IDEAS home Printed from https://ideas.repec.org/p/mos/moswps/2011-02.html
   My bibliography  Save this paper

Mathematical Economics: A Reader

Author

Listed:
  • 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.

Suggested Citation

  • Birendra K. Rai1 & Chiu Ki So & Aaron Nicholas, 2011. "Mathematical Economics: A Reader," Monash Economics Working Papers 02-11, Monash University, Department of Economics.
    • Handle: RePEc:mos:moswps:2011-02
    as

    Download full text from publisher

    File URL: http://www.buseco.monash.edu.au/eco/research/papers/2011/0211mathematicalraisonicholas.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    3. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    4. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    5. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, October.
    6. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    7. 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.
    8. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
    9. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    10. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kazeem Bello AJIDE & P.B. EREGHA, 2014. "Economic Freedom And Foreign Direct Investment In Ecowas Countries: A Panel Data Analysis," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 14(2).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Csató, László, 2019. "Journal ranking should depend on the level of aggregation," Journal of Informetrics, Elsevier, vol. 13(4).
    2. L'aszl'o Csat'o, 2019. "Journal ranking should depend on the level of aggregation," Papers 1904.06300, arXiv.org, revised Sep 2019.
    3. Zoi Terzopoulou & Ulle Endriss, 2019. "Strategyproof judgment aggregation under partial information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 415-442, October.
    4. Baumeister, Dorothea & Erdélyi, Gábor & Erdélyi, Olivia J. & Rothe, Jörg, 2015. "Complexity of manipulation and bribery in judgment aggregation for uniform premise-based quota rules," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 19-30.
    5. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 269-300, November.
    6. Zoi Terzopoulou & Ulle Endriss, 2020. "Neutrality and relative acceptability in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 25-49, June.
    7. Bouyssou, Denis & Marchant, Thierry, 2011. "Bibliometric rankings of journals based on Impact Factors: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 5(1), pages 75-86.
    8. Lars J. K. Moen, 2024. "Collective agency and positive political theory," Journal of Theoretical Politics, , vol. 36(1), pages 83-98, January.
    9. Zoi Terzopoulou & Ulle Endriss, 2022. "Strategic manipulation in judgment aggregation under higher-level reasoning," Theory and Decision, Springer, vol. 92(2), pages 363-385, March.
    10. Nuñez, M. & Valletta, G., 2012. "The information simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. Csató, László, 2017. "Tournaments with subsequent group stages are incentive incompatible," MPRA Paper 83269, University Library of Munich, Germany.
    12. Bock, Hans-Hermann & Day, William H. E. & McMorris, F. R., 1998. "Consensus rules for committee elections," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 219-232, May.
    13. Masaki Miyashita, 2021. "Premise-based vs conclusion-based collective choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 361-385, August.
    14. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2013. "Dynamics of inductive inference in a unified framework," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1399-1432.
    15. Marco LiCalzi, 2022. "Bipartite choices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 551-568, December.
    16. John C. McCabe-Dansted & Arkadii Slinko, 2006. "Exploratory Analysis of Similarities Between Social Choice Rules," Group Decision and Negotiation, Springer, vol. 15(1), pages 77-107, January.
    17. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    18. James Schummer, 1999. "Almost-dominant Strategy Implementation," Discussion Papers 1278, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Aleskerov, Fuad & Karabekyan, Daniel & Sanver, M. Remzi & Yakuba, Vyacheslav, 2012. "On the manipulability of voting rules: The case of 4 and 5 alternatives," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 67-73.
    20. Lirong Xia, 2020. "How Likely Are Large Elections Tied?," Papers 2011.03791, arXiv.org, revised Jul 2021.

    More about this item

    Keywords

    Mathematics; Set theory; Utility function; Arrow's impossibility theorem;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mos:moswps:2011-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Simon Angus (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.