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 = \T1 + vT2 They receive an income of Y1 = 40 in period 1 and an income of Y2 = 25 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.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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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 = \T1 + vT2
They receive an income of Y1 = 40 in period 1 and an income of Y2 = 25 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?
Transcribed Image Text: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 = \T1 + vT2 They receive an income of Y1 = 40 in period 1 and an income of Y2 = 25 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 $5 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?
Transcribed Image Text:b. The government has decided to set up a social security system. This system will take $5 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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