An investor has initial wealth w0 that she must divide between two risky assets. Denote the total investment into asset i by wi for i {1,2}. There are two possible states H and L for the economy. Assume that the economy will be in state H with probability p and in L with probability (1p). The first asset pays a gross return RH if the state of the economy is H and a gross return 0 if the state is L. I.e. in state H, an investment of w1 in asset 1 results in a return w1RH and in state L, the return is 0 . The second asset pays R in both states. Denote the fraction of initial wealth that is invested in asset i by i for i{1,2} so that wi=iw0 and 1+2=1. (a) For an arbitrary investment portfolio {1,2}, determine the final wealth of the investor. (b) Assume the investor has a Bernoulli utility function u(w) where w denotes the final wealth. Assume that u(w)>0 and u(w)