4 Bonus Question [5]

(Warning: DO NOT try this question before you finish all the other parts of the exam.)

Consider the two-period model of households as in Question 1. We can interpret the current

period as the working period of the household's life cycle, and the future period as the retirement

period of the household's life cycle. Suppose now the government decides to implement a social

security system to help the household save for retirement. In particular, the government will impose

a lump-sum social security tax

x

on the household in the working (current) period, in addition to

the regular lump-sum tax

t

. Then the government will lend (save) the social security tax revenue

x

in the credit market on behalf of the household, so in the retirement (future) period, the government

receives

x

(

1

+

r

)

, and transfers this back to the household as a lump-sum transfer. All the other

parts of the model remain the same as the standard two-period model in Question 1.

Question

: Explain how the introduction of this social security system would affect the hou-

sehold's current consumption

c

, future consumption

c

0

, and private savings

s

. You need to justify

your answers with rigorous reasoning rather than just using your intuition. You may use math or

graphs to help your discussion if deemed necessary.