IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1606.06720.html
   My bibliography  Save this paper

A mathematical model of demand-supply dynamics with collectability and saturation factors

Author

Listed:
  • Y. Charles Li
  • Hong Yang

Abstract

We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is chaos in the demand-supply dynamics. Our numerical simulation shows that such a chaos is not an attractor (i.e. dynamics is not approaching the chaos), instead a periodic attractor (of period 3 under the Poincar\'e period map) exists near the chaos, and co-exists with another periodic attractor (of period 1 under the Poincar\'e period map) near the market equilibrium. Outside the basins of attraction of the two periodic attractors, the dynamics approaches infinity indicating market irrational exuberance or flash crash. The period 3 attractor represents the product's market cycle of growth and recession, while period 1 attractor near the market equilibrium represents the regular fluctuation of the product's market. Thus our model captures more market phenomena besides Marshall's market equilibrium. When the fluctuation of the determinants of demand and supply is strong enough, a three leaf danger zone exists where the basins of attraction of all attractors intertwine and fractal basin boundaries are formed. Small perturbations in the danger zone can lead to very different attractors. That is, small perturbations in the danger zone can cause the market to experience oscillation near market equilibrium, large growth and recession cycle, and irrational exuberance or flash crash.

Suggested Citation

  • Y. Charles Li & Hong Yang, 2016. "A mathematical model of demand-supply dynamics with collectability and saturation factors," Papers 1606.06720, arXiv.org.
    • Handle: RePEc:arx:papers:1606.06720
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1606.06720
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dorofeenko, Victor & Lee, Gabriel S. & Salyer, Kevin D., 2014. "Risk shocks and housing supply: A quantitative analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 194-219.
    2. Tsitsiklis, John N. & Xu, Yunjian, 2014. "Efficiency loss in a Cournot oligopoly with convex market demand," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 46-58.
    3. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    4. Aleksandrov, Nikolay & Espinoza, Raphael & Gyurkó, Lajos, 2013. "Optimal oil production and the world supply of oil," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1248-1263.
    5. Plante, Michael, 2014. "How should monetary policy respond to changes in the relative price of oil? Considering supply and demand shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 1-19.
    6. Weinrich, Gerd, 2007. "New Keynesian monopolistic competition and objective demand," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 153-173, February.
    Full references (including those not matched with items on IDEAS)

    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. Goodness C. Aye & Rangan Gupta, 2019. "Macroeconomic Uncertainty And The Comovement In Buying Versus Renting In The Usa," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(3), pages 93-121, September.
    2. Andrea Ferrero & Martin Seneca, 2019. "Notes on the Underground: Monetary Policy in Resource‐Rich Economies," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(4), pages 953-976, June.
    3. Liu, Zhen & Tang, Yuk Ming & Chau, Ka Yin & Chien, Fengsheng & Iqbal, Wasim & Sadiq, Muhammad, 2021. "Incorporating strategic petroleum reserve and welfare losses: A way forward for the policy development of crude oil resources in South Asia," Resources Policy, Elsevier, vol. 74(C).
    4. Ezequiel Cabezon & Christian Henn, 2018. "Counting the Oil Money and the Elderly: Norway's Public Sector Balance Sheet," IMF Working Papers 2018/190, International Monetary Fund.
    5. Eun Jeong Heo & Vikram Manjunath, 2017. "Implementation in stochastic dominance Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 5-30, January.
    6. Ping Zhan, 2023. "A Simple Characterization of Assignment Mechanisms on Set Constraints," SN Operations Research Forum, Springer, vol. 4(2), pages 1-15, June.
    7. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    8. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    9. Fehrle, Daniel, 2019. "Housing and the business cycle revisited," Journal of Economic Dynamics and Control, Elsevier, vol. 99(C), pages 103-115.
    10. Su, Chi-Wei & Qin, Meng & Tao, Ran & Moldovan, Nicoleta-Claudia & Lobonţ, Oana-Ramona, 2020. "Factors driving oil price —— from the perspective of United States," Energy, Elsevier, vol. 197(C).
    11. Han, Xiang, 2016. "On the consistency of random serial dictatorship," Economics Letters, Elsevier, vol. 145(C), pages 168-171.
    12. Fehrle, Daniel & Heiberger, Christopher, 2024. "The return on everything and the business cycle in production economies," Economic Modelling, Elsevier, vol. 136(C).
    13. Cao, Fangzhi & Su, Chi-Wei & Sun, Dian & Qin, Meng & Umar, Muhammad, 2024. "U.S. monetary policy: The pushing hands of crude oil price?," Energy Economics, Elsevier, vol. 134(C).
    14. Piazzesi, M. & Schneider, M., 2016. "Housing and Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1547-1640, Elsevier.
    15. Nida Çakir Melek & Michael Plante & Mine K. Yücel, 2017. "The U.S. Shale Oil Boom, the Oil Export Ban, and the Economy: A General Equilibrium Analysis," NBER Working Papers 23818, National Bureau of Economic Research, Inc.
    16. Francesca Rondina, 2017. "The Impact of Oil Price Changes in a New Keynesian Model of the U.S. Economy," Working Papers 1709E, University of Ottawa, Department of Economics.
    17. Condorelli, Daniele & Szentes, Balazs, 2020. "Surplus Bounds in Cournot Monopoly and Competition," The Warwick Economics Research Paper Series (TWERPS) 1292, University of Warwick, Department of Economics.
    18. Strobel, Johannes, 2015. "On the different approaches of measuring uncertainty shocks," Economics Letters, Elsevier, vol. 134(C), pages 69-72.
    19. Akan, Taner, 2023. "Can renewable energy mitigate the impacts of inflation and policy interest on climate change?," Renewable Energy, Elsevier, vol. 214(C), pages 255-289.
    20. Nguyen, Canh Phuc & Lee, Gabriel S., 2021. "Uncertainty, financial development, and FDI inflows: Global evidence," Economic Modelling, Elsevier, vol. 99(C).

    More about this item

    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:arx:papers:1606.06720. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.