Question

Rachel earns nothing during her learning period, 1100 during her working period, and nothing during her retirement period. She has initial assets of 300. The real interset rate is zero. Rachel is not allowed to borrow by the banks. Whenever possible, Rachel wants to smooth consumption between periods. How much will she save during her working period?

a) 950 b) 550 c)700 d)400

I need to know how to solve this one because I know the answer.

Answer 1

Let the Working period be 1st period and retirement period be period 2

Consumption in 1st Period= C1

Savings in 1st period= S1

Income in 1st Period = Y1

Consumption in 2nd Period= C2

Savings in 2nd period= S2

Income in 2nd Period = Y2

C1+ S1= Y1 {Consumption and Savings in 1st period= The total income in that period as before this, there is no income)

C2=(S1)*(1+r)+Y2 {The total consumption in second period will be income in that period + Savings and interest from period 1}

r=0 and Y2=0

Therefore, C1+S1=1100

and C2=S1+0

Therefore, C1+C2=1100

So,  Rachel will save half of the earnings for her retirement and spend half at present for the equal distribution of income and hence smooth consumption between the periods. Therefore, she will save 1100 x 50% = 550