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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

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

1 introduction
1. Introduction
  • Private provision of a public good
  • International examples:
    • Greenhouse gas emission reduction
    • Military alliances
  • Nash equilibrium: Underprovision
a new solution market exchange
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
comparison
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
nash bargaining
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
outsourcing
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
literature international environmental policy
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
outline
Outline

2. The model

3. Nash bargaining without outsourcing

4. Market exchange without outsourcing

5. Outsourcing

6. Conclusion

2 the model
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
constrained pareto efficiency
Constrained Pareto efficiency
  • Without side payments
  • FOCs

or

  • Welfare weights λ1 = 1 and
  • λk and qi not determined
unconstrained pareto efficiency
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
noncooperative nash ncn
Noncooperative Nash (NCN)
  • FOCs
  • Not Pareto-efficient (underprovision)
3 nash bargaining
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’
4 market exchange solution
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
equilibrium
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:
two agents quadratic benefits and costs
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’
5 outsourcing
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
stage two
Stage two
  • qsi = production, qi contribution
  • P(Q) certificate price (perfect competition)
  • FOC
nash bargaining1
Nash bargaining
  • FOC
  • All Wi – Ai must be the same
unconstrained pareto optimum
Unconstrained Pareto optimum
  • Market clearing and perfect competition on certificate market:
  • Outsourcing as a vehicle for side payments
market exchange solution
Market exchange solution
  • FOC
  • In equilibrium:
  • Sum over i:
  • Unconstrained Pareto optimum
contributions
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
lindahl pricing
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
two agents quadratic benefits and costs1
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
6 conclusion
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
extensions
Extensions
  • Other functional forms
  • Asymmetric information
  • Coalition formation
  • Climate change policy simulations
  • Experiments
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