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Pareto-efficient solutions for shared production of a public good work in progress

Pareto-efficient solutions for shared production of a public good work in progress. Andries Nentjes , U of Groningen Bouwe Dijkstra , U of Nottingham Jan- Tjeerd Boom, Danish EPA Frans de Vries , U of Stirling. 1. Introduction. Private provision of a public good International examples:

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Pareto-efficient solutions for shared production of a public good work in progress

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  1. Pareto-efficient solutions for shared production of a public goodwork in progress AndriesNentjes, U of Groningen BouweDijkstra, U of Nottingham Jan-Tjeerd Boom, Danish EPA Frans de Vries, U of Stirling

  2. 1. Introduction • Private provision of a public good • International examples: • Greenhouse gas emission reduction • Military alliances • Nash equilibrium: Underprovision

  3. A “new” solution: Market Exchange • Nentjes (1990) • How much yi of the public good would you be willing to supply if you would get Yi = piyi from the group in return? • Equilibrium prices where all Yi = Σyj • Unique stable equilibrium

  4. Comparison • This paper: Nash bargaining • Nentjes, Rübbelke, Dijkstra, De Vries: • Kaneko ratio equilibrium • Guttman matching scheme • Andreoni-Bergman tax-subsidy scheme • Falkinger tax-subsidy scheme • Roemer’s Kantian equilibrium

  5. Nash bargaining • Constructed to have desirable outcomes • Bargaining process itself is black box • Noncooperative implementation • Binmore et al. ’86: 2 players, alternate offers • Chae&Yang ’94, Krishna&Serrano ’96, Hart&Mas-Colell ’96: n players, specific bargaining procedure, equilibrium concept • Requires full information

  6. Outsourcing • E.g. emission trading • Each agent commits to a certain public good contribution • Agent i who produces more than her contribution earns certificates which she can sell to another agent j • Agent j can produce below contribution

  7. Literature: International environmental policy • Hoel (1991): Nash bargaining without emission trading • Helm (2003): Noncooperative emission reduction with and without emission trading • Boom (2006 thesis): Nash bargaining with and without emission trading

  8. Outline 2. The model 3. Nash bargaining without outsourcing 4. Market exchange without outsourcing 5. Outsourcing 6. Conclusion

  9. 2. The model • n agents (i = 1,...,n) producing and consuming a public good Q = Σqi • Cost function Ci(qi) with Ci’, Ci’’ ≥ 0 • Benefit function Bi(Q) with Bi’ ≥ 0, Bi’’ ≤ 0 • Specific case: two agents, quadratic functions

  10. Constrained Pareto efficiency • Without side payments • FOCs or • Welfare weights λ1 = 1 and • λk and qi not determined

  11. Unconstrained Pareto efficiency • With side payments, agent i receives xi • FOC for xi: λj = μ = 1 • FOC for qi: • All λj and qi determined, but xi not determined

  12. Noncooperative Nash (NCN) • FOCs • Not Pareto-efficient (underprovision)

  13. 3. Nash bargaining • With equal bargaining weights (Aj NCN payoff) • FOCs • Constrained Pareto optimal, generally unequal welfare weights • Higher gain: Lower welfare weight, higher Ci’

  14. 4. Market Exchange Solution • How much yi of the public good would you be willing to supply if you would get Yi = piyi from the group in return? • On top of the NCN amounts qin, Qn • FOCs • Agent i supplies yi, demands Yi

  15. Equilibrium • All agents demand the same amount, which is the sum of all their supplies: • Equilibrium prices • Agent i’s supply share • Constrained Pareto optimal:

  16. Two agents, quadratic benefits and costs • MES and NBS coincide • Probably not a general result • Agent with highest gi has highest qi • c1 = c2: High-benefit agent has highest Ci’ • b1 = b2: High-cost agent has highest Ci’

  17. 5. Outsourcing • Stage 1: Each agent commits to a certain public good contribution • Stage 2: Agent i who produces more than her contribution earns certificates which she can sell to another agent j • Agent j can produce below contribution

  18. Stage two • qsi = production, qi contribution • P(Q) certificate price (perfect competition) • FOC

  19. Nash bargaining • FOC • All Wi – Ai must be the same

  20. Unconstrained Pareto optimum • Market clearing and perfect competition on certificate market: • Outsourcing as a vehicle for side payments

  21. Market exchange solution • FOC • In equilibrium: • Sum over i: • Unconstrained Pareto optimum

  22. Contributions • Substituting back into yields • Every agent contributes in proportion to her marginal benefits, adjusted by price manipulation motive • Remember with NBS: Every agent has the same gain

  23. Lindahl pricing? • Ask every public good consumer i how much he would demand at price pi • Public good is supplied efficiently • Only with outsourcing • MES contributions with outsourcing: • Lindahl • Producer’s price manipulation motive

  24. Two agents, quadratic benefits and costs • Comparing MES and NBS • Identical benefit functions: • High-cost agent pays low-cost agent • Identical cost functions: • High-benefit agent pays low-benefit agent • Payments lower in MES than in NBS • Attempts to manipulate the permit price

  25. 6. Conclusion • Comparison of Nash bargaining and market exchange solutions for public good provision • Example: Two agents, quadratic benefits and costs • Without outsourcing: both are constrained Pareto-optimal • MES and NBS coincide • With outsourcing: both are unconstrained Pareto-optimal • Smaller transfers in MES

  26. Extensions • Other functional forms • Asymmetric information • Coalition formation • Climate change policy simulations • Experiments

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