Arrow's impossibility theorem was set out in his PhD thesis, Social choice and individual values. It shows the impossibility of designing rules for social decision making that obey all of a number of 'reasonable' criteria. It is often known as Arrow's paradox.
Working with Gerard Debreu[?] (who won the Nobel prize for this work in 1983), Arrow produced the first rigorous proof of the existence of a market clearing equilibrium, given certain restrictive assumptions. See general equilibrium.
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