Problem #3 Consider the following path of income of a consumer who lives for thr

Question

Problem #3 Consider the following path of income of a consumer who lives for three periods. Table 1: Path of Income Assume that the consumer is infinitely patient, ?-1, and that the interest rate is 0. i) What is the optimal consumption profile of the consumer? ii) What is the value of assets of the consumer at the beginning of period 3? iii) Find the optimal consumption profile of the consumer assuming that the consumer is not able to secure a loan? iv) What is the value of assets of the consumer at the beginning of period 3 in this case?

Explanation / Answer

a) C1 = a + bYt

= a + 10b

C2 = a + 0b

C3 = a + 20b

So optimal consumption function will be = C2

C2 = a which means optimal consumption is equal to autonomous consumption

b) Value of assets is equal to 0 as income is 0 and optimal consumption is equal to autonomous consumption.

c) If he is not able to secure a loan then his optimal consumption will be equal to his present income

d) value of assets will be equal to net income.

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