Mandy Marguerita lives two periods. Her initial accumulated wealth (W) in period

Question

Mandy Marguerita lives two periods. Her initial accumulated wealth (W) in period 1 (inherited from Mom) is $ 20, and her income in period 1 is $ 90. Her income in period 2 is $ 110. Mandy does not leave bequests to her children (couple of deadbeats) when she dies at the end of period 2. The real interest rate is 10% per period. Mandy would like to smooth consumption completely. That is, she wants to have the same level of consumption in both period 1 and period 2.

(a) Compute Mandy’s total sources of funds in terms of their value in period 1. Remember to include W.

(b) Write the equation for Mandy’s lifetime budget constraint, and graph the budget line. For the following question, Mandy does not consume out of W in period 1. She lets it grow at the stated interest rate.

(c) How much will Mandy save and consume in period 1?

(d) How will Mandy’s saving and consumption in period 1 be affected by an increase of period 1 real income by $ 11?

(e) How will Mandy’s saving and consumption in period 1 be affected by an increase of period 2 real income by $ 11?

(f) How will Mandy’s saving and consumption in period 1 be affected by an increase of initial real wealth in period 1 by $ 11?

Explanation / Answer

A) Value of total funds in period 1 = Wealth (accumulated)+ Income earned . Therefore answer = 90+20 = 110$

C) Since mandy wants to smooth her consumption in both periods, she will want same consumption in 2 periods. Now using the NPV method, the present value of her Pd 2 incomes = 110/(1.1) = 100. Since she consumes all and does not leave anything for her children, the Pd 1 consumption = Pd 2 consumtion = 100. Accordingly in period 1, she consumes 100 and saves 10$.

D) Should real incomes increase in Pd 1 by 11$, assuming that the Figures for Pd 2 do not changes and she still wants consumption smoothing, he pd 1 incomes increases to 110+11 = 121$. However if she consumes only 100 $ out of this to equal Pd2 Consumption, then she saves 21$ in Pd 2

E) If her real income in P2 increases by 11$ then her total income in Pd 2 = 121(110+11). Now the present value of this incomes = 121/1.1 = 110. Since she consumes all, and since this must be the consumption in Pd 1 as well, due to the consumption smoothing, Mandy will consume everything in Pd 1 and save nothing.

f) If he real wealth increases by 11$, her total funds in Pd 1 = 20+11+90 = 121. However if she consumes as much as she does in Pd 2 (=100), then in this case she consumes 100 and saves 21.

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