# Chapter 4: Public Goods Econ 330: Public Finance Dr. Reyadh Faras

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Chapter 4: Public Goods Econ 330: Public Finance Dr. Reyadh Faras

Definition of A Public Good
Once it is provided, the additional resource cost of another person consuming the good is zero, which means that consumption is nonrival. To prevent anyone from consuming the good is either very expensive or impossible, which means that consumption is nonexcludable. In contrast, consumption of a private good is rival and excludable. Impure public good is a good that satisfies either condition.

Even though everyone consumes the same quantity of the good, consumption is not valued equally by all. Classification as a public good depends on market conditions and the state of technology. Private goods are not necessarily provided exclusively by the private sector. Public goods are not necessarily provided exclusively by the public sector.

Types of Goods NATURAL PRIVATE GOODS MONOPOLY COMMON RESOURCES
EXCLUDABLE RIVAL YES NO NATURAL MONOPOLY PRIVATE GOODS 1st click - “Private goods” 2nd click - “Public goods” 3rd click - “Common resources” 4th click - “Natural monopoly” COMMON RESOURCES PUBLIC GOODS

Efficient Provision Private Goods
Market demand is a horizontal summation of quantities consumed by all consumers. Equilibrium is reached where supply equals demand at quantity ____ and price _____ . Adam consumes _____ units and Eve consumes ____ units. Note that there consumption does not have to be equal, why? At equilibrium, resource allocation is pareto efficient: A utility maximizing individual sets the marginal rate of substitution of the two goods equal to the price ratio of the two goods:  MRSfa = Pf / Pa

Efficient Provision of Private Goods
Price Adam (DfA) Eve (DfA) Market (DfA+E) \$11 5 1 6 \$9 7 3 10 \$7 9 14 \$5 11 18 \$3 13 22 \$1 15 26

DfA+E DfA DfE \$ Sf Quantity of Pizza 1st click – Adam’s D curve
Sf 1st click – Adam’s D curve 2nd click – Eve’s D curve 3rd click – sum of Adam and Eve at P = 11 4th click – sum of Adam and Eve at P = 9 5t click – sum of Adam and Eve at P = 7 6th click – sum of Adam and Eve at P = 5 7th click – sum of Adam and Eve at P = 3 8th clck – sum of Adam and Eve at P = 1 9th click - Market Demand curve and dashed horizontal lines disappear 10th click – Market Supply curve DfA+E DfA DfE Quantity of Pizza

Set Pa= \$1, this reduces the condition to: MRSfa = Pf Adam and Eve both set MRS = ____ Producers set the marginal rate of transformation MRTfa  = ____ At equilibrium, MRSAfa = MRSEfa = MRTfa , which is the condition for pareto efficiency.

A. Deriving the Efficiency Contribution
Public Goods Assume Adam and Eve watch a firework show consists of 19 rockets and each extra rocket costs \$5. Adam is willing to pay \$6 for the extra rocket, while Eve is willing to pay \$4. Question, is it efficient to expand the size of the show by one extra rocket? Answer, we need to compare the marginal ________ to the marginal ________.

Efficient Provision of Public Goods
Units of Fireworks 1 2 3 4 Adam (DrA) \$300 \$250 \$200 \$150 Eve (DfE) 250 200 150 100 Market (DfA+E) \$550 \$450 \$350

DrA+E DrA DrE \$ Sr Quantity of Fireworks 1st click – Adam’s D curve
Sr DrA+E 1st click – Adam’s D curve 2nd click – Eve’s D curve 3rd click – sum of Adam and Eve at Q = 1 4th click – sum of Adam and Eve at Q = 2 5t click – sum of Adam and Eve at Q = 3 6th click – sum of Adam and Eve at Q = 4 7th click - Market Demand curve and dashed horizontal lines disappear 8th click – Market Supply curve DrA DrE Quantity of Fireworks

Because consumption is nonrival, the 20th rocket is
consumed by both. Hence, the marginal benefit of the 20th rocket is the sum of what they are willing to pay, which is \$____. Because the marginal cost is \$5, it is worthy to consume the 20th rocket. Generally: if the sum of individuals' willingness to pay for an additional unit of a public good exceeds its marginal cost, efficiency requires that the unit be purchased; otherwise it should not. Efficiency requires that provision of a public good be expanded until reaching the level at which the sum of each person's marginal valuation on the last unit just equals the marginal cost.

Efficiency is reached at the point where Adam's and
Eve's willingness to pay for an additional unit just equals the marginal cost of producing a unit. Graphically, the marginal cost schedule, S, is superimposed on the group willingness to pay curve, DA+E. The intersection occurs at quantity 45 and marginal cost \$6. At equilibrium, MRSAra + MRSEra = MRTra , which is the condition for pareto efficiency. For a public good, market demand is found by vertical summation of individual demand curves.

Note: For a private good, everyone has the same MRS, but people can consume different quantities. Therefore, demands are summed horizontally over the differing quantities.  Individuals see the same price and then decide what quantity they want.  For a public good, everyone consumes the same quantity, but people can have different MRS.  Therefore, vertical summation of quantities is required to find the group willingness to pay.

Everyone sees the same quantity and then decide what price they are willing to pay.
Problem: People have incentives to hide their true preferences for public good in order not to pay for it. This is called the free rider problem, which results in a shortage in the supply of public goods (below the efficient amount).

Solution: suppose 1) each person's demand curve is known, and 2) transferability of the good to another person is impossible, then each person is charged a price based on its willingness to pay, this is called perfect price discrimination. Conclusion: Since knowledge of individual preferences is impossible, private provision leads to inefficiency (even if a nonrival good is excludable).

B. The Free Rider Problem
Some suggest as a solution to the free rider problem that the government provides the public good. The government is able to find everyone's preference and then use its coercive power to force everyone to pay. Free ridership is based on the hypothesis that people maximize a utility function that depends only on their own consumption.

The Privatization Debate
Definition: Privatization means taking services that are supplied by the government and turning them over to the private sector for provision and/or production.

A. Public Versus Private Provision
Some services provided by publicly provided goods can be obtained privately. Examples: Protection (private policemen are 3 times public ones) and dispute settlement (40,000 cases are solved privately). Historically, in the 17th century many services were provided privately, than now. However, recent trends are towards private provisions in many communities. What is the right mix of public and private provision? What criteria used to select inputs?

There are several considerations:
1. Relative wage and materials costs: the less expensive sector is preferred on efficiency grounds. 2. Administrative costs: under public provision, fixed administrative costs are spread over a large group of people. 3. Diversity of Tastes: with diversity, private provision is more efficient because consumption can be fitted into tastes. 4. Distributional issues: community's notion of fairness requires the availability of some goods to everyone.

B. Public Versus Private Production
Even with the agreement of providing goods publicly, disagreement may arise over whether they should be produced publicly or privately. This is due to differences regarding: 1) the role of government in the economy. 2) the relative costs of public and private production. Little systematic evidence exists on the cost differences between private and public production because of differences in quality of services provided by each. Opponents of privatization argue that private contractors produce inferior goods.

Response: 1) The government writes a contract that specifies the level of desired quality, 2) Consumers switch to better quality producers, 3) Reputation makes private producers worry about quality in order to get future contracts. 4) Market environment matters. For example, a privately owned monopoly may produce inefficiently, while a public producer facing a lot of competition may produce efficiently.