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.

Multiple equilibria and protectionism

In a nonnative approach, I analyze trade policies when the industrial sector genentes positive extemalities in production, and there are adjustments costs to changing production from one sector to the other. Protectionist trade policy can make workers intemalize the benetits from moving into the industrial sector, but it is a second best policy as it also causes consumption distortions. I show that if the govemment is able to fully commit to its tariff schedule for the future, the welfare maximizing policy is to maintain a positive tariff forever, even after all adjustment has already taken place . However, if the govemment is not able to commit at all, the only time consistent policy is zero tariff at any point in time. The time inconsistency of the full commitment policy is derived from the fact that in the model only production needs interference, and the production distortion is lagged one period with respect to the tariff wbile the consumption distortion is simultaneous to the tariff. In the intermediary case, i.e., when the government can commit for a limited period of time, the time consistent optimal tariff will be positive but lower than the "full commitment" tariff. This result indicates that some institutions that have always been considered pure sources of inefficiency, such as protectionist lobbying, may in fact be welfare improving in some cases!

Existence of nash equilibrium in competitive nonlinear pricing games with adverse selection

We show that for a large class of competitive nonlinear pricing games with adverse selection, the property of better-reply security is naturally satisfied - thus, resolving via a result due to Reny (1999) the issue of existence of Nash equilibrium for a large class of competitive nonlinear pricing games.

Equilibria in exchange economies with financial constraints : beyond the Cass trick

We consider an exchange economy under incomplete financiaI markets with purely financiaI securities and finitely many agents. When portfolios are not constrained, Cass [4], Duffie [7] and Florenzano-Gourdel [12] proved that arbitrage-free security prices fully characterize equilibrium security prices. This result is based on a trick initiated by Cass [4] in which one unconstrained agent behaves as if he were in complete markets. This approach is unsatisfactory since it is asymmetric and no more valid when every agent is subject to frictions. We propose a new and symmetric approach to prove that arbitrage-free security prices still fully characterize equilibrium security prices in the more realistic situation where the financiaI market is constrained by convex restrictions, provided that financiaI markets are collectively frictionless.

Competição oligopolística em ambiente de incerteza knightiana

Este artigo aplica rn.n teori,ma de existência de equilibrios de Nash sob incerteza (Dow & Werlang, 1~4) a um problema clássico da Teoria da Competição Oligopolística. Particularmente, mostra como se pode mapear todos os equilibrios de Cournot (que incluem as soluções de monopólio e de bloqueio total da produção) unicamente em função da aversão à incerteza dos produtores. Os efeitos das variações destes parâmetros sobre as produções de equilibrio são estudados. Também, as soluções de Cournot sob incerteza são comparadas com a solução do monopolio standard. Particularmente, mostra-se: que existe um nível de incerteza tal que toda aversão à incerteza (do mercado) superior à este nível, induz os agentes a produzir, agregadamente, quantidades menores que as de monopolio. Enfim, as soluções de equilibrio são particularizadas explícitamente nos casos da Demanda Linear e do Duopolio de Cournot

First-Price auction symmetric equlibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

Common agency with informed principals

We analyze a common agency game under asymmetric information on the preferences of the non-cooperating principals in a public good context. Asymmetric information introduces incentive compatibility constraints which rationalize the requirement of truthfulness made in the earlier literature on common agency games under complete information. There exists a large class of differentiable equilibria which are ex post inefficient and exhibit free-riding. We then characterize some interim efficient equilibria. Finally, there exists also a unique equilibrium allocation which is robust to random perturbations. This focal equilibrium is characterized for any distribution of types.

Signalling and arbitrage

Given a competitive signalling game, we study a transformed game which includes the natural enrichment of contractual opportunities in a market. We show that subgame perfect equilibrium outcomes in the new game which satisfy certa in competitive hypotheses induce sequential equilibrium outcomes in the original game which satisfy the Cho-Kreps extended intuitive criterion. Arbitrage opportunities in the transformed game achieve results similar to refinements of sequential equilibria in the original game.

Bubbles, collateral and monetary equilibrium

Consider an economy where infinite-lived agents trade assets collateralized by durable goods. We obtain results that rule out bubbles when the additional endowments of durable goods are uniformly bounded away from zero, regardless of whether the asset’s net supply is positive or zero. However, bubbles may occur, even for state-price processes that generate finite present value of aggregate wealth. First, under complete markets, if the net supply is being endogenously reduced to zero as a result of collateral repossession. Secondly, under incomplete markets, for a persistent positive net supply, under the general conditions guaranteeing existence of equilibrium. Examples of monetary equilibria are provided.

Money with Bank Networks

Rio de Janeiro

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).

Equilíbrio em mercados de ativos com aversão a incerteza

Este trabalho procurará de início explicitar detalhadamente o comportamento do investidor avesso a incerteza quando atua isoladamente na economia. Dirigir-se-á, em seguida, no sentido de determinar o comportamento do preço de equilíbrio em uma economia onde os agentes econômicos possuem diferentes graus de aversão a incerteza, e como a variação desta globalmente ou individualmente altera aquele. Finalmente introduzir-se-á incerteza no modelo de Kyle (1985), estendendo o trabalho de Oliveira (1989), concernentemente aos agentes econômicos agindo racionalmente, à presente análise, onde será mostrado existir também, apenas um equilíbrio de Nash, que é o equilíbrio obtido sem negociação.

Essays on competition and returns of inside money

In an early paper, Cavalcanti and Wallace (2001) showed, using a computable version of Cavalcanti-Wallace model (CW-1999), that optimal regulation induces banks to pay interests, instead of contracting the money supply in an inside money allocation. Here, we generalize CW in two fashions, assuming inside money allocations, so that banks are supposed to issue money as they find a potential producer wishing to produce. The first generalization allows for seasonality due to real shocks on preferences with persistence and for monetary policy improvement. We found an asymmetric path for interest rates when constraints matter, even when shocks are independent. The second generalization allows for bank competition, in the sense that banks can choose between two different banking nets. We proof the existence of simple stable and unstable equilibria and also verify the existence of multiple equilibria.