A standard result for EU agents is that they always divesify their risks. You are asked to demonstrate this in the following simple example. Suppose there are two assets, A and B, both of which return $100 with 0.75 probability and -$100 with 0.25 probability. The agent can buy any fraction of an asset, getting a corresponding fraction of its returns. The agent's wealth is $w, and suppose that she can only hold fractions and 1 of assets A and B respectively, where 0 1 (this is a simplification so that the portfolio choice reduces simply to choosing , as opposed to how much of wealth to invest in each asset). (i) Consider an EU agent with utility index u(x) = x. Determine the shares and 1 of the assets that she buys. (ii) Consider a variant of EU where the agent weights probabilities using the function () = 0.5 . Does this affect portfolio choice relative to your answer in (i)?