Skip to main content
SpringerLink
Log in

Multiple equilibria and indifference-threshold points in a rational addiction model

  • Original Paper
  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

Becker and Murphy (J Polit Econ 96(4):675–700, 1988) have established the existence of unstable steady states leading to threshold behavior for optimal consumption rates in intertemporal rational addiction models. In the present paper a simple linear-quadratic optimal control model is used to illustrate how their approach fits into the framework of multiple equilibria and indifference-threshold points. By changing the degree of addiction and the level of harmfulness we obtain a variety of behavioral patterns. In particular we show that when the good is harmful as well as very addictive, an indifference-threshold point, also known in the literature as a Skiba point, separates patterns converging to either zero or maximal consumption, where the latter occurs in the case of a high level of past consumption. This implicitly shows that an individual needs to be aware in time of these characteristics of the good. Otherwise, he/she may start consuming so much that in the end he/she is totally addicted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Auld M, Grootendorst P (2004) An empirical analysis of milk addiction. J Health Econ 23(6): 1117–1133

    Article  Google Scholar 

  • Becker GS (1992) Habits, addictions, and traditions. Kyklos 45(3): 327–346

    Article  Google Scholar 

  • Becker GS, Murphy KM (1988) A theory of rational addiction. J Polit Econ 96(4): 675–700

    Article  Google Scholar 

  • Braun N, Vanini P (2003) On habits and addictions. J Inst Theor Econ 159: 603–626

    Article  Google Scholar 

  • Brock WA (1983) Pricing, predation and entry barriers in regulated industries. In: Evans DS (ed) Breaking up bell. North-Holland, New York, pp 191–229

    Google Scholar 

  • Brock WA, Dechert WD (1985) Dynamic Ramsey pricing. Int Econ Rev 26(3): 569–591

    Article  Google Scholar 

  • Brock WA, Malliaris AG (1989) Differential equations, stability and chaos in dynamic economics. North-Holland, Amsterdam

    Google Scholar 

  • Brock WA, Starrett D (2003) Nonconvexities in ecological managment problems. Environ Resour Econ 26(4): 575–624

    Article  Google Scholar 

  • Bultmann R, Feichtinger G, Tragler G (2010) Stochastic skiba sets: an example from models of illicit drug consumption. In: Lirkov I, Margenov S, Wasniewski J (eds) Large-scale scientific computing. Springer, Heidelberg, pp 239–246

    Chapter  Google Scholar 

  • Cass D. (1965) Optimum growth in an aggregative model of capital accumulation. Rev Econ Stud 32(3): 233–240

    Article  Google Scholar 

  • Caulkins JP, Feichtinger G, Grass D, Hartl RF, Kort PM, Seidl A (2010) Skiba points in free end time problems: the option to sell the firm (in submission)

  • Clark C (1971) Economically optimal policies for the utilization of biologically renewable resources. Math Biosci 12(3–4): 245–260

    Article  Google Scholar 

  • Clark CW (1976) Mathematical bioeconomics, the optimal management of renewable resources. Wiley- Interscience, New York

    Google Scholar 

  • Dechert WD (1983) Increasing returns to scale and the reverse flexible accelerator. Econ Lett 13(1): 69–75

    Article  Google Scholar 

  • Dechert WD, Nishimura K (1983) A complete characterization of optimal growth paths in an aggregated model with a non-concave production function. J Econ Theory 31(2): 332–354

    Article  Google Scholar 

  • Deissenberg C, Feichtinger G, Semmler W, Wirl F (2004) Multiple equilibria, history dependence, and global dynamics in intertemporal optimization models. In: Barnett WA, Deissenberg C, Feichtinger G (eds) Economic complexity: non-linear dynamics, multi-agents economies and learning. Elsevier, Amsterdam, pp 91–122

    Google Scholar 

  • Dockner EJ, Feichtinger G (1993) Cyclical consumption patterns and rational addiction. Am Econ Rev 83(1): 256–263

    Google Scholar 

  • Feichtinger G, Steindl A (2006) DNS curves in a production/inventory model. J Optim Theory Appl 128(2): 295–308

    Article  Google Scholar 

  • Forster BA (1975) Optimal pollution control with a nonconstant exponential rate of decay. J Environ Econ Manag 2: 1–6

    Article  Google Scholar 

  • Gavrila C, Feichtinger G, Tragler G, Hartl RF, Kort PM (2005) History-dependence in a rational addiction model. Math Soc Sci 49(3): 273–293

    Article  Google Scholar 

  • Grass D, Caulkins JP, Feichtinger G, Tragler G, Behrens DA (2008) Optimal control of nonlinear processes: with applications in drugs, corruption and terror. Springer, Heidelberg

    Book  Google Scholar 

  • Hartl RF, Kort PM, Feichtinger G, Wirl F (2004) Multiple equilibria and thresholds due to relative investment costs. J Optim Theory Appl 123(1): 49–82

    Article  Google Scholar 

  • Iannaccone LR (1986) Addiction and satiation. Econ Lett 21(1): 95–99

    Article  Google Scholar 

  • Koopmans TC (1965) On the concept of optimal economic growth. Pontificiae Academiae Scientiarum Scripta Varia 28(1): 225–300

    Google Scholar 

  • Léonard D (1989) Market behaviour of rational addicts. J Econ Psychol 10(1): 117–144

    Article  Google Scholar 

  • Lewis TR, Schmalensee R (1982) Optimal use of renewable resources with nonconvexities in production. In: Mirman LJ, Spulber DF (eds) Essays in the economics of renewable resources. North-Holland, Amsterdam, pp 95–111

    Google Scholar 

  • Lucas RE (1988) On the mechanics of economic development. J Monet Econ 22(1): 3–42

    Article  Google Scholar 

  • Mäler KG (2000) Development, ecological resources and their management: a study of complex dynamic systems. Eur Econ Rev 44(4–6): 645–665

    Article  Google Scholar 

  • Melberg HO, Rogeberg OJ (2010) Rational addiction theory: a survey of opinions. J Drug Policy Anal 3(1): 5

    Google Scholar 

  • Orphanides A, Zervos D (1994) Optimal consumption dynamics with non-concave habit-forming utility. Econ Lett 44(1–2): 67–72

    Article  Google Scholar 

  • Orphanides A, Zervos D (1995) Rational addiction with learning and regret. J Polit Econ 103(4): 739–758

    Article  Google Scholar 

  • Orphanides A, Zervos D (1998) Myopia and addictive behaviour. Econ J 108(446): 75–91

    Article  Google Scholar 

  • Ryder HE, Heal GM (1973) Optimal growth with intertemporally dependent preferences. Rev Econ Stud 40: 1–33

    Article  Google Scholar 

  • Sethi SP (1977) Nearest feasible paths in optimal control problems: theory, examples, and counterexamples. J Optim Theory Appl 23(4): 563–579

    Article  Google Scholar 

  • Sethi SP (1979) Optimal advertising policy with the contagion model. J Optim Theory Appl 29(4): 615–627

    Article  Google Scholar 

  • Skiba AK (1978) Optimal growth with a convex-concave production function. Econometrica 46(3): 527–539

    Article  Google Scholar 

  • Stigler GJ, Becker GS (1977) De gustibus non est disputandum. Am Econ Rev 67(2): 76–90

    Google Scholar 

  • Wagener FOO (2003) Skiba points and heteroclinic bifurcations, with applications to the shallow lake system. J Econ Dyn Control 27(9): 1533–1561

    Article  Google Scholar 

  • Wirl F, Feichtinger G (2005) History dependence in concave economies. J Econ Behav Organ 57(4): 390–407

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Carnegie Mellon University, H. John Heinz III College, 5000 Forbes Avenue, Pittsburgh, PA, 15213-3890, USA

    Jonathan P. Caulkins

  2. Department for Operations Research and Control Systems, Institute for Mathematical Methods in Economics, Vienna University of Technology, Argentinierstr. 8, 1040, Vienna, Austria

    Gustav Feichtinger & Andrea Seidl

  3. Department of Business Administration, University of Vienna, Bruennerstr. 72, 1210, Vienna, Austria

    Richard F. Hartl & Andreas J. Novak

  4. Department of Econometrics and Operations Research and Center, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    Peter M. Kort

  5. Department of Economics, University of Antwerp, Prinsstraat 13, 2000, Antwerp, Belgium

    Peter M. Kort

Authors
  1. Jonathan P. Caulkins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gustav Feichtinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Richard F. Hartl
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter M. Kort
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Andreas J. Novak
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Andrea Seidl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gustav Feichtinger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Caulkins, J.P., Feichtinger, G., Hartl, R.F. et al. Multiple equilibria and indifference-threshold points in a rational addiction model. Cent Eur J Oper Res 21, 507–522 (2013). https://doi.org/10.1007/s10100-012-0260-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-012-0260-9

Keywords

Search

Navigation