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Palgrave Macmillan

Herbert Scarf's Contributions to Economics, Game Theory and Operations Research

Volume 3: Production in Indivisibilities: A Contribution to the Theories of Large Firms

ISBN 9781137024404
Publication Date September 2013
Formats Hardcover Ebook (EPUB) Ebook (PDF) 
Publisher Palgrave Macmillan

Herbert Scarf is a highly esteemed distinguished American economist. He is internationally famous for his early epoch-making work on optimal inventory policies and his highly influential study with Andrew Clark on optimal policies for a multi-echelon inventory problem, which initiated the important and flourishing field of supply chain management. Equally, he has gained world recognition for his classic study on the stability of the Walrasian price adjustment processes and his fundamental analysis on the relationship between the core and the set of competitive equilibria (the so-called Edgeworth conjecture). Further achievements include his remarkable sufficient condition for the existence of a core in non-transferable utility games and general exchange economies, his seminal paper with Lloyd Shapley on housing markets, and his pioneering study on increasing returns and models of production in the presence of indivisibilities. All in all, however, the name of Scarf is always remembered as a synonym for the computation of economic equilibria and fixed points. In the early 1960s he invented a path-breaking technique for computing equilibrium prices.

This work has generated a major research field in economics termed Applied General Equilibrium Analysis and a corresponding area in operations research known as Simplicial Fixed Point Methods. This book comprises all his research articles and consists of four volumes. The volume collects Herbert Scarfs papers in the area of Production in Indivisibilities and the Theories of Large Firms.

Professor Zaifu Yang holds a chair in Economics at the University of York, UK. He has widely published in economics, game theory, operations research and applied mathematics. His articles have appeared in Econometrica, Journal of Economic Theory, Mathematics of Operations Research, Journal of Combinatorial Theory, and SIAM Journal on Control and Optimization among other leading academic journals.

1. An Observation on the Structure of Production Sets with Indivisibilities
2. Production Sets with Indivisibilities, Part I: Generalities
3. Production Sets with Indivisibilities, Part II: The Case of Two Activities
4. Integral Polyhedra in Three Space
5. Neighborhood Systems for Production Sets with Indivisibilites
6. Testing for Optimality in the Absence of Convexity
7. The Frobenius Problem and Maximal Lattice Free Bodies
8. The Complex of Maximal Lattice Free Simplices
9. Test Sets for Integer Programs
10. Matrices with Identical Sets of Neighbors
11. The Topological Structure of Maximal Lattice Free Convex Bodies - The General Case
12. Neighborhood Complexes and Generating Functions for Affine Semigroups
13. The Structure of the Complex of Maximal Lattice Free Bodies for a Matrix of Size (N + 1) x N


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