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Concepts and Properties of Substitute Goods

We distinguish two notions of substitutes for discrete inputs of a firm. Class substitutes are defined assuming that units of a given input have the same price while unitary substitutes treat each unit as a distinct input with its own price. Unitary substitutes is necessary and sufficient for such results as the robust existence of equilibrium, the robust inclusion of the Vickrey outcome in the core, and the law of aggregate demand, while the class substitutes condition is necessary and sufficient for robust monotonicity of certain auction/tatonnement processes. We analyze the concept of pseudo-equilibrium which extends, and in some sense approximates, the concept of equilibrium when no equilibrium exists. We characterize unitary substitutes as class substitutes plus two other properties. We extend the analysis to divisible inputs, with a particular focus on robustness of the concepts and their relation to the generalized law of aggregate demand.

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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2006/w2/Substitutes%20Working%20Paper.pdf
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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2006-W02.

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Length: 54 pages
Date of creation: 08 May 2006
Date of revision:
Handle: RePEc:nuf:econwp:0602
Contact details of provider: Web page: http://www.nuff.ox.ac.uk/economics/

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  1. Paul Milgrom, . "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Working Papers 98002, Stanford University, Department of Economics.
  2. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  3. Paul Milgrom, 2003. "Matching with Contracts," Working Papers 03003, Stanford University, Department of Economics.
  4. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
  5. repec:cup:cbooks:9780521551847 is not listed on IDEAS
  6. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  7. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
  8. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
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