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An algebraic theory of multi-product decisions

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  • David Hennessy
  • Harvey Lapan

Abstract

We exploit the existence of matrix group symmetries on a production possibility set to identify group symmetries on the profit function. The groups are isomorphic, and provide a pre-ordering on firm preferences over prices. Together with additional structure on the technology, symmetries generate comparative statics on price responses. Linear and other invariances place bounds on firm choice vectors. Reflection group asymmetries on the feasible choice set also support welfare rankings over prices. The methods are adapted to study consumer decisions. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • David Hennessy & Harvey Lapan, 2005. "An algebraic theory of multi-product decisions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 819-829, June.
    • Handle: RePEc:spr:joecth:v:25:y:2005:i:4:p:819-829
    DOI: 10.1007/s00199-004-0476-6
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    References listed on IDEAS

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    1. Klein, Peter G, 2001. "Were the Acquisitive Conglomerates Inefficient?," RAND Journal of Economics, The RAND Corporation, vol. 32(4), pages 745-761, Winter.
    2. John R. Graham & Michael L. Lemmon & Jack G. Wolf, 2002. "Does Corporate Diversification Destroy Value?," Journal of Finance, American Finance Association, vol. 57(2), pages 695-720, April.
    3. Matthew F. Mitchell, 2000. "The Scope and Organization of Production: Firm Dynamics Over the Learning Curve," RAND Journal of Economics, The RAND Corporation, vol. 31(1), pages 180-205, Spring.
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    Cited by:

    1. Hennessy, David A. & Lapan, Harvey E., 2009. "Harmonic symmetries of imperfect competition on circular city," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 124-146, January.

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