Johnny has a strictly increasing utility function over wealth u(.). Assume that u'(.) exists and is continuous everywhere. Show that even if Johnny is risk-averse, he will always take at least a small fraction of any bet where the expected gain is positive. You may restrict attention to bets with just two outcomes for simplicity. (Hint: Another way of stating what you're asked to show is the following: "If Gp>L(1-p), with G > 0 and L > 0, then Johnny will take a lottery offering him a gain of xG with probability p and a loss of xL with probability 1-p for some x > 0.")

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