Journal of Evolutionary Economics

, Volume 29, Issue 2, pp 763–778 | Cite as

A cobweb model with elements from prospect theory

  • Ahmad Naimzada
  • Nicolò Pecora
  • Fabio TramontanaEmail author
Regular Article


We present a cobweb model to explain price adjustment in a competitive market with homogeneous firms based on assumptions from Prospect Theory. Price changes are evaluated with respect to a psychological reference price which enters directly into the demand function. Accordingly, firms face a downward-sloping demand curve that is kinked at the consumers’ reference price. Differently from the traditional cobweb model, the economy is described by a discontinuous map. Without assuming specific non-linearities and keeping the essential underlying mechanics of the model intact, we find that the implementation of several features from Prospect Theory into our simple cobweb model may significantly influence the market dynamics. Behavioral parameters play an important role for the market stability by reducing fluctuations and by directly affecting consumers’ demand as well as production decisions.


Cobweb model Reference price Transaction utility Behavioral economics Discontinuous maps Complex dynamics 

JEL Classification

D03 E32 



Work developed in the framework of the research project on Dynamic models for behavioural economics, financed by DESP-University of Urbino.

We wish to thank two anonymous reviewers for their valuable comments and suggestions. The usual caveats apply.

Compliance with Ethical Standards

The authors declare that they have no conflict of interest.


  1. Ahrens S, Pirschel I (2017) A theory of price adjustment under loss aversion. J Econ Behav Organ 134:78–95CrossRefGoogle Scholar
  2. Barberis N (2012) A model of casino gambling. Manag Sci 58:35–51CrossRefGoogle Scholar
  3. Barberis N (2013) Thirty years of prospect theory in economics: a review and assessment. J Econ Perspect 27(1):173–195CrossRefGoogle Scholar
  4. Briesch RA, Krishnamurthi L, Mazumdar T, Raj SP (1997) A comparative analysis of reference price models. J Consum Res 24:202–214CrossRefGoogle Scholar
  5. Brock WA, Hommes CH (1997) A rational route to randomness. Econometrica: J Econ Soc 65(5):1059–1095CrossRefGoogle Scholar
  6. Cashin P, McDermott CJ, Scott A (2002) Booms and slumps in world commodity prices. J Dev Econ 69(1):277–296CrossRefGoogle Scholar
  7. Chatrath A, Adrangi B, Dhanda KK (2002) Are commodity prices chaotic? Agric Econ 27(2):123–137CrossRefGoogle Scholar
  8. Chiarella C (1988) The cobweb model: its instability and the onset of chaos. Econ Model 5(4):377–384CrossRefGoogle Scholar
  9. Deaton A, Laroque G (1996) Competitive storage and commodity price dynamics. J Polit Econ 104(5):896–923CrossRefGoogle Scholar
  10. Deaton A (1999) Commodity prices and growth in Africa. J Econ Perspect 13 (3):23–40CrossRefGoogle Scholar
  11. Ezekiel M (1938) The cobweb theorem. Q J Econ 52:255–280CrossRefGoogle Scholar
  12. Goeree JK, Hommes CH (2000) Heterogeneous beliefs and the non-linear cobweb model. J Econ Dyn Control 24(5):761–798CrossRefGoogle Scholar
  13. Gouel C (2012) Agricultural price instability: a survey of competing explanations and remedies. J Econ Surv 26(1):129–156CrossRefGoogle Scholar
  14. Greenleaf EA (1995) The impact of reference price effects on the profitability of price promotions. Mark Sci 14:82–104CrossRefGoogle Scholar
  15. Heidhues P, Koszegi B (2014) Regular Prices and Sales. Theor Econ 9:217–251CrossRefGoogle Scholar
  16. Hommes CH (1991) Adaptive learning and roads to chaos: the case of the cobweb. Econ Lett 36(2):127–132CrossRefGoogle Scholar
  17. Hommes C (1994) Dynamic of the cobweb model with adaptive expectations and nonlinear supply and demand. J Econ Behav Organ 24:315–335CrossRefGoogle Scholar
  18. Hommes CH (1998) On the consistency of backward-looking expectations: the case of the cobweb. J Econ Behav Organ 33(3):333–362CrossRefGoogle Scholar
  19. Hommes C (2013) Behavioral rationality and heterogeneous expectations in complex economic systems. Cambridge University Press, New YorkCrossRefGoogle Scholar
  20. Hommes C, Zeppini P (2014) Innovate or Imitate? Behavioural technological change. J Econ Dyn Control 48:308–324CrossRefGoogle Scholar
  21. Jensen RV, Urban R (1984) Chaotic price behavior in a non-linear cobweb model. Econ Lett 15(3):235–240CrossRefGoogle Scholar
  22. Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47:263–291CrossRefGoogle Scholar
  23. Kandil M (2010) The asymmetric effects of demand shocks: international evidence on determinants and implications. Appl Econ 42(17):2127–2145CrossRefGoogle Scholar
  24. Karle H, Peitz M (2014) Competition and consumer loss aversion. RAND J Econ 45(1):1–31CrossRefGoogle Scholar
  25. Koszegi B, Rabin M (2006) A model of reference-dependent preferences. Q J Econ 121:1133–1165CrossRefGoogle Scholar
  26. Kwapil C, Scharler J, Baumgartner J (2010) How are prices adjusted in response to shocks? Survey evidence from Austrian firms. Manag Decis Econ 31 (2-3):151–160CrossRefGoogle Scholar
  27. Li TY, Yorke JA (1978) Ergodic transformations from an interval into itself. Trans Am Math Soc 235:183–192CrossRefGoogle Scholar
  28. Ma J, Mu L (2007) Complex dynamics in a nonlinear cobweb model for real estate market. Discrete Dynamics in Nature and Society, vol 2007, Article ID 29207Google Scholar
  29. Matsumoto A (1997) Ergodic cobweb chaos. Discret Dyn Nat Soc 1:135–146CrossRefGoogle Scholar
  30. Mazumdar T, Raj SP, Sinha I (2005) Reference price research: review and propositions. J Market 69:84–102CrossRefGoogle Scholar
  31. Peterson HH, Tomek WG (2005) How much of commodity price behavior can a rational expectations storage model explain? Agric Econ 33(3):289–303CrossRefGoogle Scholar
  32. Popescu I, Wu Y (2007) Dynamic pricing strategies with reference effects. Oper Res 55:413–429CrossRefGoogle Scholar
  33. Scheinkman JA, Schechtman J (1983) A simple competitive model with production and storage. Rev Econ Stud 50(3):427–441CrossRefGoogle Scholar
  34. Sibly H (2002) Loss averse customers and price inflexibility. J Econ Psychol 23(4):521–538CrossRefGoogle Scholar
  35. Singh N, Vives X (1984) Price and quantity competition in a differentiated duopoly. RAND J Econ 15(4):546–554CrossRefGoogle Scholar
  36. Spiegler R (2012) Monopoly pricing when consumers are antagonized by unexpected price increases: a cover version of the Heidhues-Koszegi-Rabin Model. Econ Theory 51(3):695–711CrossRefGoogle Scholar
  37. Sushko I, Gardini L (2016) Nonsmooth One-dimensional maps: some basic concepts and definitions. J Difference Equ Appl 22(12):1816–1870CrossRefGoogle Scholar
  38. Thaler R (1985) Mental accounting and consumer choice. Market Sci 4 (3):199–214CrossRefGoogle Scholar
  39. Thaler R (2016) Behavioral economics: past, present, and future. Am Econ Rev 106(7):1577–1600CrossRefGoogle Scholar
  40. Thaler R, Johnson EJ (1990) Gambling with the house money and trying to break even: the effects of prior outcomes on risky choice. Manag Sci 36:643–660CrossRefGoogle Scholar
  41. Waters GA (2009) Chaos in the cobweb model with a new learning dynamic. J Econ Dyn Control 33(6):1201–1216CrossRefGoogle Scholar
  42. Williams JC, Wright BD (2005) Storage and commodity markets. Cambridge University Press, New YorkGoogle Scholar
  43. Yang SR, Brorsen BW (1992) Nonlinear dynamics of daily cash prices. Am J Agric Econ 74(3):706–715CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Economics, Quantitative Methods and ManagementUniversity of Milano - BicoccaMilanoItaly
  2. 2.Department of Economics and Social ScienceCatholic UniversityPiacenzaItaly
  3. 3.Department of Mathematical Sciences, Mathematical Finance and EconometricsCatholic UniversityMilanoItaly

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