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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 good

  • 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: goodMarket 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 good

  • 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 good

  • 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 good

  • 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 good

  • 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 good

2. The model

3. Nash bargaining without outsourcing

4. Market exchange without outsourcing

5. Outsourcing

6. Conclusion


2 the model
2. The model good

  • 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 good

  • Without side payments

  • FOCs

    or

  • Welfare weights λ1 = 1 and

  • λk and qi not determined


Unconstrained pareto efficiency
Unconstrained Pareto efficiency good

  • 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) good

  • FOCs

  • Not Pareto-efficient (underprovision)


3 nash bargaining
3. Nash bargaining good

  • 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 good

  • 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 good

  • 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 good

  • 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 good

  • 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 good

  • qsi = production, qi contribution

  • P(Q) certificate price (perfect competition)

  • FOC


Nash bargaining1
Nash bargaining good

  • FOC

  • All Wi – Ai must be the same


Unconstrained pareto optimum
Unconstrained Pareto optimum good

  • Market clearing and perfect competition on certificate market:

  • Outsourcing as a vehicle for side payments


Market exchange solution
Market exchange solution good

  • FOC

  • In equilibrium:

  • Sum over i:

  • Unconstrained Pareto optimum


Contributions
Contributions good

  • 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? good

  • 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 good

  • 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 good

  • 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 good

  • Other functional forms

  • Asymmetric information

  • Coalition formation

  • Climate change policy simulations

  • Experiments


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