Varian_Chapter36_Public_Goods

Varian_Chapter36_Public_Goods - Chapter Thirty-Six Public...

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Chapter Thirty-Six Public Goods
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Public Goods -- Definition A good is purely public if it is both nonexcludable and nonrival in consumption. Nonexcludable -- all consumers can consume the good. Nonrival -- each consumer can consume all of the good.
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Public Goods -- Examples Broadcast radio and TV programs. National defense. Public highways. Reductions in air pollution. National parks.
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Reservation Prices A consumer’s reservation price for a unit of a good is his maximum willingness-to-pay for it. Consumer’s wealth is Utility of not having the good is Utility of paying p for the good is Reservation price r is defined by U w ( , ). 0 w . U w p ( , ). - 1 U w U w r ( , ) ( , ). 0 1 = -
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Reservation Prices; An Example Consumer’s utility is U x x x x ( , ) ( ). 1 2 1 2 1 = + Utility of not buying a unit of good 2 is V w w p w p ( , ) ( ) . 0 0 1 1 1 = + = Utility of buying one unit of good 2 at price p is V w p w p p w p p ( , ) ( ) ( ) . - = - + = - 1 1 1 2 1 1
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Reservation Prices; An Example Reservation price r is defined by V w V w r ( , ) ( , ) 0 1 = - I.e. by w p w r p r w 1 1 2 2 = - = ( ) .
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When Should a Public Good Be Provided? One unit of the good costs c. Two consumers, A and B. Individual payments for providing the public good are g A and g B . g A + g B c if the good is to be provided.
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When Should a Public Good Be Provided? Payments must be individually rational; i.e. and Therefore, necessarily and U w U w g A A A A A ( , ) ( , ) 0 1 - U w U w g B B B B B ( , ) ( , ). 0 1 - g r A A g r B B .
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When Should a Public Good Be Provided? And if and then it is Pareto-improving to supply the unit of good, so is sufficient for it to be efficient to supply the good. U w U w g A A A A A ( , ) ( , ) 0 1 < - U w U w g B B B B B ( , ) ( , ) 0 1 < - r r c A B +
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Private Provision of a Public Good? Suppose and . Then A would supply the good even if B made no contribution. B then enjoys the good for free; free- riding . r c A r c B <
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Private Provision of a Public Good? Suppose and . Then neither A nor B will supply the good alone. Yet, if also, then it is Pareto-improving for the good to be supplied. A and B may try to free-ride on each other, causing no good to be supplied. r c A < r c B < r r c A B +
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Free-Riding Suppose A and B each have just two actions -- individually supply a public good, or not. Cost of supply c = $100. Payoff to A from the good = $80. Payoff to B from the good = $65.
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Free-Riding Suppose A and B each have just two actions -- individually supply a public good, or not. Cost of supply c = $100.
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Varian_Chapter36_Public_Goods - Chapter Thirty-Six Public...

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