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Alles, was Gegenstand des wissenschaftlichen Denkens iiberhaupt sein kann, verfallt, sobald es zur Bildung einer Theorie reif ist, der axiomatischen Methode und damit mittelbar der Mathematik.
The opening address on the occasion of an important retrospective of a great artist is not expected to include a detailed analysis of all exhibits. Rather, the artist and his work are set in their context in the history of art; those features that characterize his work are highlighted and related to earlier and contemporary contributions. This is what I shall try to do on the present occasion; the reprinting of twenty scientific papers of Gerard Debreu.
The striking feature that characterizes Debreu's scientific contributions is that they are both general and simple - general in the sense of universal, in contrast to ad hoc specific or particular, simple certainly not in the sense of elementary, facile, or effortless, but in the sense of pure in contrast to compound and complex. To sense the depth of Debreu's contributions, one has to understand them in full generality.
These twenty papers were selected by the author. The book includes a major introduction by Werner Hildenbrand, who assesses Professor Debreu's contribution to economic theory and explains the part played by these papers in the development of the subject.
For an economic system with given technological and resource limitations, individual needs and tastes, a valuation equilibrium with respect to a set of prices is a state where no consumer can make himself better off without spending more, and no producer can make a larger profit; a Pareto optimum is a state where no consumer can be made better off without making another consumer worse off. Theorem 1 gives conditions under which a valuation equilibrium is a Pareto optimum. Theorem 2, in conjunction with the Remark, gives conditions under which a Pareto optimum is a valuation equilibrium. The contents of both theorems (in particular that of the first one) are old beliefs in economics. Arrow and Debreu have recently treated this question with techniques permitting proofs. A synthesis of their papers is made here. Their assumptions are weakened in several respects; in particular, their results are extended from finite dimensional to general linear spaces. This extension yields as a possible immediate application a solution of the problem of infinite time horizon (see sec. 6). Its main interest, however, may be that by forcing one to a greater generality it brings out with greater clarity and simplicity the basic concepts of the analysis and its logical structure.
This volume includes papers delivered at the Fourth World Congress of the Econometric Society. It will interest economic theorists and econometricians working in universities, government, and business and financial institutions.
At the Fourth World Congress of the Econometric Society, a number of Symposia were held at which invited papers were given. The purpose of these Symposia was to survey as completely as possible those areas in Economic Theory and Econometrics where important research had come to light during the last few years. This volume includes papers delivered at the Congress.