An individual investing has a utility function U=aW-bW2 where W is wealth and a,b are constant parameters, She can hold a portfolio of the following two assets: cash that has a net interest rate of 0, or a zero dividend share which has a price of 1 today and will have a price of P₁ next period in state 1 with probability 0.5 and P₂ in state 2 with probability 0.5. Assume that P₁>1 and P₂<1. The individual also receives other income (that is added to wealth at t+1) in state 1 of zero and in state 2 of X₂. The individual has a Wealth of W, at time t and wishes to maximise expected utility over a single period. (a) Solve for the individual's optimal portfolio in terms of a, b, W. P₁, P2 and X2 (15 marks) (b) Discuss the relationship between S (the share of wealth held in the share) and W, and X₂ in the context of hedging income risk through portfolio management