Consider the two risky assets, A and B, with cumulative probability distribution functions: F(W) = w Fg(w)=% In both cases, 0wsl. (i) Show that A is preferred to B on the basis of first-order stochastic dominance. [3] (ii) Verify explicitly that A also dominates B on the basis of second-order stochastic [3] dominance. [Total 6] Suppose that Lance and Allan each have a log utility function and an initial wealth of 100 and 200 respectively. Both are offered a gamble such that they will receive a sum equal to 30% of their wealth should they win, whereas they will lose 10% of their wealth should they lose. The probability of winning is %. State whether or not the gamble is fair. [1] (ii) Calculate Lance's certainty equivalent for the gamble alone and comment briefly on your answer. [2] (iii) Repeat part (ii) in respect of Allan and compare your answer with that in part (ii). [2] (iv) Confirm that your comments in part (iii) apply irrespective of the individual's wealth. [2] [Total 7]