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Pareto-Efficient Solutions for Shared Production of Public Goods: An Analysis of Market Exchange

This paper explores Pareto-efficient solutions for the shared production of public goods, focusing on market exchange mechanisms and Nash bargaining. It compares the efficacy of private provision through outsourcing and examines various equilibrium concepts, including Nash equilibrium, Kaneko ratio equilibrium, and tax-subsidy schemes. By analyzing agent interactions and contributions, the authors aim to identify mechanisms that produce desirable welfare outcomes. The findings highlight the importance of cooperation and strategic bargaining in achieving efficient public good production.

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Pareto-Efficient Solutions for Shared Production of Public Goods: An Analysis of Market Exchange

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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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