1. Consider two lotteries F and F. Argue that if F >1 F, then EF(X) > EF(X). 2. An oil company, Pritish Betroleum, henceforth PB, has been found guilty of causing a major environmental disaster, and the court has decided that it has to pay an amount X in punitive damages. The exact amount of X will be determined after an assessment of the damages, which will be undertaken by one of two environmental laboratories, a or b. Under laboratory i, the probability distribution for X is Fi. Assume that PB is an EU maximizer and that its Bernoulli utility index is increasing in the company's wealth. a. Suppose that Fa 21 Fb and that the court allows PB to choose which laboratory to use for the assessment of damages. Which one should they choose? b. Suppose now that Fo is the uniform distribution over some interval (Xx, x*], while Fb is the uniform distribution over [X, - 1, x* + 1]. Argue that Fb is a mean-preserving spread of Fa. c. Under the same assumptions as in part 2, suppose that the court allows PB to choose which laboratory to use for the assessment of damages. Which one should they choose