# Edgeworth box

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Fig. 56 Edgeworth box.

## Edgeworth box

a conceptual device for analysing possible trading relationships between two individuals or countries, using INDIFFERENCE CURVES. It is constructed by taking the indifference map of one individual (B) for two goods (X and Y) and inverting it to face the indifference map of a second individual (A) for the same two goods, as in Fig. 56.

Individual A's preferences are depicted by the three indifference curves A1, A2 and A3, corresponding to higher levels of satisfaction as we move outward from origin OA. Individual B's preferences are depicted by the three indifference curves B1, B2 and B3, corresponding to higher levels of satisfaction as we move outward from origin OB. Both consumers’ preferences as between the two products X and Y are reflected in the slopes of their indifference curves, with the slope of a curve at any point reflecting the MARGINAL RATE OF SUBSTITUTION of X for Y.

Only where individual A's indifference curves are tangential to individual B's indifference curves (points E, F and G in Fig. 56) will A's marginal rate of substitution of product X for product Y be the same as B's marginal rate of substitution of X for Y, so that their relative valuations of the two products are the same. Starting from any other point, say Z, the two can gain by trading with one another.

At point Z, individual A has a lot of product X and little of product Y; consequently, he values product Y more highly than product X, being prepared to give up a lot of product X (X1 X3) to gain just a little of product Y (Y1 Y2). This is why his indifference curve A1 is relatively flat at point Z. On the other hand, at point Z individual B has a lot of product Y and little product X; consequently, he values product X more highly than product Y, being prepared to give up a lot of product Y (Y1 Y3) to gain just a little of product X (X2 X3). This is why his indifference curve B2 is relatively steep at point Z.

These two sets of relative valuations of product X and product Y offer the promise of mutually beneficial exchange. If individual A offers some of his plentiful and low-valued product X in exchange for extra units of scarce and high-valued product Y, he can gain from trade. Similarly, if individual B offers some of his plentiful and low-valued product Y in exchange for extra units of scarce and high-valued product X, he can also gain from trade. The two will continue to exchange product X in return for product Y (individual A) and product Y in return for product X (individual B), until they reach a point, such as E or F, where the indifference curves have the same slope, so that their marginal rates of substitution of the two products are the same.

The contract curve or offer curve in Fig. 56 traces out the path of all the points, such as E, F and G, where the indifference curves are tangential, and if individuals A and B start with any combination of products X and Y other than ones lying along the contract curve, then they have an incentive to redistribute products X and Y between themselves through exchange. Where they come to lie along the contract curve will depend upon their relative bargaining strength and skills. If individual A is the stronger, they may end up at a point like G, far from A's origin, OA, and putting individual A on a high indifference curve, A3; while individual B ends up on a low indifference curve B1 near his origin, OB. On the other hand, if individual B is the stronger, they may end up at a point like E, far from B's origin, OB, and putting individual B on a high indifference curve, B3; while individual A ends up on a low indifference curve, A1, near his origin, OA. See also PARETO OPTIMALITY, THEORY OF CONSUMER BEHAVIOUR, THEORY OF INTERNATIONAL TRADE.

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