Amir is a risk averse decision-maker with von Neumann-Morgenstern utility u(x) that is strictly increasing and continuous. Birgit is risk neutral. Amir faces a lottery over two quantities of wealth (₁, 2) with probabilities (p, 1 p), where 0 < p < 1 and x₁ < £2. Suppose that Amir and Birgit can make a bet on the outcome of the form "Amir pays Birgit Sy if outcome ₁ occurs and $z if outcome x2 occurs," where y and z are any real numbers (possibly negative). Is there a bet that makes both Amir and Birgit strictly better off in terms of expected utility?

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