Using Ellsberg Paradox, maximize expected utility.

2. Consider the following variant of the Ellsberg paradox. Box 1 contains half blue and half gold balls, and Box 2 contains blue and gold balls, where the proportion that are blue, Q, is a random variable between 0 and 1 (and l-Q are gold). You get to choose which box to draw balls from, and your objective is to maximize your expected utility. a. Show that if one ball will be drawn, and you win $1 if the ball is blue and nothing if it is gold, then you should choose Box 1 if and only if E[Q] 5 V2 (except that at E[Q] = 1/2 you are indifferent). b. Now suppose that two balls will be drawn, with replacement, 'om the urn you choose, and EQ = 1/2. Show that if your utility function is concave you should choose Box 1, and if it is convex, you should choose Box 2