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Understanding preferences: "demand types", and the existence of equilibrium with indivisibilities

Author

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  • Baldwin, Elizabeth
  • Klemperer, Paul

Abstract

We propose new techniques for understanding agents' valuations. Our classification into \demand types", incorporates existing definitions (substitutes, complements, \strong substitutes", etc.) and permits new ones. Our Unimodularity Theorem generalises previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a \demand type" for indivisible goods. Contrary to popular belief, equilibrium is guaranteed for more classes of purely-complements, than of purely-substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition-formation; and the Product-Mix Auction, introduced by the Bank of England in response to the financial crisis.

Suggested Citation

  • Baldwin, Elizabeth & Klemperer, Paul, 2016. "Understanding preferences: "demand types", and the existence of equilibrium with indivisibilities," LSE Research Online Documents on Economics 63198, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:63198
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    File URL: https://researchonline.lse.ac.uk/id/eprint/63198/
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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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