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3. [Harder] Suppose Warren did know about tornadoes, but didn’t know about insurance. His refer- ence lottery therefore includes the risk but not the insurance premium: r 3 = <w 0 - 1000 , 0 . 05; w 0 , 0 . 95 > (that is, a 5% chance of having ( w 0 - 1000) and a 95% chance of having w 0 ). (a) What is his utility now if he buys full insurance at a premium of \$ p ? (assume p < 1000) EU ( buy | r 3 ) = E [ w ] + E [ v ( w - r 3 )] = w 0 - p + (0 . 05 v ( w 0 - p - ( w 0 - 1000)) + 0 . 95 v ( w 0 - p - ( w 0 ))) = w 0 - p + (0 . 05 v (1000 - p ) + 0 . 95 v ( - p )) = w 0 - p + (0 . 05(1000 - p ) + 0 . 95( - 2 p )) = w 0 - p + 50 - . 05 p - 1 . 9 p = w 0 + 50 - 2 . 95 p 4
EC 310 - Behavioural Economics his reference point), what is the most he would pay to insure? EU [ buy ] = w 0 - p + v ( w 0 - p - ( w 0 - p )) = w 0 - p EU [ don 0 t ] = E [ w ] + E [ v ( w - r )] = w 0 - 150 + . 05 2 v ( w 0 - 3000 - ( w 0 - p )) + ( . 05)( . 95) v ( w 0 - 1000 - ( w 0 - p )) +( . 05)( . 95) v ( w 0 - 2000 - ( w 0 - p )) + . 95 2 v ( w 0 - ( w 0 - p )) = w 0 - 150 + 1 400 v ( p - 3000) + 19 400 v ( p - 1000) + 19 400 v ( p - 2000) + 361 400 v ( p ) = w 0 - 150 + 2 400 ( p - 3000) + 38 400 ( p - 1000) + 38 400 ( p - 2000) + 361 400 p = w 0 - 150 + 2 400 + 38 400 + 38 400 + 361 400 p - 1 400 [6000 + 38000 + 76000] = w 0 - 450 + 1 . 0975 p So he will buy if: w 0 - p w 0 - 450 + 1 . 0975 p 214 . 54 p So not the biggest effect in the world, but in general when Warren broadly-brackets his risks he will be willing to pay less than if he considers them one-at-a-time. Note that diminishing sensitiv- ity would make this effect much stronger, since getting hit by both a tornado and an earthquake wouldn’t be as bad as suffering each as an independent loss. 6

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