DONALD J. BROWN
Donald Brown's contributions to economics are remarkable in their variety, originality, and depth. His first work in economics, some of it developed in collaboration with the great mathematician Abraham Robinson, was to represent the concept of perfect competition by an economy with a nonstandard number of infinitesimal agents. Brown demonstrated the existence of a nonstandard equilibrium and showed that it was identical to the nonstandard core. His paper, "Testable Restrictions on the Equilibrium Manifold," written with Rosa Matzkin, initiated an entirely new field that has been actively pursued by many subsequent scholars. Brown and Matzkin presented a system of inequalities that observations on market prices, individual incomes, and aggregate endowments must satisfy in order to be consistent with the equilibrium behavior of some pure trade economy. Brown and Chris Shannon—in response to the work of Hugo Sonnenschein, Rolf Mantel, and Gerard Debreu—demonstrated, in "A Uniqueness, Stability and Comparative Statics in Rationalizable Walrasian Markets," that no significant behavior implied by individual utility maximization is preserved in the aggregate, and exhibited even more negative results on the implications of the Walrasian model. They showed that a finite dataset can never be used to refute the hypothesis that equilibria are locally unique or locally stable, or that equilibrium comparative statics are locally monotone. Brown's work with Geoffrey Heal on equilibrium analysis in economies with nonconvex technologies illuminated the major problem of economies of scale and its treatment by alternatives to conventional profit maximization. They showed that partial equilibrium prescriptions for the regulation of a public monopoly can be seen as marginal or average cost pricing equilibria. His paper with Peter DeMarzo and Curtis Eaves on incomplete markets, "Computing Zeros of Sections of Vector Bundles Using Homotopies and Relocalization," is an extremely significant piece of research. In equilibrium models with incomplete markets, demand functions are typically not continuous at prices for which a marketed asset becomes redundant. The authors showed, however, that this discontinuity disappears if a new asset is introduced when such redundancies occur. This assumption allowed them to prove generic existence and also to compute equilibria in the case of general equilibrium with incomplete markets. As further proof of his breadth, Brown has made important contributions to econometrics and to the study of economics with infinitely many goods. He is highly regarded for his leadership as chairman of the Yale University Department of Economics. He has been a wonderful colleague, teacher, and warm friend, both to fellow researchers and to young students. American Economic Review, June 2007 |
