Walras’s Law: Definition and Overview
Walras’s law is a principle from general equilibrium theory stating that the value of aggregate excess demand across all markets must equal zero. In practical terms, if every market except one is in equilibrium (supply equals demand), the remaining market must also clear. Put another way: an excess supply (or demand) in one market must be offset by excess demand (or supply) elsewhere when measured in value terms.
Historical background
The law is named for Léon Walras (1834–1910), a founder of neoclassical economics and the Lausanne School. Walras developed general equilibrium theory in his Elements of Pure Economics (1874), showing how prices across interdependent markets can adjust to clear supply and demand simultaneously.
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How it works
- Markets are linked by agents’ budget constraints: the total value of what agents demand cannot exceed the total value of what they supply.
- Formally, if p denotes the vector of prices and z(p) the vector of excess demands, Walras’s law can be written as p · z(p) = 0. This implies the value-sum of excess demands is zero.
- The mechanism often invoked is the “invisible hand”: where there is excess demand, prices tend to rise; where there is excess supply, prices tend to fall. Price adjustments across markets move the economy toward a general equilibrium.
Key assumptions
Walras’s law relies on several standard assumptions of general equilibrium models:
– Agents are rational and act to maximize utility (consumers) or profit (firms).
– Markets are flexible and prices adjust freely.
– Preferences and technologies are well-defined so that demand and supply functions exist.
– Budget constraints bind agents, linking demands across markets.
Implications
- If all but one market clear, the final market must clear too (value-wise). This property simplifies theoretical analysis of multi-market economies.
- It underpins existence proofs for general equilibrium and motivates comparative statics in multi-market models.
Limitations and criticisms
- Price rigidities, transaction costs, rationing, and other real-world frictions can prevent markets from clearing, so the law’s predictions may not hold in short run or noncompetitive settings.
- Walras’s framework depends on the ability to aggregate individual preferences into market demand; critics argue that “utility” is a subjective concept that is difficult to measure and aggregate in practice.
- Keynesian economics highlights situations where one market (e.g., labor) can remain out of equilibrium without immediate compensating imbalances elsewhere, particularly when prices or wages are sticky.
- Empirical observation often finds persistent disequilibria in particular markets even when others appear balanced.
Conclusion — Key takeaways
- Walras’s law is a foundational result of general equilibrium theory: the value-weighted sum of excess demands across all markets is zero.
- It formalizes the idea that imbalances in one market are linked to imbalances in others via agents’ budget constraints.
- The law is powerful for theoretical analysis but depends on assumptions (flexible prices, rational agents, aggregable utility) that may not hold in real-world settings, limiting its direct empirical application.