3. Han Solo is delivering illicit cargo to the rebel forces on Alderaan, a planet blockaded by the galactic empire. In order to deliver his cargo successfully, Han Solo must pass 2 checkpoints, each of which will not detect his cargo with probability q. If Han Solos cargo is detected at one or more checkpoints, then his final wealth is 0. If Han Solo passes both checkpoints undetected, then his final wealth is 100. Han Solo's riskpreference is described by Bernoulli utility function w. Thus Han Solo's wealth is described by a lottery: 100 with probability q2, 0 with probability 1 q2. (a) What is Han Solo's expected utility? Suppose an Imperial officer makes an offer to Han Solo. The officer will reduce number of checkpoints from 2 to 1, but if Han Solo gets through, he has to pay k to the officer. If Han Solo gets caught, his payoff is 0. If he agrees to this arrangement, then his final wealth is described by a lottery: 100 k with probability q, 0 with probability 1 q. (b) What is Han Solo's expected utility if he agrees to this arrangement? (c) What is the most that Han Solo would be willing to pay as a bribe? That is, what is the largest k for which Han Solo takes the deal? (d) Repeat parts (a)-(c) assuming Han Solo is risk-neutral, u(w) = w. Is he willing to pay more to the Imperial officer when he is risk-neutral, or risk-averse? Explain in a sentence or two.

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