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Edgeworth box
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==Pareto set== [[File:Edgeworthpareto1.svg|280px|left|thumb|Fig. 5. Division of the box by two tangential indifference curves]]An allocation of goods is said to 'Pareto dominate' another if it is preferable for one consumer and no worse for the other. An allocation is said to be '[[Pareto optimal]]' (or 'Pareto efficient') if no other allocation Pareto dominates it. The set of Pareto optimal allocations is known as the '''Pareto set''' (or 'efficient locus'). Consider a pair of tangential curves, one for each consumer as illustrated in Fig. 5, where the point of tangency is shown by the purple dot. Then convexity guarantees that the curves cannot intercept other than at the point of tangency, and the box is accordingly divided into 3 regions. The pale blue area is preferable to the point of tangency for Octavio but worse for Abby; the pale orange area is preferable for Abby but worse for Octavio; and the white area is worse for both. Similar considerations apply to the boundaries. It follows that the point of tangency is Pareto optimal. [[File:Edgeworthpareto.svg|280px|thumb|Fig 6. Pareto set (purple line) for an Edgeworth box]]Thus the Pareto set is the locus of points of tangency of the curves. This is a line connecting Octavio's origin (O) to Abby's (A). An example is shown in Fig. 6, where the purple line is the Pareto set corresponding to the indifference curves for the two consumers. The vocabulary used to describe different objects which are part of the Edgeworth box diverges. The entire Pareto set is sometimes called the [[contract curve]], while Mas-Colell et al. restrict the definition of the contract curve to only those points on the Pareto set which make both Abby and Octavio at least as well off as they are at their initial endowment. Other authors who have a more [[game theory|game theoretical]] bent, such as Martin Osborne and [[Ariel Rubinstein]],<ref>{{cite book |title=A Course in Game Theory |last=Osborne |first=Martin J. |author2=Rubinstein, Ariel |year=1994 |publisher=MIT Press |location=Cambridge |isbn=0-262-65040-1 }}</ref> use the term [[core (economics)|core]] for the section of the Pareto set which is at least as good for each consumer as the initial endowment. Since the Pareto set is the set of points where the consumers' indifference curves are tangential, it is also the set of points where each consumer's marginal rate of substitution is equal to that of the other person.<ref>The Cobb-Douglas Ξ±s for the illustrations are 0Β·35 (Octavio) and 0Β·65 (Abby).</ref>
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