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| Volume 2, Number 3, September 2006, pp. 469-485 | ||||||||
| Jean-Marc Bonnisseau and Oussama Lachiri | ||||||||
| Key words: | ||||||||
| multi-objective optimization, extremal principle, non-smooth analysis, non-convex programming, first-order necessary conditions, Second Theorem of Welfare economics | ||||||||
| Mathematices Subject Classification: 49K27, 49J52, 90C26, 91B50 | ||||||||
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| Abstract: | |||
| This paper discusses necessary optimality conditions for multi-objective optimization problems with application to the Second Theorem of Welfare Economics. We use the extremal principle, since we consider non-convex sets and non-smooth functions. Particularly, we develop a slight generalization of the main result of Jofr\'e--Rivera [9], which allows more flexibility in a stochastic economy with production and stock market. Formally, we define a stock market equilibrium through the necessary optimality conditions at a constrained Pareto optimal allocation. We show that the Second Theorem of Welfare Economics holds in a two-period framework. But, by mean of an example, we show that this later result is no longer true for multi-period economies. | |||
| About the second theorem of Welfare economics with stock markets | ||