Mathematical Economics: Twenty Papers of Gerard Debreu by Gerard Debreu, Werner Hildenbrand

By Gerard Debreu, Werner Hildenbrand

Those twenty papers have been chosen by way of the writer. The e-book encompasses a significant creation by way of Werner Hildenbrand, who assesses Professor Debreu's contribution to monetary idea and explains the half performed by means of those papers within the improvement of the topic.

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Debreu, A Social Equilibrium Existence Theorem, Proceedings of the National Academy of Sciences of US A , 38 (1952): 8 8 6 - 9 3 . [ C h a p t e r 2 in this b o o k . ] S. K a k u t a n i , A Generalisation of Brouwer's Fixed Point Theorem, Duke Mathematical Journal, 8 (1941): 4 5 7 - 9 . J. v o n N e u m a n n , U b e r ein okonomisches Gleichungssystem u n d eine Verallgemeinerung des Brouwerschen Fixpunktsatzes, Ergebnisse eines mathematischen Kolloquiums, No. 8 (1937): 73-83. Translated in Review of Economic Studies, 13 (1945): 1-9.

001 Cambridge Books Online © Cambridge University Press, 2015 Introduction 27 dominant role in mathematical economics. One might object to this conclusion on the grounds that the above mentioned constructions of an economy are not subject to any restriction of the distribution of agents' characteristics. Yet, in general, what are reasonable restrictions on the distribution of agents' characteristics in a pure exchange economy other than a restriction on the fixed total supply? Clearly, if/ is an excess demand function, then the total resources eh of commodity h for any exchange economy that generates the function / must be larger than bh = sup p (—fh(p))- It is true that in Debreu's construction the economy has total endowments that are much larger than this bound, namely, 3/ 2 • bh.

Z°. A proper choice of (at) can lead to any given point s° e S m a x that one wishes to attain. 12 If the activity of the economic system extends over t successive time intervals of equal length, the subscript h can be made to characterize the time interval as well. Nothing is changed in the preceding analysis; p now need only be interpreted as a set of actual prices for present and future commodities. 13 They required unnecessary restrictive assumptions on the existence of derivatives, assumptions which cannot be made, for example, in the very simple and realistic case of linear 1 * Unless, of course, 3 m i n is a smooth surface having only one normal direction at each point.

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