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Unformatted text preview: Chapter 35 NAME Public Goods Introduction. In previous chapters we studied selfish consumers con- suming private goods. A unit of private goods consumed by one person cannot be simultaneously consumed by another. If you eat a ham sand- wich, I cannot eat the same ham sandwich. (Of course we can both eat ham sandwiches, but we must eat different ones.) Public goods are a dif- ferent matter. They can be jointly consumed. You and I can both enjoy looking at a beautiful garden or watching fireworks at the same time. The conditions for eﬃcient allocation of public goods are different from those for private goods. With private goods, eﬃciency demands that if you and I both consume ham sandwiches and bananas, then our marginal rates of substitution must be equal. If our tastes differ, however, we may consume different amounts of the two private goods. If you and I live in the same town, then when the local fireworks show is held, there will be the same amount of fireworks for each of us. Eﬃciency does not require that my marginal rate of substitution between fireworks and ham sandwiches equal yours. Instead, eﬃciency requires that the sum of the amount that viewers are willing to pay for a marginal increase in the amount of fireworks equal the marginal cost of fireworks. This means that the sum of the absolute values of viewers’ marginal rates of substitution between fireworks and private goods must equal the mar- ginal cost of public goods in terms of private goods. Example: A quiet midwestern town has 5,000 people, all of whom are in- terested only in private consumption and in the quality of the city streets. The utility function of person i is U ( X i ,G ) = X i + A i G − B i G 2 , where X i is the amount of money that person i has to spend on private goods and G is the amount of money that the town spends on fixing its streets. To find the Pareto optimal amount of money for this town to spend on fixing its streets, we must set the sum of the absolute values of marginal rates of substitution between public and private goods equal to the relative prices of public and private goods. In this example we measure both goods in dollar values, so the price ratio is 1. The absolute value of person i ’s marginal rate of substitution between public goods and private goods is the ratio of the marginal utility of public goods to the marginal utility of private goods. The marginal utility of private goods is 1 and the marginal utility of public goods for person i is A i − B i G . Therefore the absolute value of person i ’s MRS is A i − B i G and the sum of absolute values of marginal rates of substitution is i ( A i − B i G ) = i A i − ( B i ) G ....
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