Consider an economy with n consumers, one private good and one public good. We think of the private good as “all other goods,” and measure it in terms of money. There are n individuals in the economy with utility functions Ui(xi, y) = αi ln y + xi, where y is the public good, xi is the private good consumed by individual i = 1, . . . , n, and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of private good of each consumer is given by wi . We donote the aggregate endowment 1of the private good by w =Pi wi . The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
Consider an economy with n consumers, one private good and one public good. We think of the private good as “all other goods,” and measure it in terms of money. There are n individuals in the economy with utility functions Ui(xi, y) = αi ln y + xi, where y is the public good, xi is the private good consumed by individual i = 1, . . . , n, and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of private good of each consumer is given by wi . We donote the aggregate endowment 1of the private good by w =Pi wi . The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
Chapter19: Externalities And Public Goods
Section: Chapter Questions
Problem 19.7P
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Consider an economy with n consumers, one private
good and one public good. We think of the private good as “all other
goods,” and measure it in terms of money. There are n individuals in
the economy with utility functions Ui(xi, y) = αi ln y + xi, where y is the
public good, xi is the private good consumed by individual i = 1, . . . , n,
and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of private
good of each consumer is given by wi
. We donote the aggregate endowment 1of the private good by w =Pi wi
. The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
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