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Tradeoff (TO) method for EU

. x 1. 200,000. ½. ½. ~. ½. ½. ½. ½. _. _. 1/2. 1/2. ( U(8000) - U(1000) ). ( U(8000) - U(1000) ). ½. ~. ½. 8000. 8000. 1000. 1000. 1/2. 1/2. ~. =. ½. ½. ½. ½. =. 1. Tradeoff (TO) method for EU. ½ ( U( x 1 ) - U( x 0 ) ) = ½ ( U(8000) - U(1000) ).

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Tradeoff (TO) method for EU

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  1. x1 200,000 ½ ½ ~ ½ ½ ½ ½ _ _ 1/2 1/2 (U(8000)-U(1000)) (U(8000)-U(1000)) ½ ~ ½ 8000 8000 1000 1000 1/2 1/2 ~ = ½ ½ . . . ½ ½ = 1 Tradeoff (TO) method for EU ½(U(x1)-U(x0)) = ½(U(8000) - U(1000)) ½U(1000) + ½U(x1) = ½U(8000) + ½U(x0) EU 8000 1000 _ 1/2 U(x1)-U(x0)= (U(8000)-U(1000))  1/2 12,000 10,000 (=x0) = U(x2)-U(x1)= x1 x2 . . . U(x4)-U(x3)= x3 x4

  2. U 3/4 2/4 1/4 x3 € 2 Let's draw a graph of U. Consequently: U(xj) = j/4. Normalize: U(x0) = 0; U(x4) = 1. 1 0 x1 x2 x0 x4

  3. x1 200,000 ½ d1 d1 d1 ~ ½ ? ! ½ ½ _ _ 1/2 1/2 (U(8000)-U(1000)) (U(8000)-U(1000)) ½ ~ ½ 8000 8000 1000 1000 d2 d2 d2 1/2 1/2 ~ = ! ? ½ ½ . . . ½ ½ = ! ? 3 Tradeoff (TO) method for nonEU Prospect theory: misperceived probs (even unknown probs) EU ½ 8000 1000 _ 1/2 U(x1)-U(x0)= (U(8000)-U(1000))  1/2 12,000 10,000 ½ (=x0) = U(x2)-U(x1)= x1 x2 . . . U(x4)-U(x3)= x3 x4

  4. U 1 3/4 2/4 0 1/4 x1 x2 x0 x4 x3 € 4 Conclusion about graph of U: Is also valid utility graph under nonEU/prospect theory.

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