An investor lives for 2 periods and has the utility function u defined over the final wealth as ?(?)=?2?20+?(??(?)?12?2?(?))u(w)=?2c02+?(?E(w)?12?2V(w)). The investor is born at ?=0t=0 with wealth ?0w0 = 2 and wants to choose a portfolio which maximizes her final wealth ?1w1, which you will recognize is a random variable. There are two assets that the investor can invest in - (i) a bond which pays a sure return 0.03 , and (ii) a stock which follows a Normal distribution N (0.02, 0.08).The investor must also eat at time ?=0,and her consumption is?0t=0,and her consumption isc0. The discount rate is given by ?=?=0.804, and her risk aversion is given by ?=?=3.8. Find her optimal consumption which maximizes her utility.

An investor lives for 2 periods and has the utility function u defined over the final wealth as u (w) = yz c3 + B(YE(w) - -yzV (w)). The investor is born at t = 0 with wealth wo = 2 and wants to choose a portfolio which maximizes her final wealth w 1, which you will recognize is a random variable. There are two assets that the investor can invest in - (i) a bond which pays a sure return 0.03 , and (ii) a stock which follows a Normal distribution N (0.02, 0.08). The investor must also eat at time t = 0, and her consumption is co. The discount rate is given by B = 0.804, and her risk aversion is given by y = 3.8. Find her optimal consumption which maximizes her utility