| 1. |
- Canovas, Jose S, et al.
(författare)
-
Detecting Chaos in a Duopoly Model via Symbolic Dynamics
- 2010
-
Ingår i: Discrete and continuous dynamical systems. Series B. - Springfield, USA : American Institute of Mathematical Sciences. - 1531-3492 .- 1553-524X. ; 13:2, s. 269-278
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 2. |
- Cánovas, J.S., et al.
(författare)
-
On the dynamics of a piecewise linear oligopoly model with capacity limits and reinvestment periods
- 2011
-
Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885 ; , s. 237-257
-
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.
|
|
| 3. |
-
Nonlinear economic dynamics
- 2011
-
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.
|
|
| 4. |
- Panchuk, Anastesiia, et al.
(författare)
-
Industry dynamics, stability of cournot equilibrium, and renewal of capital
- 2011
-
Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885 ; , s. 259-275
-
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.
|
|
| 5. |
- Puu, Tönu, 1936-
(författare)
-
Dynamics of stackelberg duopoly
- 2011
-
Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885 ; , s. 287-303
-
Bokkapitel (refereegranskat)abstract
- Stackelberg leadership is understood as a stationary supply taking account of the follower's Cournot reaction function. However, given the follower always adheres to the reaction function, the leader could also choose a dynamic, for instance, periodic sales policy over time. Using Stackelberg's exponential inverse demand function, it is shown that such periodic policies indeed are more advantageous than the stationary solution. Simple orbits can be learned by the follower, and adaptation then throws the system back to the stationary case. It is, however, shown how the leader can choose long-period orbits of sufficient irregularity (of even random or chaotic appearance) so as to prevent the follower from such learning.
|
|
| 6. |
- Puu, Tönu, 1936-
(författare)
-
Nonlinear economic dynamics and global analysis
- 2011
-
Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885 ; , s. 3-12
-
Bokkapitel (refereegranskat)abstract
- This chapter takes a historical perspective on the emergence of non-linear dynamic modelling in economics. Such models, in particular, involve multistability. In the form of piecewise linearity analysis dates back to the 1930s, with study of fixed point and periodic attractors and their basins. However, even if different cases, depending on different parameter combinations, are studied, no trace of bifurcation analysis can yet be found. Quite early is also business cycle modelling, emerging around 1940, and developed into the nonlinear format around 1950. These models include forces that repel the systems from equilibria/fixed points, but are stabilized through attracting forces far out in the phase space. The resulting trajectories, limit cycles in the case of continuous time models, quasi-periodic orbits in the case of discrete time models, are, however the unique attractors. A certain awareness of Hopf/Neimark bifurcations is there, but, again, there is no explicit study of these. A particular problem for economics as a formal science is that a true study of nonlinear dynamics requires global analysis. Economics, however, has for ages been focused on equilibria and the local study of stability. This is partly due to ideological reasons, as economists preferred convex structures providing for unique equilibrium states, which could be associated with optimality. As a consequence, formal relations are usually described qualitatively, and are seldom stated in explicit form meant to hold over a wide domain of variable values. An exception is provided by production studies, where such production functions were in fact formulated and estimated from time series or panel data. They still provide the best explicit functions to use also in the study of global dynamics even though they were not developed for this purpose.
|
|
| 7. |
- Puu, Tönu, 1936-
(författare)
-
Oligopoly : old ends - new means
- 2011
-
Bok (refereegranskat)abstract
- The book focuses classical oligopoly theory as developed in 1840-1940. By the end of this period oligopoly came under the spell of game theory in its probabilistic equilibrium format. Work by Cournot, von Stackelberg, Palander, and Hotelling, causal and dynamic in essence, but ignored, is reconsidered in the light of modern dynamics using topology and numerics. As particular features, von Stackelberg leadership is included in the dynamic Cournot model, the Hotelling problem is solved with elastic demand, thus skipping the absurd idea of quadratic transportation costs. Further, it is shown that the celebrated destabilisation of Cournot equilibrium under increased competition is due to mistakenly assuming constant returns, and that the whole idea of rational expectations is untenable in dynamic oligopoly. Early original ideas in oligopoly theory, such as coexistence and multiplicity of attractors are focused again after many undeserved decades of oblivion.
|
|
| 8. |
- Puu, Tönu, 1936-
(författare)
-
On the economics of increasing complexity : With some special focus on culture
- 2010
-
Ingår i: Journal of Economic Behavior and Organization. - : Elsevier. - 0167-2681 .- 1879-1751. ; 75:1, s. 59-68
-
Tidskriftsartikel (refereegranskat)abstract
- This contribution seeks to find a setting in which evolution in terms of changing structure, rather than growth within a given structure, can be modelled. In particular the evolution of increasing complexity is focused. The setting chosen uses Lancasterian property space as an invariant in which the changing, emerging, and disappearing actual implements are property bundles. The aim is to produce a development tree like the Darwinian, and the tool used for modelling the branching bifurcations is catastrophe theory.
|
|
| 9. |
- Puu, Tönu, 1936-, et al.
(författare)
-
Preface
- 2011
-
Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885
-
Bokkapitel (refereegranskat)
|
|
| 10. |
- 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.
|
|
