Walras's law

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Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the values of excess demand (or, conversely, excess market supplies) must sum to zero regardless of whether the prices are general equilibrium prices. That is:

${\displaystyle \sum _{j=1}^{k}p_{j}\cdot (D_{j}-S_{j})=0,}$

where ${\displaystyle p_{j}}$ is the price of good j and ${\displaystyle D_{j}}$ and ${\displaystyle S_{j}}$ are the demand and supply respectively of good j.

Walras's law is named after the economist Léon Walras^[1] of the University of Lausanne who formulated the concept in his Elements of Pure Economics of 1874.^[2] Although the concept was expressed earlier but in a less mathematically rigorous fashion by John Stuart Mill in his Essays on Some Unsettled Questions of Political Economy (1844),^[3] Walras noted the mathematically equivalent proposition that when considering any particular market, if all other markets in an economy are in equilibrium, then that specific market must also be in equilibrium. The term "Walras's law" was coined by Oskar Lange^[4] to distinguish it from Say's law. Some economic theorists^[5] also use the term to refer to the weaker proposition that the total value of excess demands cannot exceed the total value of excess supplies.