Edgeworth Box
What is Edgeworth Box?
An Edgeworth box is a diagram showing every way two people can divide two goods, used to find the trades that make both better off.
An Edgeworth box puts two consumers' indifference maps into one rectangle. The width is the total amount of good X and the height is the total amount of good Y, and one person's origin sits at the bottom left while the other's sits at the top right, flipped 180 degrees. Every point inside the box is a complete allocation, since whatever one person does not have, the other does. Starting from an endowment point, the lens shaped area between the two indifference curves through it holds all the trades that make both people better off. The tangency points, where the two people's indifference curves just touch and their marginal rates of substitution are equal, are the Pareto efficient allocations; joining them traces the contract curve.
Edgeworth Box: a worked example
Ana and Ben together hold 10 apples and 10 bananas, so the box is 10 wide and 10 tall. The endowment gives Ana 8 apples and 2 bananas, which automatically leaves Ben 2 apples and 8 bananas. Ana has so many apples that she would trade 2 of them for 2 bananas, and Ben, loaded with bananas, would take that deal; afterward Ana holds 6 apples and 4 bananas while Ben holds 4 apples and 6 bananas. Both moved to higher indifference curves, so the swap was inside the lens. Trading stops when their marginal rates of substitution match, which puts them on the contract curve.
The mistake students make with edgeworth box
The usual confusion is reading the second person's axes the normal way. Ben's origin is the top right corner, so his quantities increase down and to the left, and his indifference curves look upside down. Students also assume the contract curve is the middle diagonal. It is a curve set by both people's preferences, and it runs along the diagonal only in special symmetric cases.
Edgeworth Box questions
What does the contract curve show in an Edgeworth box?
The contract curve is the set of all Pareto efficient allocations in the box, the points where the two people's indifference curves are tangent. Anywhere off the curve, some trade still exists that helps at least one person without hurting the other. Which point on the curve they reach depends on where they started and how they bargain.
What is the core in an Edgeworth box?
The core is the part of the contract curve that both people would accept given their starting endowment, meaning neither ends up worse off than before trading. It is the overlap between the efficient allocations and the lens of mutually beneficial trades. Competitive trading at market prices lands somewhere inside the core.
How do you find the gains from trade in an Edgeworth box?
Draw each person's indifference curve through the endowment point; the lens shaped region between them contains every allocation that makes both better off. Any move into that region is a gain from trade, and moves to its edge help only one person. The gains are exhausted at the tangency point inside the lens, which lies on the contract curve.
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