By Donald G. Saari (auth.), Prof. C. D. Aliprantis, Prof. O. Burkinshaw, Prof. N. J. Rothman (eds.)

ISBN-10: 3540152296

ISBN-13: 9783540152293

ISBN-10: 3642516025

ISBN-13: 9783642516023

**Read Online or Download Advances in Equilibrium Theory: Proceedings of the Conference on General Equilibrium Theory Held at Indiana University-Purdue University at Indianapolis, USA, February 10–12, 1984 PDF**

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**Extra resources for Advances in Equilibrium Theory: Proceedings of the Conference on General Equilibrium Theory Held at Indiana University-Purdue University at Indianapolis, USA, February 10–12, 1984**

**Example text**

I ui Assuming, without loss of generality, is strictly concave we have x n - - x and so, the con- clusion follows by continuity •• REFERENCES ARROW, K. AND F. HAHN (1971), General. Competitive AnaZysis. San Francisco: Holden - Day DEBREU, G. (1959), Theory 01 VaZue. New York: Wiley MAS-COLELL, A. (1983), The price equi1ibrium existence problem in Banach 1attices, mimeographed, Harvard University. MAS-COLELL, A. (1985), The Theory 01 GeneraZ Eaonomia EquiZibrium: A DillerentiabZe Approaah. New York: Cambridge University Press DEPARTMENT OF ECONOMICS HARVARD UNIVERSITY CAMBRIDGE, MA 02138 THE OPTIMALITY OF REGULATED PRICING: AGENERAL EQUILIBRIUM ANALYSIS* Donald J.

Let i=m=l, Y=-lR+, u(x) = IX. and u is concave. ). Then x=O is optimal IX at 0 is not finite For the case of exchange economies, i. , the next and final result gives conditions different from [e] for the existence of a supergradient to V at O. [XVIII] Let Y={W}-E; and define V:A E+ as in [XVII] with respect to some x, u(x) and ). > o. We have: (a) If every ui can be extended to a concave funation defined on Ei, then V has a supergradient at o. iOhui(xi)}. Then q is a supergradient of V at o. 42 PROOF.

Suppose not, i. , z >i Xi and Xi p. z = P,xi. Pick Y E Xi such that p·y

o. By continuity, if a > 0 is small, then (ay+ (l-a)z) >i xi' But p'(ay+ (l-a)z) =ap·y+ (l-a)p·z < P,xi we obtain a contradiction to our hypothesis •• and The next three examples show, respectively, that the assumptions is convex," ">i is continuous" and H p . z: zEX i }" cannot be dispensed from the lemma. "Xi EXAMPLE 3. See Figure 4, where z >i xi but p'z = P·xi' Everything in the line {l} x:R is preferred to anything in the line {O} x lR.

### Advances in Equilibrium Theory: Proceedings of the Conference on General Equilibrium Theory Held at Indiana University-Purdue University at Indianapolis, USA, February 10–12, 1984 by Donald G. Saari (auth.), Prof. C. D. Aliprantis, Prof. O. Burkinshaw, Prof. N. J. Rothman (eds.)

by Ronald

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