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An Expository Note on Alchian-Allen Theorem When Sub-Utility Functions are Homogeneous of Degree n > 0 with Two-Stage Budgeting

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Author Info
Tetsuya Saito () (Department of Economics, SUNY at Buffalo)

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Abstract

This expository note shows a proof of Alchian and Allen's conjecture broadly known as a phrase `shipping the good apples out' meaning that consumers purchase fine quality relatively more than coarse one if a fixed charge is imposed. Their statement is often referred as the Alchian-Allen theorem (or effect). The proof requires conditions about homogeneity, inner solution and substitutability and they also justify two-stage budgeting. In order this work to be an exposition, I emphasize graphical representations, however, a comparison with the proof of Borcherding and Silberberg (JPE; 1978) is also considered. This comparison clarifies difference between proofs using Hicksian demand functions and using Marshallian demand functions (with some specific conditions). Extending sequential budgeting procedures, we also discuss perspectives toward multiple-quality analysis. That turns out a definition based on sequential budgeting may open a way of experimental study about the effect.

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File URL: http://economicsbulletin.vanderbilt.edu/2008/volume6/EB-08F10013A.pdf
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Article provided by Economics Bulletin in its journal Economics Bulletin.

Volume (Year): 6 (2008)
Issue (Month): 30 ()
Pages: 1-12
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Handle: RePEc:ebl:ecbull:v:6:y:2008:i:30:p:1-12

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Related research
Keywords: Fixed transaction cost; quality; Alchian-Allen effect; two-stage budgeting; consumption pattern;

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Find related papers by JEL classification:
F1 - International Economics - - Trade
R0 - Urban, Rural, and Regional Economics - - General

References listed on IDEAS
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  1. Irwin, Douglas A. & Temin, Peter, 2001. "The Antebellum Tariff On Cotton Textiles Revisited," The Journal of Economic History, Cambridge University Press, vol. 61(03), pages 777-798, September. [Downloadable!]
    Other versions:
  2. John Komlos & Bjorn Alecke, . "The Economics of Antebellum Slave Heights Reconsidered," Articles by John Komlos 11, Department of Economics, University of Munich.
  3. Norman, A. & Ahmed, M. & Chou, J. & Fortson, K. & Kurz, C. & Lee, H. & Linden, L. & Meythaler, K. & Rando, R. & Sheppard, K., 2003. "An ordering experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 50(2), pages 249-262, February. [Downloadable!] (restricted)
  4. William Smith & Cyril Chang, 2002. "Shipping the good apples out: a note on contributions of time and money," Economics Bulletin, Economics Bulletin, vol. 10, pages 1-14. [Downloadable!]
  5. David Hummels & Alexandre Skiba, 2004. "Shipping the Good Apples Out? An Empirical Confirmation of the Alchian-Allen Conjecture," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1384-1402, December.
    Other versions:
  6. Gould, John P & Segall, Joel, 1969. "The Substitution Effects of Transportation Costs," Journal of Political Economy, University of Chicago Press, vol. 77(1), pages 130-37, Jan./Feb.. [Downloadable!] (restricted)
  7. A. Norman & A. Ahmed & J. Chou & A. Dalal & K. Fortson & M. Jindal & C. Kurz & H. Lee & K. Payne & R. Rando & K. Sheppard & E. Sublett & J. Sussman & I. White, 2004. "On the Computational Complexity of Consumer Decision Rules," Computational Economics, Springer, vol. 23(2), pages 173-192, 03. [Downloadable!]
  8. Bertonazzi, Eric P & Maloney, Michael T & McCormick, Robert E, 1993. "Some Evidence on the Alchian and Allen Theorem: The Third Law of Demand?," Economic Inquiry, Oxford University Press, vol. 31(3), pages 383-93, July.
  9. Norman, A, et al, 2001. "Two-Stage Budgeting: A Difficult Problem," Computational Economics, Springer, vol. 18(3), pages 259-71, December. [Downloadable!]
  10. Borcherding, Thomas E & Silberberg, Eugene, 1978. "Shipping the Good Apples Out: The Alchian and Allen Theorem Reconsidered," Journal of Political Economy, University of Chicago Press, vol. 86(1), pages 131-38, February. [Downloadable!] (restricted)
  11. Laura Razzolini & William F. Shughart & Robert D. Tollison, 2003. "On the Third Law of Demand," Economic Inquiry, Oxford University Press, vol. 41(2), pages 292-298, April. [Downloadable!] (restricted)
  12. Brown, Murray & Chang, Winston W, 1976. "Capital Aggregation in a General Equilibrium Model of Production," Econometrica, Econometric Society, vol. 44(6), pages 1179-1200, November. [Downloadable!] (restricted)
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