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Continuous-Time Public Good Contribution under Uncertainty

  • Giorgio Ferrari

    (Bielefeld University)

  • Jan-Henrik Steg

    (Bielefeld University)

  • Frank Riedel

    (Bielefeld University)

We study a continuous-time problem of public good contribution under uncertainty for an economy with a finite number of agents. Each agent aims to maximize his expected utility allocating his initial wealth over a given time period between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study the corresponding social planner problem and the case of strategic interaction between the agents. These problems are set up as stochastic control problems with both monotone and classical controls representing the cumulative contribution into the public good and the consumption of the private good, respectively. We characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions, which in turn allow to identify a universal signal process that triggers the public good investments. Further we show that our model exhibits a dynamic free rider effect. We explicitly evaluate it in a symmetric Black-Scholes setting with Cobb-Douglas utilities and we show that uncertainty and irreversibility of public good provisions need not affect the degree of free-riding.

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Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics Working Papers with number 485.

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Length: 30 pages
Date of creation: Feb 2015
Date of revision:
Handle: RePEc:bie:wpaper:485
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Web page: http://www.imw.uni-bielefeld.de/

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  1. Xia Su & Frank Riedel, 2006. "On Irreversible Investment," Bonn Econ Discussion Papers bgse13_2006, University of Bonn, Germany.
  2. V. Filipe Martins-da-Rocha & Frank Riedel, 2008. "On Equilibrium Prices in Continuous Time," Papers 0802.3585, arXiv.org.
  3. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
  4. Lockwood, B. & Thomas, J.P., 1999. "Gradualism and Irreversibility," The Warwick Economics Research Paper Series (TWERPS) 550, University of Warwick, Department of Economics.
  5. 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.
  6. Varian, Hal R., 1994. "Sequential contributions to public goods," Journal of Public Economics, Elsevier, vol. 53(2), pages 165-186, February.
  7. Maria B. Chiarolla & Giorgio Ferrari, 2011. "Identifying the Free Boundary of a Stochastic, Irreversible Investment Problem via the Bank-El Karoui Representation Theorem," Papers 1108.4886, arXiv.org, revised Dec 2013.
  8. Peter Bank & Frank Riedel, 2003. "Optimal Dynamic Choice of Durable and Perishable Goods," Bonn Econ Discussion Papers bgse29_2003, University of Bonn, Germany.
  9. Parimal Bag & Santanu Roy, 2008. "On Sequential and Simultaneous Contributions under Incomplete Information," Departmental Working Papers 0805, Southern Methodist University, Department of Economics, revised Nov 2008.
  10. Kerry Back & Dirk Paulsen, 2009. "Open-Loop Equilibria and Perfect Competition in Option Exercise Games," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4531-4552, November.
  11. V. Martins-da-Rocha & Frank Riedel, 2006. "Stochastic equilibria for economies under uncertainty with intertemporal substitution," Annals of Finance, Springer, vol. 2(1), pages 101-122, January.
  12. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
  13. Marco Battaglini & Salvatore Nunnari & Thomas Palfrey, 2012. "The Free Rider Problem: a Dynamic Analysis," NBER Working Papers 17926, National Bureau of Economic Research, Inc.
  14. Wen-Kai Wang & Christian-Oliver Ewald, 2010. "Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model," Decisions in Economics and Finance, Springer, vol. 33(2), pages 97-116, November.
  15. Giorgio Ferrari, 2012. "On an integral equation for the free-boundary of stochastic, irreversible investment problems," Papers 1211.0412, arXiv.org, revised Jan 2015.
  16. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
  17. 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.
  18. Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012. "Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources," Papers 1203.3757, arXiv.org, revised Aug 2013.
  19. Jan-Henrik Steg, 2012. "Irreversible investment in oligopoly," Finance and Stochastics, Springer, vol. 16(2), pages 207-224, April.
  20. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
  21. Jean-Jacques Laffont, 1988. "Fundamentals of Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121271, June.
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