12. Equilibrium and Welfare

Find competitive equilibrium in the Edgeworth box and see Pareto efficiency and the two welfare theorems with your own eyes.

• The Edgeworth Box and Competitive Equilibrium — The box holds everything two people own. Endowments, offer curves, and the contract curve all appear in one picture. The contract curve collects points where neither person can do better without hurting the other. At the equilibrium price, one budget line touches both indifference curves at once. That tangency is the competitive equilibrium. The thick part of the curve is the core, which no one can block. For example, say you hold 7 🍎 apples and 3 🍌 bananas. Your 🧑 friend holds 7 bananas and 3 apples. You like bananas more, and your friend likes apples more. Trading makes both of you happier. When no trade helps anymore, you land on a point of the contract curve.
• The Two Welfare Theorems — Walk along the utility possibility frontier. Pick a point with the slider and move it around. The competitive equilibrium always sits on the frontier. That is the First Welfare Theorem. Other points on the frontier are reachable too. Support the point with the right price and shift income in one lump sum. Then the market lands there by itself. That is the Second Theorem, and the formula below gives the transfer. For example, say you and a 🧑 friend split 10 🍬 candies. Every split that uses all 10 is efficient. But if your friend's share feels too small, there is a fix. Hand a few candies to your friend before trading starts. Then plain market trading reaches the split you wanted.