13. The Positive Theory of Equilibrium

Does equilibrium exist, is it unique, can we get there — answered through the geometry of excess demand and tatonnement dynamics.

• Tatonnement Dynamics — Watch an auctioneer hunt for equilibrium by calling out prices. Each call compares demand with supply, then moves the price. If 🧑 people queue up to buy, the price goes up. If goods pile up unsold, the price goes down. Small careful steps land right on the equilibrium. Huge hasty steps overshoot and drift away. The formula below is exactly this adjustment rule. For example, a 🏪 shop owner rewrites the 🍎 apple price tag every day. Sold out means the price goes up; rotting leftovers mean it goes down. Raise it all at once and every customer walks away. Nudge it little by little and the right price appears.
• Excess Demand: Existence and Uniqueness — Measure how much extra people want at each price and draw it as a curve. Where the curve crosses zero is the equilibrium. A positive excess means buyers want more than sellers offer. A negative excess means the opposite. In a well-behaved economy the curve crosses zero exactly once. But that is a gift, not a guarantee. Switch the mode and you can watch it cross three times. For example, call out 🍞 bread prices from 100 up to 1,000 won. Priced too cheap, 🧑 people line up to buy. Priced too dear, loaves pile up unsold. Only at the right price is there no line and no leftovers. That price is the equilibrium.