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 0_{A}*. *The preferences of consumer B are represented by the set of indifference curves (denoted by *B *) which are convex to *0 _{B}*

*.*

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 *(0_{A} 0_{B} 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

*MRS ^{A} _{Y,X} *=

*MRS*

^{B}_{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 *OX _{A }*of commodity

*x*and

*OY*of commodity

_{A }*y,*with the remaining quantities

*(X*and

_{A}X*Y*owned by consumer

_{A}Y)*B.*With this distribution of the two commodities consumer

*A*is on indifference curve A4 while consumer

*B*is on indifference curve

*B*

*5 •*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 Y_{A}Y’_{A }of commodity y in exchange for X_{A}X’_{A }of commodity x), consumer *A *will reach a higher welfare situation (moving from indifference curve *A _{4}* to the higher one

*A*

_{6}*)*while consumer

*B*retains his initial level of satisfaction (both Z and

*R*lying on the same indifference curve

*B*

*5 ).*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

*A*) while consumer

_{4}*B*will attain a higher indifference curve (B

_{7}). 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

*(A*

_{5 }

*and*

*B*respectively) as compared to their initial positions at

_{6}*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.

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