Comparative Statics, English Auctions, and the Stolper-Samuelson Theorem

Changes in the parameters of an n-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight the existence of a common thread, our "own effect" assumption, in formally diverse areas of economics. We discuss several applications; among them we establish the existence of efficient equilibria in English auctions with interdependent valuations, and a version of the Stopler-Samuelson Theorem for an n X n trade model.