15. General Equilibrium under Uncertainty

State-contingent commodities and Arrow–Debreu equilibrium — the mutuality principle of full insurance and the scarcity premium in state prices.

• Arrow–Debreu Equilibrium — An Edgeworth box for consumption in each state. Two people share each other's risk here. With no risk for the whole economy, they insure each other. Both consume exactly the same in every state. That is full insurance, the mutuality principle. When the whole economy shakes, everyone shakes together. For example, Minsu grows 🍎 apples and Jihoon grows 🍌 bananas. If only Minsu's harvest fails, Jihoon shares. If only Jihoon's fails, Minsu shares. Both eat the same every year. But if the whole country's harvest fails, there is nothing to share.
• State Prices and Scarcity — Three states, with probabilities and state prices side by side. A state price is not a raw probability. It is a probability weighted by marginal utility. A dollar in the scarcest state costs the most. The formula below shows exactly that weighting. For example, a village usually has plenty of 🍞 bread. In a famine year, bread is very scarce. Money to spend in that year is worth far more than money in a normal year.