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A small town has 300 people, all of whom are interested only in private consumption and in the quality of the city streets. The utility function of person i is given by U(X₁, G) = X₁ + A₁G - B₁G², where X₂ 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. There are 3 types of people, and each type has 100 people. The parameters in their utility function s given by

A small town has 300 people, all of whom are interested only in private consumption and in the quality of the city streets. The utility function of person i is given by U(X₁, G) = X₁ + A₁G - B₁G², where X₂ 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. There are 3 types of people, and each type has 100 people. The parameters in their utility function s given by

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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A small town has 300 people, all of whom are interested only in private consumption and in the quality of the city streets. The utility function of person i is given by U(X₁, G) = X₁ + AG - B₂G², where X, 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. There are 3 types of people, and each type has 100 people. The parameters in their utility function is given by Туре | A | B 1 2 3 6 0.5 8 0.5 10 1 (a) Find the absolute value of the marginal rate of substitution between public goods (spending on streets) and private goods for person i for each type. (Hint: visualize the indifference curve between public goods (G) and private goods (X₂), in which G is on the horizontal axis and X, is on the vertical axis.) (b) How much spending on streets is socially optimal?
Transcribed Image Text:A small town has 300 people, all of whom are interested only in private consumption and in the quality of the city streets. The utility function of person i is given by U(X₁, G) = X₁ + AG - B₂G², where X, 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. There are 3 types of people, and each type has 100 people. The parameters in their utility function is given by Туре | A | B 1 2 3 6 0.5 8 0.5 10 1 (a) Find the absolute value of the marginal rate of substitution between public goods (spending on streets) and private goods for person i for each type. (Hint: visualize the indifference curve between public goods (G) and private goods (X₂), in which G is on the horizontal axis and X, is on the vertical axis.) (b) How much spending on streets is socially optimal?
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how do we get the value of G in part b ? or can we simply not get it ? kindly explain please, thanks

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