Skip to main content
Log in

Existence of equilibrium in OLG economies with increasing returns

  • Research Article
  • Published:
Economic Theory Aims and scope Submit manuscript

Abstract

We consider a standard overlapping generations (OLG) economy with a simple demographic structure where a new cohort of agents appears at each period and whose economic activity is extended over two successive periods, and finitely many firms may be active. The production possibilities are described by a sequence of production set-valued mappings and the main innovation comes from the fact that we allow for increasing returns to scale of more general type of non-convexities. To describe the behavior of the firms, we consider loss-free pricing rules, which cover the case of the average pricing rule, the competitive behavior when the firms have convex production sets, and the competitive behavior with quantity constraints à la Dehez–Drèze. We prove the existence of an equilibrium under assumptions, which are at the same level of generality than the ones for the existence in an exchange OLG economy.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. \(C_t^+=\{v \in {\mathbb {R}}^{L_t} \mid v \cdot u \ge 0, \forall u \in C_t\}\)

References

  • Balasko, Y., Shell, K.: The overlapping generations model I: the case of pure exchange without money. J. Econ. Theory 23, 281–306 (1980)

    Article  Google Scholar 

  • Balasko, Y., Shell, K.: The overlapping generations model II: the case of pure exchange with money. J. Econ. Theory 24, 112–142 (1981)

    Article  Google Scholar 

  • Balasko, Y., Cass, D., Shell, K.: Existence of competitive equilibrium in a general overlapping generations model. J. Econ. Theory 23, 307–322 (1980)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bonnisseau, J.M., Cornet, B.: Existence of equilibria when firms follow bounded losses pricing rules. J. Math. Econ. 17, 119–147 (1988)

    Article  Google Scholar 

  • Bonnisseau, J.M., Jamin, A.: Equilibria with increasing returns: sufficient conditions on bounded production allocations. J. Public Econ. Theory 10, 1033–1068 (2008)

    Article  Google Scholar 

  • Cornet, B.: General equilibrium theory and increasing returns: presentation. J. Math. Econ. 17, 103–118 (1988)

    Article  Google Scholar 

  • Dehez, P., Drèze, J.: Competitive equilibria with quantity-taking producers and increasing returns to scale. J. Math. Econ. 17, 209–230 (1988a)

    Article  Google Scholar 

  • Dehez, P., Drèze, J.: Distributive production sets and equilibria with increasing. J. Math. Econ. 17, 231–248 (1988b)

    Article  Google Scholar 

  • Dierker, E., Guesnerie, R., Neuefeind, W.: General equilibrium where some firms follow special pricing rules. Econometrica 53, 1369–1393 (1985)

    Article  Google Scholar 

  • Gourdel, P.: Existence of intransitive equilibria in nonconvex economies. Set-Valued Anal. 3, 307–337 (1995)

    Article  Google Scholar 

  • Magill, M., Quinzii, M.: The Stock Market in the Overlapping Generations. UC Davis Working Paper, No. 99–13 (1999)

  • Marshall, A.: Principles of Economics, 8th edn. Macmillan & Co, London (1920)

    Google Scholar 

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

    Article  Google Scholar 

  • Tvede, M.: Overlapping Generations Economies. Palgrave Macmillan, Basingstoke (2010)

    Book  Google Scholar 

  • Villar, A.: Equilibrium and Efficiency in Production Economies. Springer, Berlin, Heidelberg (2000)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jean-Marc Bonnisseau.

Additional information

This work was supported by the French National Research Agency, through the program Investissements d’Avenir, ANR-10–LABX-93-01.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bonnisseau, JM., Rakotonindrainy, L. Existence of equilibrium in OLG economies with increasing returns. Econ Theory 63, 111–129 (2017). https://doi.org/10.1007/s00199-016-0955-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00199-016-0955-6

Keywords

JEL Classification

Navigation