Edgeworth Box

An Edgeworth box, named after Francis Ysidro Edgeworth, is a way of representing various distributions of resources. Imagine two people (Mahesh and Abhay) with a fixed amount of resources between the two of them - say, 10 liters of water and 20 cakes. If Mahesh takes 5 liters of water and 4 cakes, then Abhay is left with 14 cakes and 6 liters of water. The Edgeworth box is a rectangular diagram (see below) with Mahesh's origin on one corner (represented by the O) and Abhay's origin on the opposite corner (represented by the A). The width of the box is the total amount of one good (here cakes), and the height is the total amount of the other good (here water). Thus, all possible distributions of the goods between the two people can be represented as a point in the box.

The curve connecting points O and A is often called the contract curve. In above figure two different combination of goods distribution is shown between Mahesh and Abhay. There may be infinite numbers of curves. The goods distribution represented by points will lie over the distribution curves. The solid dot shows goods taken by Mahesh (4 cakes and 2.5 lt water) and hollow dot shows goods taken by Abhay(16 cakes and 7.5 lt water). The sum of identical goods taken by both are equal to the total available goods.  Edgeworth's original two-axis depiction was developed into the now familiar box diagram by Pareto in 1906 and was popularised in a later exposition by Bowley. The modem version of the diagram is commonly referred to as the Edgeworth-Bowley box.