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Thinking and Deciding

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256 NORMATIVE THEORY OF CHOICE UNDER UNCERTAINTY<br />

8. If X is the amount for person 1, then $50K − X is the amount for person 2. Total utility U =<br />

u(X)+u($50K −X). dU<br />

dX = .5·X −.5 −.5·($50K −X) −.5 =0,so.5·X −.5 = .5·($50K −X) −.5 ,<br />

so (multiplying by 2 <strong>and</strong> squaring both sides), X = $50K − X, 2X = $50K, X = $25K. (If we<br />

graph these functions, the sum of the two curves should have a smooth peak in the middle.)

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