lecture 4 - public goods

Public Goods

Key Concepts

• What distinguishes public goods from private goods?

  • Public goods are non-rivalrous and non-excludable, meaning that one person's consumption does not reduce availability to others, and it is difficult to prevent non-payers from consuming the good.

  • Private goods are rivalrous and excludable, where consumption by one person prevents consumption by others, and access can be restricted to those who pay.

• Why do private markets undersupply pure public goods? Free rider problem.

  • The free-rider problem occurs because individuals can benefit from public goods without contributing to their cost, leading to under-provision by private markets.

• What determines an efficient supply of pure public goods?

  • Efficient supply is achieved when the sum of individual marginal benefits equals the marginal cost of providing the public good. This is represented by the equation \sum MRS = MRT, where MRS is the marginal rate of substitution and MRT is the marginal rate of transformation.

Public Goods: Key Concepts

• Non-Rival Consumption:

  • One person's use of the good does not prevent its use by another. This means that the marginal cost of providing the good to an additional person is zero.

  • Example: National defense. Everyone in a country benefits from national defense, and one person's protection does not diminish the protection available to others.

• Non-Excludability:

  • It is not possible to exclude individuals from the benefits of the good without incurring great cost. This often leads to the free-rider problem.

  • Example: Street lighting. Once street lights are installed, it is difficult to prevent anyone from benefiting from the illumination.

Public vs. Private Goods

• Private Goods:

  • Rival consumption and excludability. These goods are efficiently provided by private markets.

  • Example: iPhone. Only the person who owns the iPhone can use it (excludable), and if someone else is using it, you cannot use it at the same time (rivalrous).

• Pure Public Goods:

  • Non-rival consumption and non-excludability. These goods are typically under-supplied by private markets due to the free-rider problem.

  • Example: Street lighting, national defense.

Pure and Impure Public Goods

• Pure Private Good:

  • Health services, education (though often subsidized or publicly provided due to positive externalities).

• Pure Public Good:

  • National defense.

• Impure Public Goods:

  • Fire protection, congested highway. These goods exhibit some degree of rivalry or excludability.

• The categorization depends on marginal cost of use and ease of exclusion.

  • Diagram illustrating where different types of goods fall on a spectrum of marginal cost of use (y-axis) versus ease of exclusion (x-axis).

Market Failure

• Market failure is a reason for public provision of public goods. Private markets fail to efficiently provide public goods due to non-rivalry and non-excludability.

• If charging is possible:

  • For non-rival goods, exclusion (via prices) is undesirable because it results in underconsumption. The efficient price is zero, but private firms cannot operate at this price.

• If charging is not possible:

  • Non-exclusion results in undersupply. Since firms cannot charge for the good, they have little incentive to produce it.

Paying for Public Goods

• How much to charge? (In case that excludability is possible):

  • Public vs. private provision. Even with some private provision, there will be undersupply. The government often steps in to provide or subsidize these goods.

• In case of no excludability: Free Rider Problem:

  • Private provision: voluntary contribution.

  • Example: Voluntary contribution to the National Theater streaming plays during the pandemic.

  • Free Rider Problem:

  • Reluctance of individuals to contribute voluntarily to the support of public goods.

  • If the good will be provided anyway, why should I pay? This leads to a suboptimal level of provision.

  • Public provision: taxation. Taxes can ensure that everyone contributes to the provision of public goods, overcoming the free-rider problem.

Recap of Public Goods

• Pure Public Good:

  • Perfectly non-rival consumption and non-excludability.

  • Marginal cost of providing it to an additional person is strictly zero.

• With non-rival consumption: underconsumption and/or undersupply.

• With non-excludability: free rider problem and undersupply.

Publicly Provided Private Goods - Distortions

• Large marginal costs associated with the provision.

• Diagrams illustrating welfare loss from excessive consumption due to publicly provided private goods.

• Figure 5.3 A: Welfare loss from excessive consumption (Qe - Qm). Illustrates the deadweight loss when the quantity consumed exceeds the efficient quantity.

• Figure 5.3 B: Welfare loss from excessive consumption (Qe - Qm). Shows a similar deadweight loss under different market conditions.

Three Methods of Rationing Publicly Provided Goods

1. User Charges:

   • Advantage: Those who benefit bear the costs. This can improve efficiency by aligning costs with benefits.

   • Disadvantages: Leads to underconsumption, transaction costs. Some individuals may be excluded due to inability to pay, and administering the charges can be costly.

2. Uniform Provision:

   • Advantage: Saves on transaction costs. This is simple and easy to administer.

   • Disadvantages: Leads some to underconsume, others to overconsume. A uniform level may not satisfy everyone's needs.

3. Queuing:

   • Advantage: Goods are not allocated based on wealth. Everyone has an equal opportunity to obtain the good.

   • Disadvantages: Basis of allocation (who has time to spare) may be undesirable. Those with higher opportunity costs of time may be excluded.

Efficiency Condition for Public Good Provision

• What is the optimal level supply of public goods?

• Pure public goods are efficiently supplied when the marginal social benefit of the public good equates the marginal social costs.

• Or when the sum of the marginal rates of substitution of private good for public good (over all individuals) is equal to the marginal rate of transformation of private good for private good: \sum MRS = MRT

Free-Riding and Preference Revelation

• Markets work by consumers expressing their true preferences.

• When goods are private, there is no incentive to make false statements.

• Free-riding with public goods involves understating the preference for the public good with the intention of shifting the burden of payment onto other consumers.

• Therefore, it is possible for a consumer to spend more on private goods and less on public goods.

• Why does the free-rider problem make it difficult for markets to provide the efficient level of public goods?

  • The free-rider problem leads to an under-revelation of true demand, resulting in suboptimal provision.

Efficiency Examples

• Consider two consumers with the following demand functions for a public good:

  • p1 = 10 - (1/10)G

  • p2 = 20 - (1/10)G

  • where pi is the price that i is willing to pay for quantity G.

  • a) What is the optimal level of the public good if the marginal cost of the public good is $25?

  • Solve for G where the sum of marginal benefits (willingness to pay) equals marginal cost.

  • 25 = p1 + p2 = 10 - (1/10)G + 20 - (1/10)G

  • 25 = 30 - (2/10)G

  • -5 = -(2/10)G

  • G = 25

  • b) What is the optimal level of the public good if the marginal cost of the public good is $5?

  • 5 = p1 + p2 = 10 - (1/10)G + 20 - (1/10)G

  • 5 = 30 - (2/10)G

  • G = 125

  • c) What is the optimal level of the public good if the marginal cost of the public good is $40?

  • 40 = p1 + p2 = 10 - (1/10)G + 20 - (1/10)G

  • 40 = 30 - (2/10)G

  • 10 = -(2/10)G

  • G = 0

  • d) Should the consumers make an honest statement of their demand functions?

  • Depends on the consequences of the announcement.

  • Case 1: Government uses the announcement to choose whether the public good is provided, but the consumers do not have to pay… In this case, understating demand is rational if the good will still be provided.

• There are three consumers of a public good. The demand for consumers are as follows:

  • p1 = 50 - G

  • p2 = 110 - G

  • p3 = 150 - G

  • where G measures the number of units of the good and pi the price in pounds. The marginal cost of the public good is $190.

  • What is the optimal level of provision of the public good? Illustrate your answer with a graph.

  • sum of WTP = marginal cost

  • 50 - G + 110 - G + 150 - G = 190

  • 310 - 3G = 190

  • 3G = 120

  • G = 40

  • Explain why the public good may not be supplied at all because of the free-rider problem.

  • Because individuals may not want to pay, and it may not be possible to exclude them, the public good would not be supplied at all.

  • If the public good is not supplied at all, what is the size of the deadweight loss arising from this market failure?

  • Loss with respect to the situation, Sum WTP=190 (show graphically).

Demand Curves for Publicly Provided Private Goods

• Budget constraint: C + pG = Y

  • C: consumption of private good

  • G: consumption of public good

  • P: Tax price

  • Y: Income

Collective Demand Function - Public Good

• Diagram illustrating individual demand curves and the collective demand curve for a public good.

• Tax price paid by Crusoe and Friday, with the collective demand curve being the vertical summation of individual demand curves.

• Figure 5.7.

Efficient Production of Public Goods

• Supply curve: The price represents how much of other goods have to be forgone to produce one more unit of public good (this is the marginal cost or the marginal rate of transformation).

• Collective demand equals the sum of marginal rates of substitution.

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