Abstract
Single-product oligopolies without product differentiation are examined with linear production, production adjustment, flexible workforce and investment costs. The price function is assumed to be hyperbolic which makes the nonlinearity of the model much stronger than in the case of linear price function examined earlier in the literature. The best responses of the firms are determined which are not monotonic in contrast to the linear case. The set of all steady states is then characterized and in the case of a duopoly it is illustrated. The asymptotical behavior of the steady states is examined by using simulation. We analyze the effects of such costs on the industry dynamics and compare them to the prediction by the well known model with hyperbolic price function and no product adjustment and investments costs.
Highlights
Theory and its applications became one of the central issues in the literature of mathematical economics since the pioneering work of Cournot [1]
The existence and uniqueness of the equilibrium was the main focus of research in early stages and later the focus of studies turned to the dynamic extensions of these model variants
Keeping the linearity of the price and production cost functions, production adjustment costs were introduced and their effect on the asymptotic properties of the equilibrium were examined by Howroyd and Rickard [4], Macleod [5], Reynolds [6, 7], Szidarovszky and Yen [8] among others
Summary
Theory and its applications became one of the central issues in the literature of mathematical economics since the pioneering work of Cournot [1]. Keeping the linearity of the price and production cost functions, production adjustment costs were introduced and their effect on the asymptotic properties of the equilibrium were examined by Howroyd and Rickard [4], Macleod [5], Reynolds [6, 7], Szidarovszky and Yen [8] among others. Hyperbolic price functions result in interesting dynamic properties Such oligopoly models are equivalent to rent-seeking games [16,17,18] as well as to market-share attraction models [19, 20]. In this paper we reconsider the model of Matsumoto et al [10] with keeping linear production, flexible workforce and additional adjustment costs but introducing hyperbolic price function which makes the nonlinearity of the model much stronger leading to more interesting dynamic properties.
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