Gale and Mas-Collel and Shafer and Sonnenschein introduced powerful new theorems on the existence of competitive equilibrium which used the assumption that the graph of the strict preference relation P is an open set. We show when this condition is satisfied and when it is not.

One of the most disconcerting results in welfare economics is the "paradox of the second best". In a general equilibrium, if there are distortions in more than one market, it may not be efficient to remove distortions in a single market if the other distortions are not removed as well. In 1970, Sonnenschein and Foster proved a remarkable result that reduced the sting of this paradox. They showed that fairly generally, at least one form of piecemeal reform, namely proportional reduction of price distortions would improve welfare in a one-consumer general equilibrium economy. Trout Rader wrote an interesting paper that extended the Sonnenschein-Foster result. The current paper, examines Rader's contribution and that of Foster and Sonnenschein.