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What is Optimization in Welfare Economics about?

Optimization in Welfare Economics ### 8.1. Static and dynamic optimization Optimal social welfare is generally defined with Pareto's mathematical definition of optimality of a vector objective function (see section 2.8). The analysis of social welfare and social choice (see Arrow and Reynaud, 1986; Arrow, Sen and Susumura, 2003; Schulz, 1988) also depend on vector optimization. Economic developments of these ideas are presented e.g in Sengupta and Fox (1969), Ehrgott (2000). In Islam (2001a), such ideas are applioed to decentralized and to centrally planned economies. Social welfare cannot always be measured by summing individual utilities, and a vector of utilities must be studied, with appropriate vector ordering (see e.g. Arrow and Scitovsski, 1969; Arrow and Intriligator, 1985; Sen, 1969). An economic model may maximize (in Pareto's sense) several competing welfare criteria or utilities u i (•), or maximize some welfare function W (u 1 (•), u 2 (•), . . .), subject to constraints g i (x) ≥ 0, and perhaps also equality constraints. The classical economic assumptions of nonsatiety of utility, and convexity of preference and production sets, are usually made here, but may be relax

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