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Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.
A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the marginal rate of substitution is the same for all consumers. [5] A formal statement can be derived by considering a system with m consumers and n goods, and a utility function of each consumer as = where = (,, …,) is the vector of goods, both for all i.
Constrained Pareto efficiency is a weakening of Pareto optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual ...
Still, Pareto efficiency could also characterize one dimension of a particular social welfare function with distribution of commodities among individuals characterizing another dimension. As Bergson noted, a welfare improvement from the social welfare function could come from the "position of some individuals" improving at the expense of others.
There are as many optima as there are points on the aggregate production–possibility frontier. Hence, Pareto efficiency is a necessary, but not a sufficient condition for social welfare. Each Pareto optimum corresponds to a different income distribution in the economy. Some may involve great inequalities of income.
A government facing the same information constraints as the private individuals in the economy can nevertheless find Pareto-improving policy interventions. [ 34 ] Greenwald and Stiglitz noted several relevant situations, including how moral hazard may render a situation inefficient (e.g. an alcohol tax may be pareto improving as it reduces ...
The benefits formula includes "bend points," which are adjusted annually based on wage inflation. These adjustments are crucial because the actual amount of the WEP reduction is determined the ...
Pareto efficiency is achieved when the marginal rate of transformation (slope of the frontier/opportunity cost of goods) is equal to all consumers' marginal rate of substitution. Similarly, not all Pareto efficient points on the frontier are Allocative efficient. Allocative efficient is only achieved when the economy produces at quantities that ...