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Walras's law is stated for an exchange market: each agent comes to the market with a certain endowment of each commodity, a price-vector is determined, and the demand of each agent is the best bundle that the agent can afford by selling his endowment in the given prices. Walras's law says that, in any price-vector, the total value of the excess demand (i.e., the price-vector times the excess-demand vector) is zero.

There is a different model called a Fisher market, in which each agent comes with a certain budget of fiat money, the market-manager comes with a fixed quantity of each commodity, a price is determined, and the demand of each agent is the best bundle that the agent can afford with his given budget. In such a market, it does not seem true that the total value of the excess demand is zero. For example, if the prices are very low, then all agents will want to buy all commodities, so the excess demand will be positive. Is there a variant of Walras's law that holds in a Fisher market?

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  • $\begingroup$ In equilibrium, the excess demand for each and every commodity is zero. Walras's law says that, in any price-vector, while there may be positive excess-demand in one commodity, there is negative excess-demand in other commodities, so that the sum of the prices of all excess demands equals zero. This law is a key part in proving the existence of general equilibrium. $\endgroup$ – Erel Segal-Halevi Dec 25 '18 at 14:29
  • $\begingroup$ In your Fisher market, prices should increase until an equilibrium is reached $\endgroup$ – Henry Dec 26 '18 at 12:17

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