An Edgeworth box (named after Irish philosopher and economist Francis Ysidro Edgeworth,) is a two-dimensional depiction of a simple, closed economy consisting of two individuals and two goods (or resources) that are limited in supply. It is a graphical representation of the exchange problem facing these people and also gives a clear-cut solution to their exchange problem.
Let us assume that there are only two individuals, A and B, and two commodities, x and y. These quantities are measured along the opposite sides of the Edgeworth box. Any point of the Edgeworth box shows a certain distribution of the available quantities of x and y between individuals A and B. The preferences of consumer A are represented by a set of indifference curves (denoted by A) which are convex to the origin 0A. The preferences of consumer B are represented by the set of indifference curves (denoted by B ) which are convex to 0B .
Figure 1: Edgeworth Box Diagram
Further down an indifference curve of B lies, the greater is the satisfaction. The two sets of indifference curves, being of opposite curvature, have points of tangency which form the so-called Edgeworth’s contract curve (0A 0B in figure 1). In other words the contract curve is the locus of points of tangency of the indifferencecurves of A and B, and therefore the locus of points at which the MRS of thetwo commodities is the same for both consumers
MRSA Y,X = MRSB Y,X
Only points lying on the contract curve represent the optimal distribution of the available quantities of x and y between the two consumers, in the sense that any divergence from this curve implies a lower level of satisfaction for at least one individual.
For example, consider point Z off the contract curve. At this point consumer A owns OXA of commodity x and OYA of commodity y, with the remaining quantities (XAX and YAY) owned by consumer B. With this distribution of the two commodities consumer A is on indifference curve A4 while consumer B is on indifference curve B5 • The point Z represents a suboptimal distribution of x and y, because if A and B exchange some of the quantities of the two commodities so as to move to any point on the section WR of the contract curve at least one (and probably both) of them will be better off (on a higher indifference curve) without the other being worse off.
If the consumers exchange x for y so that they arrive at the distribution denoted by R (consumer A giving away YAY’A of commodity y in exchange for XAX’A of commodity x), consumer A will reach a higher welfare situation (moving from indifference curve A4 to the higher one A6 ) while consumer B retains his initial level of satisfaction (both Z and R lying on the same indifference curve B5 ). If the consumers reach, via exchanging commodity x for y, to the distribution denoted by W the opposite situation will obtain: consumer A will retain his initial level of satisfaction (since Z and W lie on the initial indifference curve A4 ) while consumer B will attain a higher indifference curve (B7). If the consumers reach any other distribution between Wand R, e.g. the one denoted by H, they will both be better off, reaching higher indifference curves (A5 and B6 respectively) as compared to their initial positions at Z.
If exchange takes place who will benefit more, A or B? The answer to this question cannot be given on purely economic criteria. The final distribution of x and y and the ‘gains’ from the exchange of these commodities will largely depend on the bargaining skills and power of the two individuals. Usually, the consumers will reach a point between W and R, both gaining some welfare in the process.