An individual has the following separable lifetime utility function U =lnc0 +lnc1.

(a) If y0 = 10 and y1 = 12 and if there is no credit market, measure the value of the resistance to intertemporal substitution (k). Explain why it is equal in this case to the growth rate of income.

(b) Oncethere is a perfect credit market with a strictly positive interest rate, which income stream do you prefer:

y0 = 10and y1 = 12 or y0 = 12and y1 = 10.

Is your answer affected by the features of U?

(c) With the income stream as in (a), what is the optimal value of c0 when r =0?Whathappens to c0 when r becomes strictly positive?

(d) Supposenowthatintheincomestreamof(a)thereislaborincomeriskso that y1 = 12isreplacedbyarandomvariable ˜ y1 givenby(10, 1 2;14, 1 2).

Assuming that r = 0, what happens to the optimal value of c0? (Hint:

you will have to solve a second-degree equation in c0. The fact that prudence is positive when U is logarithmic will help you to select the appropriate root between the two positive ones.)

(e) Answer questions

(c) and

(d) if the lifetime utility function becomes:

U = c0 +lnc1. Explain in words why the individual now wants to consume (much) more in the initial period.