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The Free Rider Problem: a Dynamic Analysis

  • Marco Battaglini
  • Salvatore Nunnari
  • Thomas Palfrey

We present a dynamic model of free riding in which n infinitely lived agents choose between private consumption and contributions to a durable public good g. We characterize the set of continuous Markov equilibria in economies with reversibility, where investments can be positive or negative; and in economies with irreversibility, where investments are non negative and g can only be reduced by depreciation. With reversibility, there is a continuum of equilibrium steady states: the highest equilibrium steady state of g is increasing in n, and the lowest is decreasing. With irreversibility, the set of equilibrium steady states converges to a unique point as depreciation converges to zero: the highest steady state possible with reversibility. In both cases, the highest steady state converges to the efficient steady state as agents become increasingly patient. In economies with reversibility there are always non-monotonic equilibria in which g converges to the steady state with damped oscillations; and there can be equilibria with no stable steady state, but a unique persistent limit cycle.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 17926.

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Date of creation: Mar 2012
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Handle: RePEc:nbr:nberwo:17926
Note: PE POL
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  1. Gaitsgory, Vladimir & Nitzan, Shmuel, 1994. "A folk theorem for dynamic games," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 167-178, March.
  2. Marco Battaglini & Stephen Coate, 2008. "Fiscal Policy over the Real Business Cycle: A Positive Theory," NBER Working Papers 14047, National Bureau of Economic Research, Inc.
  3. Battaglini, Marco & Nunnari, Salvatore & Palfrey, Thomas, 2011. "Legislative bargaining and the dynamics of public investment," Discussion Papers, Research Unit: Market Behavior SP II 2011-205, Social Science Research Center Berlin (WZB).
  4. Marco Battaglini & Steve Coate, 2006. "A Dynamic Theory of Public Spending, Taxation and Debt," Levine's Bibliography 122247000000001094, UCLA Department of Economics.
  5. Stephen Coate & Marco Battaglini, 2005. "Inefficiency in Legislative Policy-Making: A Dynamic Analysis," 2005 Meeting Papers 209, Society for Economic Dynamics.
  6. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
  7. Palfrey, Thomas R. & Rosenthal, Howard, 1984. "Participation and the provision of discrete public goods: a strategic analysis," Journal of Public Economics, Elsevier, vol. 24(2), pages 171-193, July.
  8. Kenji Fujiwara & Norimichi Matsueda, 2009. "Dynamic Voluntary Provision of Public Goods: A Generalization," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(1), pages 27-36, 02.
  9. Marco Battaglini, 2009. "On the Case for a Balanced Budget Amendment to the U.S. Constitution," 2009 Meeting Papers 131, Society for Economic Dynamics.
  10. Leslie M. Marx & Steven A. Matthews, 1997. "Dynamic Voluntary Contribution to a Public Project," Discussion Papers 1188, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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