Suppose that the utility function is given by u(w)=awbw2, where a,b>0 and w>0 denotes income. (a) Find the coefficient of absolute risk aversion, r(w,u). Does it increase or decrease in wealth? Interpret. (b) Let us now consider that this decision maker is deciding how much to invest in a risky asset. This risky asset is given by a cumulative distribution function (or gamble) G over returns x, with mean G=EG[x]>0 and variance G2= EG[x2]G2. Assuming that the DM's initial wealth is w, state the decision maker's expected utility maximization problem, and find first-order conditions. Use the definition of the variance to express your answer explicitly in terms of the mean return G and variance G2. (c) What is the optimal investment in risky assets? (d) Show that the optimal amount of investment in risky assets is a decreasing function in wealth. Interpret. Suppose that the utility function is given by u(w)=awbw2, where a,b>0 and w>0 denotes income. (a) Find the coefficient of absolute risk aversion, r(w,u). Does it increase or decrease in wealth? Interpret. (b) Let us now consider that this decision maker is deciding how much to invest in a risky asset. This risky asset is given by a cumulative distribution function (or gamble) G over returns x, with mean G=EG[x]>0 and variance G2= EG[x2]G2. Assuming that the DM's initial wealth is w, state the decision maker's expected utility maximization problem, and find first-order conditions. Use the definition of the variance to express your answer explicitly in terms of the mean return G and variance G2. (c) What is the optimal investment in risky assets? (d) Show that the optimal amount of investment in risky assets is a decreasing function in wealth. Interpret