Indifference Curve vs Edgeworth Box
Indifference Curve and Edgeworth Box are two Microeconomic Theory concepts in AP Economics that students often mix up. An indifference curve shows all combinations of two goods that give a consumer the same total satisfaction (utility). 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. Here is how they compare side by side.
Consumers are indifferent among points on the same curve. Curves farther from the origin represent higher utility. They slope downward and are bowed inward (convex) because of the diminishing marginal rate of substitution; the optimal bundle is where the budget line is tangent to the highest reachable curve.
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.
Indifference Curve vs Edgeworth Box: One Person's Map and Two Maps Facing Each Other
| Indifference Curve | Edgeworth Box | |
|---|---|---|
| How many people are in the picture | One | Two, the second map rotated a half turn |
| What the axes measure | Quantities of two goods a single person could hold | How a fixed total of two goods is split between two people |
| Where the origin sits | Bottom left, and there is only one of them | Two origins, at opposite corners of the box |
| What limits the reachable set | A budget line drawn separately from income and prices | The size of the box, fixed by how much of each good exists |
| What a tangency means | The best bundle this person can afford | A split no further trade can improve, a point on the contract curve |
| Where prices come from | Handed to the consumer from outside the diagram | Settled inside the box, by whatever makes both plans add up |
| Question it answers | What one buyer chooses when prices are given | Which splits are efficient, and which trades both sides accept |
The box is two indifference maps facing each other, and its dimensions are not anybody's choice
Start with one person's map and you have the ordinary picture: apples across, bananas up, curves bending toward the origin. Now add a second person and a fixed stock of goods. Ann and Ben between them hold twelve apples and twelve bananas, so draw a box twelve wide and twelve tall, put Ann's origin at the bottom left and Ben's at the top right with his axes running backwards. Every point inside the box now names two allocations at once, because whatever Ann does not hold, Ben does. Give Ann ten apples and two bananas and Ben automatically holds two apples and ten bananas. Suppose both rank bundles by the square root of the product of what they hold, so each person's rate of substitution equals bananas divided by apples. Ann's is a fifth: she would part with an apple for a fifth of a banana. Ben's is five: he would give five bananas for one more apple. Any exchange rate between those two numbers leaves both better off, which is what unequal rates of substitution always mean. Trade one for one and Ann moves to six apples and six bananas while Ben lands on the same holdings, both rates now equal to 1, and Ann's index climbs from the square root of twenty, near 4.47, to 6. Those gains were sitting on the table only because the starting point left each person rich in the good the other wanted.
Efficient does not mean fair, and the contract curve makes that impossible to hide
Set the two rates of substitution equal and the algebra picks out a line. With Ann holding a apples and b bananas, her rate is b divided by a, and Ben's is twelve minus b divided by twelve minus a. Those match only when b equals a, so the contract curve here is the diagonal running corner to corner, and every point along it is Pareto efficient. That includes the split where Ann holds eleven of each good and Ben holds one of each. Nothing there can be improved without taking something from Ann, so it passes the efficiency test while her index sits at 11 and his at 1. Efficiency asks whether anything has been left on the table, never who ended up holding it. What the endowment decides is which efficient split trade actually reaches. Ann's ten apples and two bananas is off the diagonal, gains from trade exist, and exchange carries the pair to six and six. Start her at eleven and eleven instead and the market leaves her exactly there, because no unexploited trade remains. Arguments about redistribution are therefore arguments about endowments rather than about whether markets work, and ranking the points along the diagonal takes a value judgment the diagram cannot supply on its own. See /glossary/pareto-efficiency and /glossary/social-welfare-function.
Frequently asked questions
Why does an Edgeworth box have two origins?
Each person needs a corner to measure from. Ann's holdings are counted rightward and upward from the bottom left, while Ben's are counted leftward and downward from the top right. Rotating his map a half turn is what allows a single point to describe both people at once, since whatever Ann does not hold must be in Ben's hands. The width and height of the box are the total quantities available, so no point inside it can hand out more than exists.
What does the contract curve show?
Every allocation where the two people's marginal rates of substitution are equal, which is the same as every allocation no further trade can improve. Off the curve, one person values a good more than the other does, and a swap at any rate between their two valuations leaves both better off. On the curve that gap has closed, and helping one person now requires hurting the other. Where trade lands along the curve depends on the endowment the pair started from.
Can a Pareto efficient allocation be unfair?
Handing one person nearly everything is usually efficient. In the example above, Ann holding eleven of each good while Ben holds one of each sits squarely on the contract curve, because moving anything toward Ben costs Ann. The efficiency test asks only whether gains from trade remain, and it stays silent about distribution. Comparing efficient allocations against each other calls for a separate standard, which is the job a social welfare function does.
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