Competitive equilibria in infinite-horizon collateralized economies with default penalties

Araújo, Páscoa and Torres-Martinez (2002) have shown that, without imposing either debt constraints or transversality conditions, Ponzi schemes are ruled out in infinite horizon economies with default when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2008) subsequently show that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. They also claim that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is ensured. The objective of this paper is two fold. First, contrary to what is claimed by Páscoa and Seghir (2008), we show that moderate default penalties do not always prevent agents to run a Ponzi scheme. Second, we provide an alternative condition on default penalties that is sufficient to rule out Ponzi schemes and ensure the existence of a competitive equilibrium.

On Ponzi schemes in infinite horizon collateralized economies with default penalties

Araujo, Páscoa and Torres-Martínez (2002) showed that, without imposing any debt constraint, Ponzi schemes are ruled out in infinite horizon economies with limited commitment when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2009) presented two examples in which they argued that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. Moreover, they claimed that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is restored. This paper questions the validity of the claims made in Páscoa and Seghir (2009). First, we show that it is not true that harsh default penalties lead to Ponzi schemes in the examples they have proposed. A competitive equilibrium with no trade can be supported due to unduly pessimistic expectations on asset deliveries. We subsequently refine the equilibrium concept in the spirit of Dubey, Geanakoplos and Shubik (2005) in order to rule out spurious inactivity on asset markets due to irrational expectations. Our second contribution is to provide a specific example of an economy with moderate default penalties in which Ponzi schemes reappear when overpessimistic beliefs on asset deliveries are ruled out. Our finding shows that, contrary to what is claimed by Páscoa and Seghir (2009), moderate default penalties do not always prevent agents to run a Ponzi scheme.

Collateral, default penalties and almost finite-time solvency

We argue that it is possible to adapt the approach of imposing restrictions on available plans through finitely effective debt constraints, introduced by Levine and Zame (1996), to encompass models with default and collateral. Along this line, we introduce in the setting of Araujo, Páscoa and Torres-Martínez (2002) and Páscoa and Seghir (2008) the concept of almost finite-time solvency. We show that the conditions imposed in these two papers to rule out Ponzi schemes implicitly restrict actions to be almost finite-time solvent. We define the notion of equilibrium with almost finite-time solvency and look on sufficient conditions for its existence. Assuming a mild assumption on default penalties, namely that agents are myopic with respect to default penalties, we prove that existence is guaranteed (and Ponzi schemes are ruled out) when actions are restricted to be almost finite-time solvent. The proof is very simple and intuitive. In particular, the main existence results in Araujo et al. (2002) and Páscoa and Seghir (2008) are simple corollaries of our existence result.

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.

A general lagrangian approach for non-concave moral hazard problems

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.

A general lagrangian approach for non-concave moral hazard problems

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.

Endogenous debt constraints in collateralized economies with default penalties

In infinite horizon financial markets economies, competitive equilibria fail to exist if one does not impose restrictions on agents' trades that rule out Ponzi schemes. When there is limited commitment and collateral repossession is the unique default punishment, Araujo, Páscoa and Torres-Martínez (2002) proved that Ponzi schemes are ruled out without imposing any exogenous/endogenous debt constraints on agents' trades. Recently Páscoa and Seghir (2009) have shown that this positive result is not robust to the presence of additional default punishments. They provide several examples showing that, in the absence of debt constraints, harsh default penalties may induce agents to run Ponzi schemes that jeopardize equilibrium existence. The objective of this paper is to close a theoretical gap in the literature by identifying endogenous borrowing constraints that rule out Ponzi schemes and ensure existence of equilibria in a model with limited commitment and (possible) default. We appropriately modify the definition of finitely effective debt constraints, introduced by Levine and Zame (1996) (see also Levine and Zame (2002)), to encompass models with limited commitment, default penalties and collateral. Along this line, we introduce in the setting of Araujo, Páscoa and Torres-Martínez (2002), Kubler and Schmedders (2003) and Páscoa and Seghir (2009) the concept of actions with finite equivalent payoffs. We show that, independently of the level of default penalties, restricting plans to have finite equivalent payoffs rules out Ponzi schemes and guarantees the existence of an equilibrium that is compatible with the minimal ability to borrow and lend that we expect in our model. An interesting feature of our debt constraints is that they give rise to budget sets that coincide with the standard budget sets of economies having a collateral structure but no penalties (as defined in Araujo, Páscoa and Torres-Martínez (2002)). This illustrates the hidden relation between finitely effective debt constraints and collateral requirements.

Non-emptiness of the alpha-core

We prove non-emptiness of the alpha-core for balanced games with non-ordered preferences, extending and generalizing in several aspects the results of Scarf (1971), Border (1984), Florenzano (1989), Yannelis (1991) and Kajii (1992). In particular we answer an open question in Kajii (1992) regarding the applicability of the non-emptiness results to models with infinite dimensional strategy spaces. We provide two models with Knightian and voting preferences for which the results of Scarf (1971) and Kajii (1992) cannot be applied while our non-emptiness result applies.

Arte-educação: um desafio de muitas faces

Esta dissertação resultou do desenvolvimento de algumas reflexões sobre a Arte-Educação no ensino regular, e visa trazer contribuições ao debate sobre as dificuldades encontradas na sua prática. Uma abordagem histórica é apresentada, com o objetivo de enriquecer os caminhos para o esclarecimento das questões de fundo que permeiam as discussões do momento atual. O trabalho se baseia no pressuposto de que a arte é uma linguagem, como o são, o falar e o escrever, e como tal deve ser considerada no âmbito escolar, levando em conta suas especificidades. Como linguagem livre e criadora, a matéria da arte e primordialmente a vivência do ser humano; seus pensamentos, sua emoção, sua imaginação e sua capacidade simbólica, que se revelam através dos meios físicos disponíveis, que o arte-educador adequará à sua prática. E neste sentido que algumas questões metodológicas são discutidas a partir de situações objetivas, referentes principalmente ao ensino público. Procurou-se mostrar, ainda, que estar sensível ao infinito universo da criação artística é fundamental à formação do arte-educador para que, através de sua atuação junto aos alunos contribua para a democratização das práticas expressivas criadoras nos meios educacionais.

Solução de conflitos: análise de dez casos.

A prática da negociação é tão antiga quanto a existência do ser humano. Segundo Shell (1999, p. 6, tradução nossa), “todos nós negociamos muitas vezes ao dia”. Negociam-se sobre infinitos assuntos com pessoas da mesma cultura ou de outra totalmente distinta, nos mais diversos ambientes. Na verdade, a negociação está tão presente que não se passa um dia sequer sem que se negocie algo, desde aumentos de salário até a construção de plantas industriais no exterior, em cenário de conflito político. O objetivo geral deste trabalho é levá-lo a compreender por que algumas dessas negociações são bem-sucedidas enquanto outras fracassam. Afim de que este objetivo seja atingido, é preciso inicialmente descrever o que se passa no momento em que a negociação está ocorrendo. Todavia, a descrição do processo em si tão somente não leva a maiores conquistas. É preciso também diagnosticar o que está acontecendo de errado para então prescrever soluções corretivas ou preventivas, conforme o caso. Em suma, os objetivos do presente trabalho visam responder às seguintes perguntas de pesquisa: 1. Qual é o perfil do negociador brasileiro? 2. O brasileiro negocia assuntos diferentes da mesma maneira? 3. Quando confrontado com outras culturas, como o brasileiro se comporta?O trabalho contempla um levantamento, pesquisa na forma de questionário, submetido com sucesso à apreciação de algumas centenas de brasileiros, com o intuito de saber como se comportam diante de dez situações reais em cenários diferentes, cuidadosamente escolhidos e que serão analisados ao longo do presente trabalho. Alguns resultados obtidos foram bastante curiosos. O leitor é convidado a explorar as conclusões sobre os desafios enfrentados pelos brasileiros nos dez cenários citados.

Contracting with repeated moral hazard and private evaluations

A repeated moral hazard setting in which the Principal privately observes the Agent’s output is studied. It is shown that there is no loss from restricting the analysis to contracts in which the Agent is supposed to exert effort every period, receives a constant efficiency wage and no feedback until he is fired. The optimal contract for a finite horizon is characterized, and shown to require burning of resources. These are only burnt after the worst possible realization sequence and the amount is independent of both the length of the horizon and the discount factor (δ). For the infinite horizon case a family of fixed interval review contracts is characterized and shown to achieve first best as δ → 1. The optimal contract when δ << 1 is partially characterized. Incentives are optimally provided with a combination of efficiency wages and the threat of termination, which will exhibit memory over the whole history of realizations. Finally, Tournaments are shown to provide an alternative solution to the problem.

Auctions with options for re-auction

We examine the role of seller bidding and reserve prices in an infinitely repeated independent-private-value (IPV) ascending-price auction. The seller has a single object that she values at zero. At the end of any auction round, she may either sell to the highest bidder or pass-in the object and hold a new auction next period. New bidders are drawn randomly in each round. The ability to re-auction motivates a notion of reserve price as the option value of retaining the object for re-auctioning. Even in the absence of a mechanism with which to commit to a reserve price, the optimal “secret” reserve is shown to exceed zero. However, despite the infinite repetition, there may be significant value to the seller from a binding reserve price commitment: the optimal binding reserve is higher than the optimal “secret” reserve, and may be substantially so, even with very patient players. Furthermore, reserve price commitments may even be socially preferable at high discount factors. We also show that the optimal “phantom” bidding strategy for the seller is revenue-equivalent to a commitment to an optimal public reserve price.