Skip to main content

Advertisement

SpringerLink
Log in

Conditions for indeterminacy and thresholds in neoclassical growth models

  • Published:
Journal of Economics Aims and scope Submit manuscript

Abstract

This paper considers externalities and investigates which general properties and respectively their magnitudes induce complex behavior like thresholds and indeterminacy (and cycles). The objective is to obtain general mechanisms within a general setting in order to complement the much advanced but model specific literature. It turns out that these arithmetic and simultaneously economic conditions for thresholds or indeterminacy require complementarity and non-moderate dynamic social influence. In other words, complexities can be related (necessary and sufficient) to a familiar static property that social interactions turn the (stationary) demand for the private stock into a Giffen good. Indeterminacy requires in addition ‘low’ subjective discounting and proper interactions between control, stock and externality. These conditions provide an easy way to construct models that allow for the targeted outcome, stability, thresholds or indeterminacy.

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

  • Ayong Le Kama AD (2001) Sustainable growth, renewable resources and pollution. J Econ Dyn Control 25: 1911–1918

    Article  Google Scholar 

  • Benhabib J, Farmer RE (1994) Indeterminacy and increasing returns. J Econ Theory 63: 19–41

    Article  Google Scholar 

  • Benhabib J, Nishimura K, Shigoka T (2008) Bifurcation and sunspots in the continuous time equilibrium model with capacity utilization. Int J Econ Theory 4: 337–355

    Article  Google Scholar 

  • Benhabib J, Perli R (1994) Uniqueness and indeterminacy: on the dynamics of endogenous growth. J Econ Theory 63(1): 113–142

    Article  Google Scholar 

  • Benhabib J, Rustichini A (1994) Introduction to the symposium on growth, fluctuations, and sunspots: confronting the data. J Econ Theory 63: 1–18

    Article  Google Scholar 

  • Bosi S, Magris F, Venditti A (2007) Sunspot fluctuations in two-sector economies with heterogeneous agents. Econ Theory 33: 311–331

    Article  Google Scholar 

  • Brock WA (1983) Pricing, predation and entry Barriers in regulated Industries. In: Evans DS (eds) Breaking up bell. North-Holland, Amsterdam, pp 191–229

    Google Scholar 

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

    Article  Google Scholar 

  • Chen J, Shieh J, Chang J, Lai C (2009) Growth, welfare and transitional dynamics in an endogenously growing economy with abatement labor. J Macroecon (in press, 2009)

  • Daisuke O (2009) History versus expectations in economic geography reconsidered. J Econ Dyn Control 33: 394–408

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Eusepi S (2009) On expectations-driven business cycles in economies with production externalities. Int J Econ Theory 5: 9–23

    Article  Google Scholar 

  • Feichtinger G, Novak A, Wirl F (1994) Limit cycles in intertemporal adjustment models—theory and applications. J Econ Dyn Control 18: 353–380

    Article  Google Scholar 

  • Fisher WH, Hof FX (2000) Relative consumption, economic growth, and taxation. J Econ 72(3): 241–262

    Google Scholar 

  • Glaeser EL, Scheinkman JA (2003) Nonmarket interaction. In: Dewatripoint M, Hansen LP, Turnovsky S (eds) Advances in economics and econometrics: theory and applications. Proceedings of the eighth World Congress, vol 1. Cambridge University Press, Cambridge, UK, pp 339–369

  • Gliksberg B (2009) Monetary policy and multiple equilibria with constrained investment and externalities. Econ Theory 4: 443–463

    Article  Google Scholar 

  • Graham BS, Temple JRW (2006) Rich nations, poor nations: how much can multiple equilibria explain?. J Econ Growth 11: 5–41

    Article  Google Scholar 

  • Itaya J (2008) Can environmental taxation stimulate growth? Next term the role of previous indeterminacy in endogenous previous growth models with environmental externalities. J Econ Dyn Control 32: 1156–1180

    Article  Google Scholar 

  • Karp L, Thierry P (2007) Indeterminacy with environmental and labor dynamics. Struct Change Econ Dyn 18: 100–119

    Article  Google Scholar 

  • Khibnik A, Yu I, Kuznetsov A, Levitin VV, Nikolaev EV (1992) Interactive local bifurcation analyzer, manual. CAN, Amsterdam

  • Krugman P (1991) History versus expectations. Q J Econ 106: 651–667

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mäler K-G, Xepapadeas A, de Zeeuw A (2003) The economics of shallow lakes. Environ Resour Econ 26: 603–624

    Article  Google Scholar 

  • Mattana P, Nishimura K, Shigoka T (2009) Homoclinic bifurcation and global indeterminacy of equilibrium in a two-sector endogenous growth model. Int J Econ Theory 5: 25–47

    Article  Google Scholar 

  • Pintus PA (2006) Indeterminacy with almost constant returns to scale: capital-labor substitution matters. Econ Theory 28: 633–649

    Article  Google Scholar 

  • Romer P (1986) Increasing returns and long-run growth. J Political Econ 94: 1002–1037

    Article  Google Scholar 

  • Ryder HE Jr, Heal GM (1973) Optimal Growth with intertemporally dependent preferences. Rev Econ Stud 40:1–31

    Google Scholar 

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

    Article  Google Scholar 

  • Shimokawa T (2000) Existence and local indeterminacy of periodic equilibrium paths in infinite horizon models with external effects?. Econ Theory 16: 199–208

    Article  Google Scholar 

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

    Google Scholar 

  • Wirl F (1997) Stability and limit cycles in one-dimensional dynamic optimizations of competitive agents with a market externality. J Evol Econ 7: 73–89

    Article  Google Scholar 

  • Wirl F (2002) Stability and limit cycles in competitive equilibria subject to adjustment costs and dynamic spillovers. J Econ Dyn Control 26: 375–398

    Article  Google Scholar 

  • Wirl F (2004) Sustainable growth, renewable resources and pollution: thresholds and cycles. J Econ Dyn Control 28: 1149–1157

    Article  Google Scholar 

  • Wirl F (2007) Social interactions within a dynamic competitive economy. J Optim Theory Appl 133: 385–400

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wirl F, Feichtinger G (2006) History versus expectations: increasing returns or social influence?. J Socio Econ 35: 877–888

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Vienna, BWZ, Brünnerstr. 72, 1210, Vienna, Austria

    Franz Wirl

Authors
  1. Franz Wirl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Franz Wirl.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wirl, F. Conditions for indeterminacy and thresholds in neoclassical growth models. J Econ 102, 193–215 (2011). https://doi.org/10.1007/s00712-010-0179-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00712-010-0179-3

Keywords

JEL Classification

Search

Navigation