We present a finite system of polynomial inequalities in unobservable endogenous variables and market data that observations on market prices, individual incomes and aggregate endowments must satisfy to be consistent with the equilibrium behavior of some pure exchange economy. We also derive a corresponding family of polynomial inequalities for production economies. For these economies, we give necessary and sufficient conditions in terms of observations on market prices, aggregate endowments, individual profit shares, and individuals' income from their endowments for these observations to be consistent with the equilibrium behavior of some production economy. We use quantifier elimination to derive for both the two-person model of pure exchange and the two-sector general equilibrium model comparative statics relationships between two observations on market data that are necessary and sufficient for the existence of utility functions and production functions which are consistent with equilibrium behavior in the pure exchange economy and the two-sector model.
