelling's migration model revisited
- 1991
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Ingår i: Environment and planning A. - 0308-518X .- 1472-3409. ; 23:8, s. 1209-1216
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 29. |
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| 30. |
- Puu, Tönu, 1936-
(författare)
-
Layout of a New Industry : From Oligopoly to Competition
- 2005
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Ingår i: Pure Mathematics and Applications. - Budapest : SAAS Publishing. - 1218-4586. ; 16:4, s. 475-492
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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