Consider an agent with a well-behaved utility function who must balance his portfolio between a riskless asset and a risky asset. The first asset, with price p1 has the certain payoff z1 while the second asset, with price p2 pays off z~2 which is a random variable. The agent has an initial wealth Y0 and he only cares about next period. Assuming that he holds x1 units of the riskless asset and x2 units of the risky asset. - Write down his expected utility function in terms of Y0,x1,x2,z1,z2. Write down his budget constraint as well. Find the equation (the FOC) that the optimal demand for the risky asset has to satisfy. - Assume now that his utility function is of the form: U(Y)=abexpAY with a,b>0. Show that the demand for the risky asset is independent of the initial wealth. Explain