# Comparative Statics, English Auctions, and the Stolper-Samuelson Theorem

## Author Info

• Federico Echenique

(Caltech)

• Alejandro Manelli

(Arizona State University)

## Abstract

Changes in the parameters of an $n$-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight the existence of a common thread, our own effect'' assumption, in formally diverse areas of economics. We discuss several applications; among them, we establish the existence of efficient equilibria in English auctions with interdependent valuations, and a version of the Stolper-Samuelson Theorem for an $n \times n$ trade model.

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File URL: http://128.118.178.162/eps/ge/papers/0309/0309005.pdf

## Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0309005.

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Length: 16 pages
Date of revision:
Handle: RePEc:wpa:wuwpge:0309005

Note: Type of Document - PDF; prepared on Unix; to print on PostScript; pages: 16
Contact details of provider:
Web page: http://128.118.178.162

## Related research

Keywords: effficient auctions; international trade theory; implicit function theorem;

Other versions of this item:

Find related papers by JEL classification:
• C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
• D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
• F11 - International Economics - - Trade - - - Neoclassical Models of Trade

## References

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1. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
2. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
3. Alvaro Forteza & Daniel Buquet & Mario Ibarburu & Jorge Lanzaro & Andrés Pereyra & Eduardo Siandra & Marcel Vaillant, 2003. "Understanding reform. The Uruguayan case," Documentos de Trabajo (working papers) 0603, Department of Economics - dECON.
4. Ethier, Wilfred J., 1984. "Higher dimensional issues in trade theory," Handbook of International Economics, in: R. W. Jones & P. B. Kenen (ed.), Handbook of International Economics, edition 1, volume 1, chapter 3, pages 131-184 Elsevier.
5. Robert Wilson, 1998. "Sequential equilibria of asymmetric ascending auctions: The case of log-normal distributions," Economic Theory, Springer, vol. 12(2), pages 433-440.
6. Federico Echenique & Alejandro Manelli, 2003. "Comparative Statics, English Auctions and the Stolper-Samuelson Theorem," Documentos de Trabajo (working papers) 0503, Department of Economics - dECON.
7. Dubra, Juan & Echenique, Federico & Manelli, Alejandro M., 2009. "English auctions and the Stolper-Samuelson theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 825-849, March.
8. Chipman, John S, 1969. "Factor Price Equalization and the Stolper-Samuelson Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 399-406, October.
9. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
10. Silvia Laens & Inés Terra, 2003. "Integration of the Americas: Welfare Effects and Options for the MERCOSUR," Documentos de Trabajo (working papers) 0903, Department of Economics - dECON.
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## Citations

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Cited by:
1. Carlos Casacuberta & Ianina Rossi & Máximo Rossi, 2003. "El arte y el éxito: un matrimonio incómodo," Documentos de Trabajo (working papers) 0303, Department of Economics - dECON.
2. Andrés Pereyra, 2003. "Competencia en telefonía móvil en Uruguay: diseño de subastas, contratos y marco institucional," Documentos de Trabajo (working papers) 0103, Department of Economics - dECON.
3. Federico Echenique & Alejandro Manelli, 2003. "Comparative Statics, English Auctions and the Stolper-Samuelson Theorem," Documentos de Trabajo (working papers) 0503, Department of Economics - dECON.
4. Cecilia González & Máximo Rossi, 2003. "Participación femenina en el mercado de trabajo: efectos sobre la distribución del ingreso en el Uruguay," Documentos de Trabajo (working papers) 1203, Department of Economics - dECON.
5. Marisa Bucheli & Máximo Rossi, 2003. "El grado de conformidad con la vida: evidencia para las mujeres del Gran Montevideo," Documentos de Trabajo (working papers) 1003, Department of Economics - dECON.

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