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Unformatted text preview: Public goods and Externalities 1 Public Good Traditionally, a public good is de&ned as one with the property that one person&s consumption of the good does not diminish the supply available to others . ("jointness of consumption" or "inapplicability of the exclusion principle" ). Examples of public goods are national defence, infrastructures, ...). The exposition of public goods is essentially that of Samuelson. Consider a model with 2 goods ( x and y ) and 2 consumers ( i = 1 ; 2 ). x ( & 0) is a public good, y is a private good: y i ( & 0) is the quantity of the private good consumed by i: The utility function of agent i is denoted by U i ( x;y i ) [ note that the same quantity x is consumed by all agents i ] : U i : R 2 + ! R is continuous on R 2 + and has all the second order partials and these are continuous on R 2 ++ . The economy has 1 unit of private good; however, there is a technology which can be used to transform the private good into a public good: x = &z is an example of this technology [ z is the quantity of input of private good needed to produce &z of the public good ]; & > : An allocation ( x;y 1 ;y 2 ) & satises x & ;y i & for all i...
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