An adult's life can be divided into time spent working (W) and time spent in retirement...

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An adult's life can be divided into time spent working (W) and time spent in retirement (R). Although it is plainly difficult to know how long you will spend in each period of life, this question assumes that there is no uncertainty about this at all. Assume that a worker gains total income mw during her working life and m during retirement. She chooses to consume Cw and CR during these two periods of life and the interest rate is r > 0. Her utility function is u(CW, CR). Show that the individual's budget constraint can be written as CR = (1+r)mw + MR = (1+r)cw. Draw this budget constraint (with CR on the vertical axis) and show what happens if the interest rate increases. Show that this, in turn, can be written in the following way and interpret this result: CR MR Cw + = mw + 1+r 1+r An adult's life can be divided into time spent working (W) and time spent in retirement (R). Although it is plainly difficult to know how long you will spend in each period of life, this question assumes that there is no uncertainty about this at all. Assume that a worker gains total income mw during her working life and m during retirement. She chooses to consume Cw and CR during these two periods of life and the interest rate is r > 0. Her utility function is u(CW, CR). Show that the individual's budget constraint can be written as CR = (1+r)mw + MR = (1+r)cw. Draw this budget constraint (with CR on the vertical axis) and show what happens if the interest rate increases. Show that this, in turn, can be written in the following way and interpret this result: CR MR Cw + = mw + 1+r 1+r