## Three lectures on the Walrasian hypotheses for exchange economies |

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Afriat inequalities Afriat's theorem agent aggregate axiom of revealed Balasko budget constraint concave function concave utility function convex convex function convolution distribution economies equilibrium manifold equilibrium price system equivalent excess demand function exchange economies existence theorem family of polynomial finite data sets finite family Fourier-Motzkin elimination income distribution indirect utility function individual consumption individual demand individual endowments Koichi Hamada lecture linear inequalities locally monotone marginal utilities market clearing market data market excess demand meaningful theorem monotone comparative statics monotone utility function non-satiated utility function observed equilibrium price Observed market demand polynomial inequalities price adjustment mechanism price vector prices and consumption properties provides an algorithm quantifier elimination rationalize the data refutable revealed preference Samuelson satisfied second derivative set of inequalities smooth characteristics Sonnenschein-Debreu-Mantel theorem system of polynomial T. N. Srinivasan Tarski-Seidenberg algorithm Tarski-Seidenberg theorem tatonnement price adjustment testable restrictions uniqueness unobservables utility levels utility maximization subject variables Walrasian correspondence Walrasian hypotheses Walrasian model