Edgeworth Box - Pareto Set

Pareto Set

Wherever one of these curves for Abby happens to just touch (but not cross) a curve of Octavio's (that is, the two curves are tangent at a single point), a combination of the two goods is identified that yields both consumers a level of utility that could not be improved for one person by a reallocation without decreasing the utility of the other person. Such a combination of goods is said to be Pareto optimal. The set of tangential points of contact between pairs of indifference curves, if all traced out, will form a trace connecting Octavio's origin (O) to Abby's (A). This curve connecting points O and A, which will not in general be a straight line, is called the Pareto set or the efficient locus, since each point on the curve is Pareto optimal.

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, Winston, and Green (1995) 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 theoretical bent, such as Martin Osborne and Ariel Rubinstein (1994), use the term core for the section of the Pareto set which is at least as good for each consumer as the initial endowment.

In order to calculate the Pareto set, the slope of the indifference curves for both consumers must be calculated at each point. That slope is the negative of the marginal rate of substitution, so since the Pareto set is the set of points where both indifference curves are tangent, it is also the set of points where each consumer's marginal rate of substitution is equal to that of the other person.