Consider an economy that is composed of identical individuals who live for twoperiods. These individuals have preferences over consumption in periods 1 and 2 givenby U = /(C,) + (C2). They receive an income of 45 in period 1 and an income of 20in period 2. They can save as much of their income as they like in bank accounts,earning an interest rate of 10% per period. They do not care about their children, sothey spend all their money before the end of period 2.Each individual's lifetime budget constraint is given by C1 + C2/(1 + r) = Y1 + Y2/(1 + r).Individuals choose consumption in each period by maximizing lifetime utility subject tothis lifetime budget constraint.(a) What is the individual's optimal consumption in each period? How much saving doeshe or she do in the first period?(b) The government has decided to set up a social security system. This system will take$10 from each individual in the first period, put it in the bank, and transfer it to eachperson with interest in the second period. Write out the new lifetime budgetconstraint. How does the system affect the amount of private savings? How does thesystem affect national savings (total savings in society)? What is the name for this typeof social security system?

Each individual's lifetime budget constraint is given by C1 + C2/(1 + r) = Individuals choose consumption in each period by maximizing lifetime ut this lifetime budget constraint. (a) What is the individual's optimal consumption in each period? How he or she do in the first period? (b) The government has decided to set up a social security system. Thi $10 from each individual in the first period, put it in the bank, and person with interest in the second period. Write out the new constraint. How does the system affect the amount of private savin system affect national savings (total savings in society)? What is the of social security system?

Each individual's lifetime budget constraint is given by C1 + C2/(1 + r) = Individuals choose consumption in each period by maximizing lifetime ut this lifetime budget constraint. (a) What is the individual's optimal consumption in each period? How he or she do in the first period? (b) The government has decided to set up a social security system. Thi $10 from each individual in the first period, put it in the bank, and person with interest in the second period. Write out the new constraint. How does the system affect the amount of private savin system affect national savings (total savings in society)? What is the of social security system?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider an economy that is composed of identical individuals who live for two
periods. These individuals have preferences over consumption in periods 1 and 2 given
by U = /(C,) + (C2). They receive an income of 45 in period 1 and an income of 20
in period 2. They can save as much of their income as they like in bank accounts,
earning an interest rate of 10% per period. They do not care about their children, so
they spend all their money before the end of period 2.
Each individual's lifetime budget constraint is given by C1 + C2/(1 + r) = Y1 + Y2/(1 + r).
Individuals choose consumption in each period by maximizing lifetime utility subject to
this lifetime budget constraint.
(a) What is the individual's optimal consumption in each period? How much saving does
he or she do in the first period?
(b) The government has decided to set up a social security system. This system will take
$10 from each individual in the first period, put it in the bank, and transfer it to each
person with interest in the second period. Write out the new lifetime budget
constraint. How does the system affect the amount of private savings? How does the
system affect national savings (total savings in society)? What is the name for this type
of social security system?

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