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?