Exchange

Two people, two goods, gains from trade

Market analysis so far took prices as given. General equilibrium asks where prices come from. The simplest laboratory is a pure exchange economy: two consumers (A and B), two goods, fixed total supplies, no production. Everything they consume, they already own between them — the question is how they’ll trade.

The Edgeworth box draws it all at once. Its width is the total of good 1, its height the total of good 2. Measure A’s bundle from the bottom-left corner and B’s bundle from the top-right. Every point in the box is a complete allocation — what each person ends up with.

• The endowment ■ is where they start.
• At a price ratio \(p = p_1/p_2\), each consumer trades to their favorite affordable bundle. A competitive equilibrium is a price at which the two plans are compatible — markets clear, so the chosen point is a single dot ● in the box.
• At equilibrium both indifference curves are tangent to the budget line (and to each other). Points where they’re tangent trace the contract curve — the efficient allocations.

With Cobb–Douglas tastes (\(U_A=x^{a}y^{1-a}\), \(U_B=x^{b}y^{1-b}\)) the market-clearing price has a closed form: \[ p=\frac{a\,\omega^A_2+b\,\omega^B_2}{(1-a)\,\omega^A_1+(1-b)\,\omega^B_1}. \]

Try it. Move the endowment and A’s taste. The equilibrium price adjusts so markets clear; the dot ● is the equilibrium allocation, with both indifference curves tangent to the budget line through ■. The grey curve is the contract curve.

A's endowment of good 1 (ω₁ᴬ): 3 A's endowment of good 2 (ω₂ᴬ): 7 A's taste for good 1 (a): 0.60

▬ A indiff.▬ B indiff.▬ budget

What to notice

• Put the endowment ■ off the contract curve and the equilibrium ● sits elsewhere — the two trade their way to an efficient point where neither can do better without hurting the other.
• The equilibrium price line always passes through the endowment: trade is a movement along it, swapping one good for the other at the market rate.
• When A’s taste a equals B’s (both 0.5) and the endowment is already efficient, the price makes the chosen point coincide with the endowment — no trade, because there were no gains to exploit.