Consider an economy with n consumers, one private good and one public good. Wethink 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 U₁(x,y) = α₁= a.lny + x,where y is the public good, x, is the private good consumed by individual i 1,..., ni12nand 0 < α₁ < α₂ <... a are parameters. Initial endowment of private good of eachconsumer is given by w. We donote the aggregate endowment 1 of the private goodby w = Σw w = P i w₁. The cost of producing the public good is c(y) = cy for somei ic > 0. Find the optimal provision of the public good as well as how much isprovided under voluntary contributions.

Social welfare maximization is a concept in economics that refers to the process of maximizing the…

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 U₁(x, y) = a. ln y + x, where y is the public good, x is the private good consumed by individual i = 1,..., n and 0 < α₁ < α₂ <... αare parameters. Initial endowment of private good of each consumer is given by w. We donote the aggregate endowment 1 of the private good 1 n by w = Σ,w₁ w = P i w. The cost of producing the public good is c(y) = cy for some i i 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 U₁(x, y) = a. ln y + x, where y is the public good, x is the private good consumed by individual i = 1,..., n and 0 < α₁ < α₂ <... αare parameters. Initial endowment of private good of each consumer is given by w. We donote the aggregate endowment 1 of the private good 1 n by w = Σ,w₁ w = P i w. The cost of producing the public good is c(y) = cy for some i i c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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