Portfolio choice (with expected utility): An agent has Y=1 to invest. On the market two financial assets exist. The first one is riskless. Its price is one and its return is 2. Short selling on this asset is allowed. The second asset is risky. Its price is 1 and its return z~, where z~ is a random variable with probability distribution: z=(1,2,3) with probability (p1,p2,p3). No short selling is allowed on this asset. - If the agent invests a in the risky asset, what is the probability distribution of the agent's portfolio return (R~) ? - The agent maximizes a von Neumann-Morgenstern utility (U). Show that the ptimal choice of a is positive if and only if the expectation of z~ is greater than 2. Hint: Find the first derivative of U and calculate its value when a=0. - Give the first-order condition of the agent's problem. - Find a when U(Y)=1expbY,b>0 and when U(Y)=(11)Y1;0