The Edgeworth Box:

The pure exchange case is conveniently illustrated in a so called Edgeworth box (see Figure). There are two consumers and two goods; each consumer has an initial endowment of both goods,

ω¹ = (ω¹₁, ω¹₂), and ω² = (ω²₁, ω²₂),

for consumer 1 and 2, respectively. This initial endowment determines the size of the box, and the indifference curves through the endowment point, (ω¹, ω²), determines the consumers’ initial utility levels. The cross-hatched area shows allocations which are better for both, i.e., it shows all mutually beneficial trades. If it is voluntary to engage in trading activity, we can predict that the final allocation will lie somewhere inside this area, e.g., at point (x¹, x²). If this is the final allocation, consumer 1 will sell (ω¹₁ − x¹₁) units of good 1, and buy (x¹₂ − ω¹₂) units of good 2, consumer 2 will sell (ω²₂ − x²₂) units of good 2, and buy (x²₁ − ω²₁) units of good 1.

The curve which is drawn from origin to origin is called a contract curve and it joins together all tangency points of the two consumers’ indifference curves. It is called the contract curve since voluntary negotiations which does not leave out any possibilities for mutually advantage trades (so called “efficient bargaining”) could be predicted to end up somewhere on this curve, the exact point depending on the starting point, i.e., the position of the endowment point.

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