4 To think of the social security problem, assume the economy is populated by two overlapping generation populations, theyoung and the old. Population follows the growth rate n. Each person lives two period, young (t = 1) and old (t = 2).The utility function is given by%3DU(c1, c2) = In ci +B In c2.When he is young, he receives wage w. At old period, he receives social security s. The life time budget constraint isC2=w (1-T)+1+r1+rCi +where T is income tax. 1+r is the interest rate. To balance the social security payment. The following condition mustholdwT (1 + n) = 5where the wT (1+n) if the tax revenue received from the young and s is the expenditure transferred to the old. 1+n isthe population growth rate. Therefore, when s is decided, the tax rate T =w(1+n)1. Show a person's efficiency condition is choosing ei and c2. Explain the intuition.2. Solve c, ez and explain how would this being affeeted by s, r and n3. Now suppose we change the tax from income tax to lump sum tax T. That is, a person's budget constraint becomes= W -T1+r1+rFor the government, to balance the budget, what is the lump-sum tax T?4. Are people happier in the new tax regime? (show the proof).

A Budget constraint represents the bounds at the intake picks of a character or a household based on…

Answered: utility function

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utility function

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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

To think of the social security problem, assume the economy is populated by two overlapping generation populations, the
young and the old. Population follows the growth rate n. Each person lives two period, young (t = 1) and old (t = 2).
The utility function is given by
%3D
U(c1, c2) = In ci +B In c2.
When he is young, he receives wage w. At old period, he receives social security s. The life time budget constraint is
C2
=w (1-T)+1+r
1+r
Ci +
where T is income tax. 1+r is the interest rate. To balance the social security payment. The following condition must
hold
wT (1 + n) = 5
where the wT (1+n) if the tax revenue received from the young and s is the expenditure transferred to the old. 1+n is
the population growth rate. Therefore, when s is decided, the tax rate T =
w(1+n)
1. Show a person's efficiency condition is choosing ei and c2. Explain the intuition.
2. Solve c, ez and explain how would this being affeeted by s, r and n
3. Now suppose we change the tax from income tax to lump sum tax T. That is, a person's budget constraint becomes
= W -T
1+r
1+r
For the government, to balance the budget, what is the lump-sum tax T?
4. Are people happier in the new tax regime? (show the proof).

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Step 1: Define Utility Function and Budget constraints

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Step 2: Explain the Person's Efficiency Condition:

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Step 3: Explain the calculation of C1 and C2

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Step 4: Calculate the Lump Sum Tax (T):

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Step 5: Explain the Happiness under Lump-Sum Tax

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