3. Consider a society of identical individuals who live for two periods. They have the following utility:

ln c0 + 3/ 5 ln 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 individuals lifetime budget constraint

(b) Solve for this individuals consumption in period, and savings, as a function of r.

(c) Suppose now that there is a Social Security program. The government 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 individuals welfare?

(d) Suppose some individuals have utility ln c0 + 1/9 ln c1

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 imperfect. 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