Suppose You Divide Your Life into Two Periods: Working Age

Suppose you divide your life into two periods: working age and retirement age.When you work,you earn labor income Y; when retired,you earn no labor income,but must live off your savings and the interest it earns.You have no initial assets.You save the amount S while working,earning interest at rate r,so you have (1 + r)S to live on when retired.Because you don't need to consume as much when retired,you want to set consumption when working twice as high as consumption when retired.
(a)Suppose you earn $1 million over your working life,and the real interest rate for retirement saving is 50%.How much will you save,and how much will you consume in each part of your life?
(b)Suppose your current income went up to $2 million when working.Now what will you save and how much will you consume each period?
(c)Suppose a social security system will pay you 25% of your working income when you are retired.Now (with Y = $1 million as in part (a)how much will you save and how much will you consume each period?
(d)Suppose the interest rate rises.Will you save more or less?