Example
Imagine two people (Octavio and Abby) with a fixed amount of resources between the two of them — say, 10 liters of water and 20 hamburgers. If Abby takes 4 liters of water and 5 hamburgers, then Octavio is left with 15 hamburgers and 6 liters of water. The Edgeworth box is a rectangular diagram with Octavio's Origin on one corner (represented by the O) and Abby's origin on the opposite corner (represented by the A). The width of the box is the total amount of one good, and the height is the total amount of the other good. Thus, every possible division of the goods between the two people can be represented as a point in the box.
Indifference curves (derived from each consumer's utility function) can be drawn in the box for both Abby and Octavio. The points on, for example, one of Octavio's indifference curves represent equally-liked combinations of quantities of the two goods. Hence Abby is indifferent between one combination of goods and another on any one of her indifference curves, and the same is true for Octavio. For example, Abby might value 1 liter of water and 13 hamburgers the same as 5 liters of water and 4 hamburgers, or 3 liters and 10 hamburgers. There are an infinite number of such curves that could be drawn among the combinations of goods for each consumer (Octavio or Abby).
With Octavio's origin (the point representing zero of each good) at the lower left corner of the Edgeworth box and with Abby's origin at the upper right corner, typically Octavio's indifference curves would be convex to his origin and Abby's would be convex to her origin.
When an indifference curve for Abby crosses one of the indifference curves for Octavio at more than one point (so the two curves are not tangent to each other), a space in the shape of a lens is created by the crossing of the two curves; any point in the interior of this lens represents an allocation of the two goods between the two people such that both people would be better off, since the point is on an indifference curve farther from both of their respective origins.
Read more about this topic: Edgeworth Box
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