This paper analyses the optimal timing of switching between alternative and consecutive regimes i... more This paper analyses the optimal timing of switching between alternative and consecutive regimes in optimal growth models. We derive the appropriate necessary conditions for such problems by means of standard techniques from the calculus of variations and some basic properties of Sobolev spaces.
We prove existence of competitive equilibrium in a version of a Ramsey model in which leisure ent... more We prove existence of competitive equilibrium in a version of a Ramsey model in which leisure enters the utility function. The analysis is carried out by means of a direct and technically simple approach that allows us to obtain detailed results concerning the behaviour of equilibrium allocations and prices.
The paper concerns a model of influence in which agents make their decisions on a certain issue. ... more The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative and important element of the model with respect to other studies of this influence framework is the introduction of weights reflecting the importance that one agent gives to the others. These importance weights can be positive, negative or equal to zero, which corresponds to the stimulation of the agent by the 'weighted' one, the inhibition, or the absence of relation between the two agents in question, respectively. The exhortation obtained by an agent is defined by the weighted sum of the opinions received by all agents, and the updating rule is based on the sign of the exhortation. The use of continuous variables permits the application of differential equations systems to the analysis of the convergence of agents' decisions in long-time. We study the dynamic of some influence functions introduced originally in the discrete model, e.g., the majority and guru influence functions, but the approach allows the study of new concepts, like e.g. the weighted majority function. In the dynamic framework, we describe necessary and sufficient conditions for an agent to be follower of a coalition, and for a set to be the boss set or the approval set of an agent.
In this chapter, we provide a unified treatment of a class of optimal growth models by using dyna... more In this chapter, we provide a unified treatment of a class of optimal growth models by using dynamic programming methods. In the economies we consider in this chapter, a social planner maximizes a discounted sum of utilities which depend on the current and past period states subject ...
This paper proves the existence of competitive equilibrium in a single-sector dynamic economy wit... more This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply and complete assets markets. The method of proof relies on some recent results concerning the existence of Lagrange multipliers in infinite dimensional spaces and their representation as a summable sequence and a direct application of the inward boundary fixed point theorem.
We incorporate a production technology that exhibits increasing returns to scale for small values... more We incorporate a production technology that exhibits increasing returns to scale for small values of the capital stock and diminishing returns for the higher stocks at the firm level in a discrete-time version of Romer's endogenous growth model. We study the social ...
The purpose of this paper is to provide a unified treatment to find sufficient conditions for the... more The purpose of this paper is to provide a unified treatment to find sufficient conditions for the existence of a subgradient of the value function associated with a convex optimization problem. We recall basic results in convex programming with linear constraints. In ...
The paper extends the canonical representative agent Ramsey model to include heterogeneous agents... more The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.
This paper considers an endogenous growth model with human capital accumulation. It gives suffici... more This paper considers an endogenous growth model with human capital accumulation. It gives sufficient conditions and a necessary condition for the existence of a unique competitive equilibrium with externalities. These conditions are more stringent than those which prevail for the existence of an equilibrium defined as the solution to a fixed-point problem.
We address the fundamental issues of existence and efficiency of a Ramsey equilibrium with hetero... more We address the fundamental issues of existence and efficiency of a Ramsey equilibrium with heterogenous discounting, elastic labor supply and borrowing constraints.
We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in wh... more We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinitedimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics.
The main contribution of the paper is to provide a weaker nonsatiation assumption than the one co... more The main contribution of the paper is to provide a weaker nonsatiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points inside the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends (See Aumann and Dreze (1986), ) is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner's (1987) assumption. JEL classification codes: D51, C71.
In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, We... more In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (Econometrica, 1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner's existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents' preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades -that is, as long as agents' preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to * The authors are grateful to an anonymous referee for many helpful comments. transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation -a condition considerably weaker than local or global nonsatiation -that makes possible this transformation.
In order to link production prices and general equilibrium theories, we consider an intertemporal... more In order to link production prices and general equilibrium theories, we consider an intertemporal discrete time economy with fmitely many, infinitely lived consumers, and finitely many, infinitely lived firms. On the production side, our assumptions are those of a Leontief economy. We obtain two main results: Under standard assumptions, this intertemporal model has an equilibrium such that at each period the rate of maximum profit is uniform among producers. The second result is in the spirit of the Samuelson-Solow theorem. Let us consider prices of production as stationary prices which equalize the rate of maximum profit. Under mild conditions such a price system exists and is unique and the sequence of the undiscounted prices of the equilibrium defined above converges to it. 0304-4068/89/$3.50 0 1989, Elsevier Science Publishers B.V.
This paper analyses the optimal timing of switching between alternative and consecutive regimes i... more This paper analyses the optimal timing of switching between alternative and consecutive regimes in optimal growth models. We derive the appropriate necessary conditions for such problems by means of standard techniques from the calculus of variations and some basic properties of Sobolev spaces.
We prove existence of competitive equilibrium in a version of a Ramsey model in which leisure ent... more We prove existence of competitive equilibrium in a version of a Ramsey model in which leisure enters the utility function. The analysis is carried out by means of a direct and technically simple approach that allows us to obtain detailed results concerning the behaviour of equilibrium allocations and prices.
The paper concerns a model of influence in which agents make their decisions on a certain issue. ... more The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative and important element of the model with respect to other studies of this influence framework is the introduction of weights reflecting the importance that one agent gives to the others. These importance weights can be positive, negative or equal to zero, which corresponds to the stimulation of the agent by the 'weighted' one, the inhibition, or the absence of relation between the two agents in question, respectively. The exhortation obtained by an agent is defined by the weighted sum of the opinions received by all agents, and the updating rule is based on the sign of the exhortation. The use of continuous variables permits the application of differential equations systems to the analysis of the convergence of agents' decisions in long-time. We study the dynamic of some influence functions introduced originally in the discrete model, e.g., the majority and guru influence functions, but the approach allows the study of new concepts, like e.g. the weighted majority function. In the dynamic framework, we describe necessary and sufficient conditions for an agent to be follower of a coalition, and for a set to be the boss set or the approval set of an agent.
In this chapter, we provide a unified treatment of a class of optimal growth models by using dyna... more In this chapter, we provide a unified treatment of a class of optimal growth models by using dynamic programming methods. In the economies we consider in this chapter, a social planner maximizes a discounted sum of utilities which depend on the current and past period states subject ...
This paper proves the existence of competitive equilibrium in a single-sector dynamic economy wit... more This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply and complete assets markets. The method of proof relies on some recent results concerning the existence of Lagrange multipliers in infinite dimensional spaces and their representation as a summable sequence and a direct application of the inward boundary fixed point theorem.
We incorporate a production technology that exhibits increasing returns to scale for small values... more We incorporate a production technology that exhibits increasing returns to scale for small values of the capital stock and diminishing returns for the higher stocks at the firm level in a discrete-time version of Romer's endogenous growth model. We study the social ...
The purpose of this paper is to provide a unified treatment to find sufficient conditions for the... more The purpose of this paper is to provide a unified treatment to find sufficient conditions for the existence of a subgradient of the value function associated with a convex optimization problem. We recall basic results in convex programming with linear constraints. In ...
The paper extends the canonical representative agent Ramsey model to include heterogeneous agents... more The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.
This paper considers an endogenous growth model with human capital accumulation. It gives suffici... more This paper considers an endogenous growth model with human capital accumulation. It gives sufficient conditions and a necessary condition for the existence of a unique competitive equilibrium with externalities. These conditions are more stringent than those which prevail for the existence of an equilibrium defined as the solution to a fixed-point problem.
We address the fundamental issues of existence and efficiency of a Ramsey equilibrium with hetero... more We address the fundamental issues of existence and efficiency of a Ramsey equilibrium with heterogenous discounting, elastic labor supply and borrowing constraints.
We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in wh... more We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinitedimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics.
The main contribution of the paper is to provide a weaker nonsatiation assumption than the one co... more The main contribution of the paper is to provide a weaker nonsatiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points inside the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends (See Aumann and Dreze (1986), ) is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner's (1987) assumption. JEL classification codes: D51, C71.
In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, We... more In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (Econometrica, 1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner's existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents' preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades -that is, as long as agents' preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to * The authors are grateful to an anonymous referee for many helpful comments. transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation -a condition considerably weaker than local or global nonsatiation -that makes possible this transformation.
In order to link production prices and general equilibrium theories, we consider an intertemporal... more In order to link production prices and general equilibrium theories, we consider an intertemporal discrete time economy with fmitely many, infinitely lived consumers, and finitely many, infinitely lived firms. On the production side, our assumptions are those of a Leontief economy. We obtain two main results: Under standard assumptions, this intertemporal model has an equilibrium such that at each period the rate of maximum profit is uniform among producers. The second result is in the spirit of the Samuelson-Solow theorem. Let us consider prices of production as stationary prices which equalize the rate of maximum profit. Under mild conditions such a price system exists and is unique and the sequence of the undiscounted prices of the equilibrium defined above converges to it. 0304-4068/89/$3.50 0 1989, Elsevier Science Publishers B.V.
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