What is the ecient amount of public good for them to consume


Problem

Consider three consumers (i = 1; 2; 3) who care about their consumption of a private good and their consumption of a public good. Their utility functions are respectively u1 = x1G, u2 = x2G, and u3 = x3G, where xi is consumer i's consumption of private good and G is the amount of public good jointly consumed by all of them. The unit cost of the private good is $1 and the unit cost of the public good is $10. Individual wealth levels in $ are w1 = 30, w2 = 50, and w3= 20. What is the ecient amount of public good for them to consume?

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International Economics: What is the ecient amount of public good for them to consume
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