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The aim of this paper is to study the differentiability property of optimal paths in dynamic economic models. We address this problem from the point of view of the differential calculus in sequence spaces which are infinite-dimensional Banach spaces. We assume that the return or utility function is concave, and that optimal paths are interior and bounded. We study the C r differentiability of optimal paths vis-à-vis different parameters. These parameters are: the initial vector of capital stock, the discount rate and a parameter which lies in a Banach space (which could be the utility function itself). The method consists of applying an implicit function theorem on the Euler-Lagrange equation. In order to do this, we make use of classical conditions (i.e., the dominant diagonal block assumption) and we provide new ones. (2000): 90A16, 49K40, 93C55 Mathematics Subject ClassificationJournal of Economic Literature Classification: C161, D99, O41

International audienceIn this paper we study the efficient points of a closed production set with free disposal. We first provide a condition on the boundary of the production set, which is equivalent to the fact that all boundary points are efficient. When the production set is convex, we also give an alternative characterization of efficiency around a given production vector in terms of the profit maximization rule. In the non-convex case, this condition expressed with the marginal pricing rule is sufficient for efficiency. Then we study the Luenberger's shortage function. We first provide basic properties on it. Then, we prove that the above necessary condition at a production vector implies that the shortage function is locally Lipschitz continuous and the efficient points in a neighborhood are the zeros of it and conversely

This article is devoted to a study of the optimal monetary and fiscal policies within the framework of an overlapping generations model with cash-in-advance constraints. We first characterize the intertemporal equilibrium. Then we show how to decentralize the optimal growth path using available policy instruments~i.e., labor income and capital taxes, public debt, money supply!. Between the four instruments: wages and capital taxes, debt and monetary policy, one is redundant among the three last which implies that the Friedman Rule is only a special case.

Social pressures, in addition to the law, incite more and more firms to pursue multiple and separate objectives. This trend raises the following question: will the change in the number of objectives pursued by firms affect their strategic interactions? To address this issue we focus on a dynamic duopoly where each firm has two objectives: one of the firms’ objectives is financial and the other is environmental. Production is a polluting activity and the actual level of pollution depends on current and past emissions. We analyze both open-loop Nash and cooperative equilibria (these equilibria are also trivially feedback as the equilibrium strategies are constant). We show that contrary to the case where firms’ unique objective is the financial one, there are Nash equilibria where production is lower than in the cooperative equilibrium. This stems from the fact that in a Nash equilibrium firms do not coordinate the choice of the relative weight given to the environmental objective. We obtain the same conclusion when firms can mitigate pollution. In this case, we also show that there are Nash equilibria where the sum of the firms’ mitigation efforts is higher than its value in the cooperative equilibrium.