(3) Find the amount of B to maximize the sum of n people's utilities. (4) Suppose that n = 3 and the amount of B is determined by the equilibrium of the Downs model of the two parties. Compare the amount of B between the cases when all three are I₁=100 and when I₁ = 40, 1₂ = 60, and I3 = 200.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Only answer 3 and 4.

I. There is a society consisting of n voters, and voters' utility function is given as
u;(B) = log B + (1 – t)l;
where B is government spending on a public good, t is the income tax rate (proportional tax), and I
is voter i's income. The government's budget constraint is given as E¡ t I¡ = B
(1) Find voter i's utility function excluding t by substituting the government's budget constraint and
using n and the average income I.
(2) As an illustrative example, create a rough graph where the horizontal axis is B, and the vertical
axis is a voter's utility.
(3) Find the amount of B to maximize the sum of n people's utilities.
(4) Suppose that n = 3 and the amount of B is determined by the equilibrium of the Downs model
of the two parties. Compare the amount of B between the cases when all three are l;=100 and
when I = 40,12 = 60, and I3 = 200.
Transcribed Image Text:I. There is a society consisting of n voters, and voters' utility function is given as u;(B) = log B + (1 – t)l; where B is government spending on a public good, t is the income tax rate (proportional tax), and I is voter i's income. The government's budget constraint is given as E¡ t I¡ = B (1) Find voter i's utility function excluding t by substituting the government's budget constraint and using n and the average income I. (2) As an illustrative example, create a rough graph where the horizontal axis is B, and the vertical axis is a voter's utility. (3) Find the amount of B to maximize the sum of n people's utilities. (4) Suppose that n = 3 and the amount of B is determined by the equilibrium of the Downs model of the two parties. Compare the amount of B between the cases when all three are l;=100 and when I = 40,12 = 60, and I3 = 200.
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