Lesson preview · Edgeworth Box
The Edgeworth Box
~7 min · Free to read
Imagine John and Lisa stranded on an island with a fixed pile of coconuts and bananas. Each starts with some of each good. Can they trade and both end up happier? To answer this we need a single picture that shows both consumers’ preferences and all ways the goods could be split between them. That picture is the Edgeworth box.
The trick is to draw John’s indifference map normally, then flip Lisa’s map upside-down and slide it on top of John’s. The width of the resulting box equals the total amount of coconuts; the height equals the total amount of bananas. Every point inside the box is a feasible allocation — whatever John doesn’t have, Lisa has.
Key Term
Reading the Edgeworth Box
At any point inside the box:
- John’s bundle is read from the bottom-left origin (right = more coconuts, up = more bananas).
- Lisa’s bundle is read from the top-right origin (left = more coconuts, down = more bananas).
- John’s amount plus Lisa’s amount equals the total endowment, by construction.
John’s indifference curves bow toward the bottom-left; Lisa’s bow toward the top-right.
Now overlay John’s and Lisa’s indifference curves. Wherever the two curves cross, a lens-shaped region opens up between them. Every point inside that lens is better for both consumers than the starting allocation. So crossing curves signal room for mutually beneficial trade.
Trade keeps producing gains as long as the curves keep crossing. Gains are exhausted only when the indifference curves are tangent — touching but not crossing. At a tangency, both consumers’ marginal rates of substitution are equal: . From there, helping one person necessarily hurts the other.
A trade is a Pareto improvement when no one is worse off and at least one person is better off
Worked Example
John has 7 coconuts and 2 bananas. Lisa has 3 coconuts and 8 bananas. At the endowment, John’s (coconuts for bananas) is about 0.15; Lisa’s is about 1.43. Is there room for trade?
Check yourself · no marks
If an allocation is Pareto efficient, does that mean it’s fair?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Practice · 1 / 5
In an Edgeworth box, any point inside the box represents:
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