Optimal Allocation of Public Goods: A Solution to the “Free Rider” Problem

By Theodore Groves and John Ledyard

Summary

Assumptions

• Arrow-Debreu Economy with public goods

Decentralized and competitive, competitive consumers taking aggregate effect of others’ messages as given, competitive producers maximizing profits taking prices as given

• Neo-classical Economy

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Problem

• In a competitive economy, Pareto-optimal allocation of resources in the presence of public goods is incompatible with individual incentives.

“Free-rider problem”

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Solution

• Establishing an optimal government characterized by a certain 1) language (messaging system), 2) public goods allocation rule, and 3) taxation rule.

Assumptions (The Economy)

Assumptions (The Economy)

Assumptions (The Government)

Assumptions (Producer Behavior)

• Price-taking profit maximizers

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Assumptions (Consumer Behavior)

Assumptions (Equilibrium)

Assumptions (Optimality)

• Fundamental Welfare Theorems slightly redefined for economies with public goods
• Every competitive allocation is Pareto optimal (First FWT)
• Every Pareto optimal allocation is competitive for some initial distribution of endowments and profit shares (Second FWT)

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Problem (Two Conventional Government Models)

• The Naïve Government

Consumer reports how many of each public goods he is willing to buy.

Then, government purchases the aggregate amount.

Each consumer pays for the amount.

• The Lindahl Government

Consumer reports marginal willingness-to-pay (MRS given a numeraire private goods) for each public goods.

Then, government provides the amount such that the sum of the MRS for each public goods equals the marginal cost of the public goods.

Each consumer is taxed per unit as much as his reported MRS.

• Neither government optimally allocates resources.

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Solution (Abstract Government)

• Broad idea, experimental approach, simplified, not the final solution provided by the author

Solution (Abstract Government)

Rules

Solution (Abstract Government)

• Reported MRS is equal to true willingness-to-pay

Solution (Limits of the Abstract Government)

• Message space is complicated (Unfeasible in real life)
• Biased (Does not satisfy the second FWT)

Solution (Limits of the Abstract Government)

• Satisfied properties

First fundamental welfare theorem, incentive compatibility

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• Unsatisfied properties

Second fundamental welfare theorem, message space feasibility

Solution (The Optimal Government)

Solution (The Optimal Government)

Abstract Government

Abstract Government

Solution (The Optimal Government)

M Ƒ

• Properties satisfied

First FWT, Second FWT, Incentive Compatibility, message space feasibility

+ More general economy than Neo-classical economy.

Recap

Limitation (presenter’s opinion)