course readings---Chapter07b

course readings---Chapter07b - Chapter 7 (Part II) Public...

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-1- 1 Chapter 7 (Part II) Public Goods Contents: Excludable Public Goods Heterogeneous Demand for a Public Good The Case of Increasing Marginal Costs The Second-Best Problem of Balanced-Budget Provision Public Goods, Environmental Amenities and Nonuse Benefits Heterogeneous Demand for a Public Good Low Marginal Cost for Provision of a Public Good Excludable Public Goods We have seen that with non-excludable public goods, the free-rider problem may lead to the inefficient provision of public goods by the private market. With excludable public goods , private markets may either provide the efficient level or inefficient level of public goods. Two key issues determine whether the private market will provide the efficient level of public goods: • heterogeneity of consumer demand, and • the ability of private providers to price discriminate. However, in every case, the distribution of welfare among producers and consumers under private provision of public goods varies significantly from the distribution of welfare among these groups under public (government) provision of public goods. The Socially-Optimal Level of an Excludable Public Good The socially optimal level of provision of an excludable public good is the same as it is for a non-excludable public good, namely, X*. When public goods are excludable, a private firm can build some kind of barrier to prevent consumers from free riding. Let's call this barrier a "fence." With excludable public goods, the private owner of the resource will build a fence and charge each consumer their willingness to pay (area under the individual demand curve). Different cases arise depending on whether consumers are homogeneous or heterogeneous. We will first consider the case of homogeneous individuals. Excludable Public Goods with Homogeneous Consumers A private firm will build a fence and attempt to act as a monopoly by charging each individual their maximum willingness to pay (area under the individual demand curve). The sum of willingness to pay across all individuals is the monopoly Total Revenue function: TR(X) = 0 X n D(X) dx
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-2- 2 The monopolist maximizes profits: Max . X π = nD ( x ) dx MC ( x ) dx 0 X 0 X When nD(X) = n(a - bX) and MC(X) = c + d X, as in the social problem, the FOC is: nD(X) = MC(X) or n(a - bX) = c + dX Solving for Xm, we get: X m = (na - c)/(nb + d) and find, comparing X m with X*, that X m = X*. Thus, in the case of homogeneous consumers, we get the surprising result that the monopolist provides the optimal level, X*. Of course, the distribution of welfare between consumers and the monopolist is very different from the case of public provision of the public good. When the monopolist provides the public good, the monopolist gets all of the benefits. This is the case of first-degree price discrimination.
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course readings---Chapter07b - Chapter 7 (Part II) Public...

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