macro question pls solve

[mphil]

Assuming life cycle hypothesis let a person starts working when he s 20 yrs old ,works until age 60 and expects to die at 70.if this person earns say 1.50 Lac annually when 20-30 years, 2lac annually when 30-45,3 Lac annually when 40-60 then his life time average propensity to consume s?                                      a).60 b).70 c) .80 d ) .90.  pls help

[Dreyfus]

Is APC = 0.8?

[mphil]

Yes ,hw U got dat?

[Dreyfus]

Life time , T= 50 yrs
Years to retirement = 40 yrs
Life time income = (10*1.5)+(15*2)+(15*3) = 90 Lac
So optimal consumption to smooth it over the life time, C = Life time income/T = 90/50=1.8 lac/yr
APC is defined by C/Y where Y is annual income but in life cycle hypothesis it is assumed that Y is constant! But here Y is changing. So, The average Y must be taken (Weighted average with weights being 10, 15 nd 15) to get average yearly income, Y*.
Y* = ((10*1.5)+(15*2)+(15*3))/(40) = 2.25
Thus , lifetime APC = 1.8/2.25 = 0.8

[mphil]

Thanks man ..