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Mathematical Economics: A Reader

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  • Birendra K. Rai1
  • Chiu Ki So
  • Aaron Nicholas

Abstract

This paper is modeled as a hypothetical first lecture in a graduate Microeconomics or Mathematical Economics Course. We start with a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across Mathematical concepts and results that are used by economists. In the process we arrive at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of fixed-point theorems and Arrow's impossibility theorem. Several appendices provide a step-wise description of some mathematical concepts often used by economists and a few useful results in microeconomics.

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File URL: http://www.buseco.monash.edu.au/eco/research/papers/2011/0211mathematicalraisonicholas.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Economics in its series Monash Economics Working Papers with number 02-11.

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Length: 57 pages
Date of creation: Jun 2011
Date of revision:
Handle: RePEc:mos:moswps:2011-02

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Postal: Department of Economics, Monash University, Victoria 3800, Australia
Phone: +61-3-9905-2493
Fax: +61-3-9905-5476
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Web page: http://www.buseco.monash.edu.au/eco/
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Related research

Keywords: Mathematics; Set theory; Utility function; Arrow's impossibility theorem;

This paper has been announced in the following NEP Reports:

References

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  1. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
  2. Gilboa, I. & Schmeidler, D., 2001. "Inductive Inference: An Axiomatic Approach," Papers 2001-19, Tel Aviv.
  3. Ignacio Palacios-Huerta & Oscar Volij, 2002. "The Measurement of Intellectual Influence," Economic theory and game theory 015, Oscar Volij.
  4. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer, vol. 18(2), pages 327-386.
  5. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
  6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  7. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  8. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
  9. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
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