An Arrow-Debreu state price is the price today of one unit of payoff delivered only if a particular future state of the world occurs.
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Why state prices matter
State prices decompose asset values into prices for individual contingencies. If an asset pays (x_s) in state (s), then under the Arrow-Debreu framework its price can be written as:
$$
P_0 = \sum_s q_s x_s
$$
where (q_s) is the state price for state (s).
Economic interpretation
A high state price means payoff in that state is especially valuable today. That can happen because the state is likely, because people particularly value consumption there, or both. State prices therefore combine beliefs about probability with preferences about risk and timing.
Why economists use them
State prices are a foundation for asset pricing, risk sharing, and no-arbitrage valuation. Even when markets are not literally complete, the concept helps explain how securities can be valued by decomposing payoffs across future states.
Knowledge Check
### An Arrow-Debreu state price is the price of:
- [x] one unit of payoff in one specific future state
- [ ] one unit of GDP today
- [ ] one share of any company
- [ ] a guaranteed risk-free bond coupon only
> **Explanation:** State prices are contingent on a particular state of the world.
### Why can state prices differ across states?
- [x] Because states differ in probability and in how valuable consumption is there
- [ ] Because all states are economically identical
- [ ] Because prices ignore risk
- [ ] Because assets pay the same in every state
> **Explanation:** State prices reflect both uncertainty and how much agents value resources in each outcome.
### Why are state prices useful in valuation?
- [x] They let economists express an asset price as the sum of state-contingent payoff values
- [ ] They eliminate the need for expectations
- [ ] They apply only to labor markets
- [ ] They make arbitrage impossible by assumption alone
> **Explanation:** Decomposing payoffs by state is one of the basic ideas behind contingent-claim pricing.