Equilibrio de Cournot en el mercado eléctrico.

(EN) My project is about the Cournot equilibrium in the electric power market. The differences in this situacion depend on the number of the firms in the market.

2001: el año Cournot

Durante la noche del día 23 de noviembre de 1654, aproximadamente entre las diez y media y las doce y media de la noche, experimentó Pascal una especie de éxtasis religioso que lo impulsó a abandonar la matemática para dedicarse a la teología. Afortunadamente, una noche de 1658 en que un dolor de muelas u otra dolencia le impedía dormir, decidió dedicarse al estudio de la cicloide. Milagrosamente el dolor cesó, lo que interpretó Pascal como un signo de que el estudio de la matemática agradaba a Dios.

Signalling in an international cournot model

We consider a trade policy model, where the costs of the home firm are private information but can be signaled through the output levels of the firm to a foreign competitor and a home policymaker. We study the influences of the non-homogeneity of the goods and of the uncertainty on the production costs of the home firm in the signalling strategies by the home firm. We show that some results obtained for homogeneous goods are not robust under non-homogeneity.

Environmental policies in an international mixed duopoly

The purpose of this paper is to study the effects of environmental and trade policies in an international mixed duopoly serving two markets. We suppose that the firm in the home country is a welfare-maximizing public firm, while the firm in the foreign country is its own profit-maximizing private firm. We find that the environmental tax can be a strategic instrument for the home government to distribute production from the foreign private firm to the home public firm. An additional effect of the home environmental tax is the reduction of the foreign private firm's output for local consumption, thereby expanding the foreign market for the home public firm.

Cournot competition between a non-profit firm and a for-profit firm with uncertainty

In this paper, we consider a Cournot competition between a nonprofit firm and a for-profit firm in a homogeneous goods market, with uncertain demand. Given an asymmetric tax schedule, we compute explicitly the Bayesian-Nash equilibrium. Furthermore, we analyze the effects of the tax rate and the degree of altruistic preference on market equilibrium outcomes.

Bertrand and Cournot oligopolies when rivals' costs are unknown

We study Bertrand and Cournot oligopoly models with incomplete information about rivals’ costs, where the uncertainty is given by a uniform distribution. We compute the Bayesian- Nash equilibrium of both games, the ex-ante expected profits and the ex-post profits of each firm. We see that, in the price competition, even though only one firm produces in equilibrium, all firms have a positive ex-ante expected profit.

Privatization and government preference in a public Stackelberg leader duopoly

We analyse the relationship between the privatization of a public firm and government preferences for tax revenue in a Stackelberg duopoly with the public firm as the leader. We assume that the government payoff is given by a weighted sum of tax revenue and the sum of consumer and producer surplus. We get that if the government puts a sufficiently larger weight on tax revenue than on the sum of both surpluses, it will not privatize the public firm. In contrast, if the government puts a moderately larger weight on tax revenue than on the sum of both surpluses, it will privatize the public firm.

Environmental taxes in a public Stackelberg leader duopoly

We study whether privatization of a public firm improves (or deteriorates) the environment in a mixed Stackelberg duopoly with the public firm as the leader. We assume that each firm can prevent pollution by undertaking abatement measures. We get that, since in the mixed market the industry output is higher than in the private market, the abatement levels are also higher in the mixed market, and, thus, environmental tax rate in the mixed duopoly is higher than that in the privatized duopoly. Furthermore, the environment is more damaged in the mixed than in the private market. The overall effect on the social welfare is that it will becomes higher in the private than in the mixed market.

Stackelberg duopoly with demand uncertainty

We consider a symmetric Stackelberg model in which there is asymmetric demand information owned by first and second movers. We analyse the advantages of leadership and flexibility, and prove that when the leading firm faces demand uncertainty, but the follower does not, the first mover does not necessarily have advantage over the second mover. Moreover, we show that the advantage of one firm over the other depends upon the demand fluctuation and also upon the degree of substitutability of the products.

Cournot model with investments to change the market size

We present a new deterministic dynamical model on the market size of Cournot competitions, based on Nash equilibria of R&D investment strategies to increase the size of the market of the firms at every period of the game. We compute the unique Nash equilibrium for the second subgame and the profit functions for both firms. Adding uncertainty to the R&D investment strategies, we get a new stochastic dynamical model and we analyse the importance of the uncertainty to reverse the initial advantage of one firm with respect to the other.

2001 : el año Cournot.

Resumen basado en el de la publicación

Collusion in a Bertrand duopoly model with decreasing returns and product differentiation

We study cartel stability in a differentiated price-setting duopoly with returns to scale. We show that a cartel may be equally stable in the presence of lower differentiation, provided that the decreasing returns parameter is high. In addition we demonstrate that for a given factor of discount, there are technologies that can have decreasing returns to scale where the cartel always is stable independent of the differentiation degree.

Oligopolistic competition under knightian uncertainty

This artic/e applies a theorem of Nash equilibrium under uncertainty (Dow & Werlang, 1994) to the classic Coumot model of oligopolistic competition. It shows, in particular, how one can map all Coumot equilibrium (which includes the monopoly and the null solutions) with only a function of uncertainty aversion coefficients of producers. The effect of variations in these parameters over the equilibrium quantities are studied, also assuming exogenous increases in the number of matching firms in the game. The Cournot solutions under uncertainty are compared with the monopolistic one. It shows principally that there is an uncertainty aversion level in the industry such that every aversion coefficient beyond it induces firms to produce an aggregate output smaller than the monopoly output. At the end of the artic/e equilibrium solutions are specialized for Linear Demand and for Coumot duopoly. Equilibrium analysis in the symmetric case allows to identify the uncertainty aversion coefficient for the whole industry as a proportional lack of information cost which would be conveyed by market price in the perfect competition case (Lerner Index).

Bertrand, Cournot and monopolistically competitive equilibria

Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria.