By Gerard Debreu, Werner Hildenbrand
Those twenty papers have been chosen by means of the writer. The publication features a significant advent by way of Werner Hildenbrand, who assesses Professor Debreu's contribution to financial conception and explains the half performed by way of those papers within the improvement of the topic.
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Additional info for Mathematical Economics: Twenty Papers of Gerard Debreu
We impose on the economic system the constraints defined by (1) the set of possibilities of each production unit and (2) the condition that for each consumption unit the satisfaction sf is at least equal to a given value s°. We cannot decrease indefinitely the / quantities of available physical resources. In trying to do so we would find situations where it is impossible to decrease one of them without making at least one other one increase. In any one of these situations the prescribed levels of satisfaction have been attained with as small an amount of physical resources as possible, and it can be considered optimal.
44 However, I would like to emphasize that Debreu's fundamental insight when writing the short but profound paper, "A Social Equilibrium Existence Theorem" (1952), turned out much later to be extremely fruitful. In fact, the excess demand approach fails to work if preferences are not necessarily transitive and complete because then the demand correspondence need not be convex-valued. The remarkable existence theorem of A. Mas-Colell (1974)45 and extensions of it to the case where externalities in comsumption and production are allowed can most easily be obtained by a generalization of Debreu's "Social Equilibrium Existence Theorem" (1952) due to W.
N o . 171, Paris (1968), pp. 85-90. ] P. A. Samuelson (1947), p. 257. 212 Cambridge University Press, 2006 Downloaded from Cambridge Books Online by IP on Mon Jan 12 12:20:11 GMT 2015. 001 Cambridge Books Online © Cambridge University Press, 2015 26 Mathematical economics Now the reason for this sterility of the Walrasian system is largely, I believe, that he (Walras) did not go on to work out the laws of change for his system of General Equilibrium. He could tell what conditions must be satisfied by the prices established with given resources and given preferences, but he did not explain what would happen if tastes or resources changed.
Mathematical Economics: Twenty Papers of Gerard Debreu by Gerard Debreu, Werner Hildenbrand