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Installment4 - 4 Public Goods Chapter 6 in Stiglitz 4.1...

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4 Public Goods Chapter 6 in Stiglitz 4.1 Terminology A good is said to be rival if two consumer cannot consume the same unit. When we considered the Edgeworth boxes we assumed that goods are rival because the market clearing conditions were x A 1 + x B 1 = e A 1 + e B 1 x A 2 + x B 2 = e A 2 + e B 2 : Obvious examples are anything that can be eaten. A good is non-rival possibilities for any other consumer. The ultimate example is knowledge. ...if one person ±gures out how to make a wheel, then that knowledge can be used over and over again without a/ecting the wheel making of the original inventor. For rival goods, a good is excludable if the owner can prevent theft. For non-rival goods, a good is excludable if there is a technology that can prevent a consumer from getting access to the good (eg., a fence around a national park or successful anti-copying software on DVDs). . A non-rival good is non-excludable if it is impossible to prevent any consumers to get access to the good. The best example of this is probably investments in reducing carbon dioxide emissions (or any other investment that would only global environmental gains without any particular localized bene±ts). Traditionally, non-excludable public goods are called pure public goods . Excludable rival goods (like apples) are called private goods . 37
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4.2 Example of an Economy with a Pure Public Good We will try to keep things as simple as possible: economy with two agents. Label the agents A and B: Agent J = A;B consumes two goods. Let x J denote the consumption of the private good and y the (common) consumption of the public good. Agent J ±s preferences described by utility function u J ( x;y ) . initially, there is no public good available, but each agent J has an endowment e J > 0 of the private good and each agent can turn a unit private good into a unit public good on a one-to-one basis. That is, think of x as dollars and y as public radio. Obviously, it is sort of unclear what one unit of public radio is, but the assumption in the model is that there is constant returns to scale in the public radio production. ...which can be thought of as a choice of units. 4.3 Private Provision of Public Goods In order to formalize the idea of citizens voluntarily providing a public good we need to write down a strategic model. The reason is imply that if everyone took the aggregate supply of the public good as given, then nobody would have an incentive to contribute at all. Let y A and y B be the contribution towards the public good by consumers A and B respectively. Clearly, the associated consumptions of the private good are x A = e A ± y A x B = e B ± y B The associated happiness of agents A and B are u A e A ± y A ;y A + y B ± (1) u B e B ± y B ;y A + y B ± : 38
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4.4 The Game Well assume that the two players decide on their contributions towards the public good
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This note was uploaded on 11/02/2008 for the course ECON 440 taught by Professor Peternorman during the Spring '08 term at UNC.

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Installment4 - 4 Public Goods Chapter 6 in Stiglitz 4.1...

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