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 turn out 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.
Highlights
This paper considers Cournot [2] duopoly dynamics for a model with isoelastic demand and cost functions that asymptotically go to infinity as the capacity limits are approached
It could be derived from a CES production function, so like the isoelastic demand function, which resulted from any Cobb-Douglas utility function, it was firmly based on generally accepted principles of economic modelling
The particular sense of the present model in terms of economics is that a duopoly firm, which during some period cannot make any positive profit, may not close down completely, but rather supply some small stand by quantity of output
Summary
This paper considers Cournot [2] duopoly dynamics for a model with isoelastic demand and cost functions (total and marginal) that asymptotically go to infinity as the capacity limits are approached. In accordance with an argument by Edgeworth who in the late 19th Century insisted on the necessity of introducing capacity limits, a smooth model with asymptotic capacity limits has been proposed It could be derived from a CES production function, so like the isoelastic demand function, which resulted from any Cobb-Douglas utility function, it was firmly based on generally accepted principles of economic modelling. Another important point of the model we are going to propose is that we let firms to choose small ”stand-by" outputs rather than closing down when they can not get positive profits.
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