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Stefano BOSI (University of Evry and CNRS)

On the existence, efficiency and bubbles of a Ramsey equilibrium with endogenous labor supply and borrowing constraints, with Robert Becker, Cuong Le Van and Thomas Seegmuller.
Abstract: In this paper, we study the existence of an intertemporal equilibrium in a Ramsey model with heterogenous discounting, elastic labor supply and borrowing constraints. Applying a fixed-point argument by Gale and Mas-Colell (1975), we prove the existence of an equilibrium in a truncated bounded economy. This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. Then, we prove the
existence of an equilibrium in an infinite-horizon economy as a limit of a sequence of truncated economies. On the one hand, our paper generalizes Becker et al. (1991) because of the elastic labor supply and, on the other hand, Bosi and Seegmuller (2010) because of a proof of global existence. Our methodology can be also applied to other Ramsey models with different market imperfections. At the end of the paper, we prove the impossibility of bubbles in our productive economy and we provide a sufficient condition for equilibrium efficiency.

Miltos MAKRIS (Southampton University)

Optimal Redistribution under Learning-by-doing

Gaëtano BLOISE (University of Roma III)

Fragility of competitive equilibrium with risk of default, with Pietro Reichlin and Mario Tirelli

Abstract. We study competitive equilibrium in sequential economies under limited commitment. Default induces permanent exclusion from nancial markets and endogenously determined solvency constraints prevent debt  repudiation. Our analysis shows that such an enforcement mechanism is essentially fragile, possibly, leading to dramatic consequences on equilibrium multiplicity and inefficiency. We accomplish this by establishingWelfare Theorems under a weaker notion of constrained efficiency, inspired by Malinvaud, corresponding to the absence of welfare improving feasible redistributions over nite (though indenite) horizons. A Negishi's Method permits to show that, for any arbitrary value of social welfare in between autarchy and constrained optimality,
there exists an equilibrium attaining that value.

Bertrand WIGNIOLLES (University of Paris 1)

Optimism, pessimism and financial bubbles
Abstract: This paper shows that it is possible to extend the scope for the existence of rational bubbles when uncertainty is introduced associated with a rank-dependent expected utility. RDU assumption can be viewed as a transformation of probabilities depending on the pessimism/optimism of the agent. Our results show that pessimism favors the existence of deterministic bubbles, when optimism may promote the existence of stochastic bubbles. Moreover, under pessimism, RDU assumption can generate multiple bubbly equilibria. The RDU assumption also leads to new conditions ensuring the (absence of) Pareto-optimality of the competitive equilibrium without bubbles. These conditions still govern the existence of bubbles.

Frank PAGE (Indiana University)

Stationary Markov Equilibria in Discounted Stochastic Games.

Cuong LE VAN (CNRS-CERMSEM)

Monotone concave (convex) operators: applications to stochastic dynamic programming with unbounded returns, with Yiannis Vailakis
Abstract : We propose a new approach to the issue of existence and uniqueness of solutions to the stochastic Bellman equation exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel'skii (1964) and Krasnosel'skii-Zabreiiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of xed points for monotone concave (convex) operators dened on partially order spaces.

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