Walras's law is ensured if every agent's budget constraint holds with equality. An agent's budget constraint is an equation stating that the total market value of the agent's planned expenditures, including saving for future consumption, must be less than or equal to the total market value of the agent's expected revenue, including sales of financial assets such as bonds or money. When an agent's budget constraint holds with equality, the agent neither plans to acquire goods for free (e.g., by stealing), nor does the agent plan to give away any goods for free. If every agent's budget constraint holds with equality, then the total market value of "all" agents' planned outlays for "all" commodities (including saving, which represents future purchases) must equal the total market value of all agents' planned sales of all commodities and assets. It follows that the market value of total excess demand in the economy must be zero, which is the statement of Walras's law. Walras's law implies that if there are "n" markets and "n" – 1 of these are in equilibrium, then the last market must also be in equilibrium, a property which is essential in the proof of the existence of equilibrium. Consider an exchange economy with formula_5 agents and formula_6 divisible goods. For every agent formula_7, let formula_8 be their initial endowment vector and formula_9 their Marshallian demand function (demand vector as a function of prices and income). Given a price vector formula_10, the income of consumer formula_7 is formula_12. Hence, their demand vector is formula_13. The excess demand function is the vector function:  Walras's law can be stated succinctly as:  PROOF: By definition of the excess demand:  The Marshallian demand is a bundle formula_17 that maximizes the agent's utility, given the budget constraint. The budget constraint here is: Hence, all terms in the sum are 0 so the sum itself is 0. Neoclassical macroeconomic reasoning concludes that because of Walras's law, if all markets for goods are in equilibrium, the market for labor must also be in equilibrium. Thus, by neoclassical reasoning, Walras's law contradicts the Keynesian conclusion that negative excess demand and consequently, involuntary unemployment, may exist in the labor market, even when all markets for goods are in equilibrium. The Keynesian rebuttal is that this neoclassical perspective ignores financial markets, which may experience excess demand (such as a "liquidity trap") that permits an excess supply of labor and consequently, temporary involuntary unemployment, even if markets for goods are in equilibrium.