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1. Given that John lives for two periods and has utility ln C 1 + ln C 2 . If John has labor income of

1. Given that John lives for two periods and has utility ln C1 + ln C2.

If John has labor income of Y1 in the rst period of life and zero in the secondperiod.And that the second-periodconsumptionis thus (1 + r )(Y1 C1); r, the rate of return, is potentially random.

i) Find the rst-order condition for John's choice of C1.

ii) Suppose r changes from being certain to being uncertain, without any change in E [r ]. How, if at all, does C1 respond to this change?

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2. Given that the individual has labor income of zero in the rst period and Y2 in the second. Second-period consumption is thus Y2(1r )C1. Y2 is certain; again, r may be random.i) Find the rst-order condition for the individual's choice of C1. ii) Suppose r changes from being certain to being uncertain, without any change in E [r ]. How, if at all, does C1 respond to this change?

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