(i) According to the random-walk hypothesis, uncertainty about future income does not affect consumption, however, uncertainty does affect utility. Discuss how uncertainty about consumption affects expected lifetime utility using the log utility function u(ct) = log(1act) as your instantaneous utility. (ii) Using the instantaneous utility above, show that the utility function exhibit increasing relative risk aversion (IRRA) as wealth increases, and which individuals is it consistent within the economy? (iii) The random-walk hypothesis argues that change in consumption is unpredictable. Discuss this with the necessary derivations. (iv) Derive the equity premium puzzle and discuss the intuition behind your derivation. How can governments benefit from the equity premium puzzle?