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Quasi-linear peferences with Auspitz-Lieben-Pareto complementarity


  • Christian Weber

    () (Seattle University)


I show that if preferences are quasi-linear (non-linear in goods x1, …, xn but linear in xn+1) and the sub-utility function defined over [x1, …, xn] is strongly concave and exhibits Auspitz-Lieben-Pareto complementarity, then goods x1-xn must be gross and compensated complements for each other and xn+1 must be a compensated substitute for all other goods. Also, an increase in its price of xn+1 must reduce the demand for goods x1-xn. The effects of uncompensated changes in the prices of goods x1-xn on the demand for good xn+1 vary predictably with income.

Suggested Citation

  • Christian Weber, 2004. "Quasi-linear peferences with Auspitz-Lieben-Pareto complementarity," Economics Bulletin, AccessEcon, vol. 4(12), pages 1-5.
  • Handle: RePEc:ebl:ecbull:eb-04d10001

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    References listed on IDEAS

    1. Shi, Shou Yong, 1988. "Rational expectation equilibrium under quasilinear preferences : A diagrammatic approach," Economics Letters, Elsevier, vol. 26(2), pages 107-110.
    2. Weber, Christian E., 2000. "Two further empirical implications of Auspitz-Lieben-Edgeworth-Pareto complementarity," Economics Letters, Elsevier, vol. 67(3), pages 289-295, June.
    3. Silberberg, Eugene, 1972. "Separability and Complementarity," American Economic Review, American Economic Association, vol. 62(1), pages 196-197, March.
    4. Che, Yeon-Koo & Gale, Ian, 2000. "The Optimal Mechanism for Selling to a Budget-Constrained Buyer," Journal of Economic Theory, Elsevier, vol. 92(2), pages 198-233, June.
    5. Weymark, John A, 1987. "Comparative Static Properties of Optimal Nonlinear Income Taxes," Econometrica, Econometric Society, vol. 55(5), pages 1165-1185, September.
    6. Christian E. Weber, 2005. "Edgeworth on Complementarity, or Edgeworth, Auspitz-Lieben, and Pareto De-Homogenized," History of Political Economy, Duke University Press, vol. 37(2), pages 293-307, Summer.
    7. Liebhafsky, H H, 1969. "New Thoughts About Inferior Goods," American Economic Review, American Economic Association, vol. 59(5), pages 931-934, December.
    8. Chipman, John S., 1977. "An empirical implication of Auspitz-Lieben-Edgeworth-Pareto complementarity," Journal of Economic Theory, Elsevier, vol. 14(1), pages 228-231, February.
    9. Boylan, Richard T., 1998. "Coalition-Proof Implementation," Journal of Economic Theory, Elsevier, vol. 82(1), pages 132-143, September.
    10. Shi, Shou Yong, 1988. "Rothschild-Stiglitz competitive insurance market under quasilinear preferences," Economics Letters, Elsevier, vol. 27(1), pages 27-30.
    11. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, July.
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    More about this item


    Auspitz-Lieben-Pareto complementarity;

    JEL classification:

    • D1 - Microeconomics - - Household Behavior


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