3. Consider a society of identical individuals who live for two periods. They have the following utility: 3 In co +In c₁ Each individual earns $600 when young, in period 0, and no income in period 1, when old. They can borrow and lend at interest rate r, and the price of consumption is 1. (a) Write down this individual's lifetime budget constraint (b) Solve for this individual's consumption in period, and savings, as a function of r. (c) Suppose now that there is a Social Security program. The gov- ernment collects $ 60 from this individual in period 0, and gives it back with interest r in period 1. i. What kind of social security system is this? ii. What is the new amount of savings? iii. What is the impact of this program on the individual's wel- fare?

3. Consider a society of identical individuals who live for two periods. They have the following utility: 3 In co +In c₁ Each individual earns $600 when young, in period 0, and no income in period 1, when old. They can borrow and lend at interest rate r, and the price of consumption is 1. (a) Write down this individual's lifetime budget constraint (b) Solve for this individual's consumption in period, and savings, as a function of r. (c) Suppose now that there is a Social Security program. The gov- ernment collects $ 60 from this individual in period 0, and gives it back with interest r in period 1. i. What kind of social security system is this? ii. What is the new amount of savings? iii. What is the impact of this program on the individual's wel- fare?

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

3. Consider a society of identical individuals who live for two periods.
They have the following utility:
In co +
3
5
In ci
Each individual earns $600 when young, in period 0, and no income
in period 1, when old. They can borrow and lend at interest rate r,
and the price of consumption is 1.
(a) Write down this individual's lifetime budget constraint
(b) Solve for this individual's consumption in period, and savings,
as a function of r.
(c) Suppose now that there is a Social Security program. The gov-
ernment collects $ 60 from this individual in period 0, and gives
it back with interest r in period 1.
i. What kind of social security system is this?
ii. What is the new amount of savings?
iii. What is the impact of this program on the individual's wel-
fare?
(d) Suppose some individuals have utility
1
In co +In c₁
9
The social security system still forces them to save $60.
i. If they are still free to borrow and lend at r, what will their
optimal choice of consumption and savings be, under the
social security program?
ii. Suppose they cannot borrow, because credit market are im-
perfect. Show that the social security system makes them
worse off than if there were no social security.
iii. In reality, we often observe very low savings rates. Some
say this justifies social security. Explain how the preceding
preferences refute this argument.

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