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.
... out of which 35.3% have children under the age of 18 living with them, 59.8% are married couples living together, 11.1% have a female householder with no husband ...