Only answer 3 and 4. I. There is a society consisting of n voters, and voters' utility function is given asu;(B) = log B + (1 – t)l;where B is government spending on a public good, t is the income tax rate (proportional tax), and Iis 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 andusing n and the average income I.(2) As an illustrative example, create a rough graph where the horizontal axis is B, and the verticalaxis 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 modelof the two parties. Compare the amount of B between the cases when all three are l;=100 andwhen I = 40,12 = 60, and I3 = 200.

A want satisfying power of a commodity or service is known as its utility. Utility is a significant…

(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.

(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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter12: The Partial Equilibrium Competitive Model

Section: Chapter Questions

Problem 12.11P

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

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.

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