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utility function

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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).
Transcribed Image Text: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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