Growth and convergence in a model with renewable and non-renewable resources: existence, transitional dynamics, and empirical evidence

This paper studies an optimal endogenous growth model using physical capital, labor and two kinds of natural resources in the final goods sector and employing labor to accumulate knowledge. Based on results in calculus of variations, a direct proof of existence of optimal solution is provided. Analytical solutions for the planner case and the balanced growth paths are found for a specific CRRA utility and Cobb-Douglas production function. Transitional dynamics to the steady state from the theoretical model are used to derive three convergence equations of output intensity growth rate, exhaustible resource growth rate and renewable growth rate, which are tested based on data on production and energy consumption in 27 OECD countries.Optimal growth, existence of equilibrium, transitional dynamics, energy, renewable resource, non-renewable resource.

The Lagrange multipliers and existence of competitive equilibrium in an intertemporal model with endogenous leisure

This paper proves the existence of competitive equilibrium in a single sector dynamic economy with elastic labor supply. The method of proof relies on some recent results (see Le Van and Saglam [2004]) concerning the existence of Lagrange multipliers in infinite dimensional spaces and their representation as a summable sequence.Optimal growth model, Lagrange multipliers, competitive equilibrium, elastic labor supply.

ON NECESSARY CONDITIONS FOR EFFICIENCY IN DIRECTIONALLY DIFFERENTIABLE OPTIMIZATION PROBLEMS

This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions. A theorem of the alternative of Tucker type is established, and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Theorem of the alternative, Kuhn-Tucker necessary conditions, direc- tionally differentiable functions.

On constraint qualifications with generalized convexity and optimality conditions

This paper deals with a multiobjective programming problem involving both equality constraints in infinite dimensional spaces. It is shown that some constraint qualifications together with a condition of interior points are sufficient conditions for the invexity of constraint maps with respect to the same scale map. Under a new constraint qualification which involves an invexity condition and a generalized Slater condition a Kuhn-Tucker necessary condition is established.Invexity, scale, constraint qualification, nearly S-convelike mapping.

Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure

We prove the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents and elastic labor supply. The method of proof relies on exploiting the existence of Lagrange multipliers in infinite dimensional spaces and the link between Pareto-optima and competitive equilibria.Optimal growth model, Lagrange multipliers, single-sector growth model, competitive equilibrium, elastic labor supply.

The Lagrange multipliers and existence of competitive equilibrium in an intertemporal model with endogenous leisure

URL des Cahiers : https://halshs.archives-ouvertes.fr/CAHIERS-MSECahiers de la MSE 2005.41 - Série Bleue - ISSN : 1624-0340This paper proves the existence of competitive equilibrium in a single sector dynamic economy with elastic labor supply. The method of proof relies on some recent results (see Le Van and Saglam [2004]) concerning the existence of Lagrange multipliers in infinite dimensional spaces and their representation as a summable sequence.Cet article prouve l'existence de l'équilibre concurrentiel dans une économie dynamique d'un seul vecteur avec l'offre de travail élastiques. La méthode de preuve se fonde sur quelques résultats récents (voir Le Van et Saglam [2004]) au sujet de l'existence des multiplicateurs de Lagrange dans les espaces dimensionnels infinis et leur représentation comme une série sommable