※ 引述《chris1 (小刀)》之銘言：
: Suppose that each individual has the utility function U1(I)=I when there is
: no accident, but when there is an accident, an individual will feel that
: his life is hopeless and his utility function becomes U0(I)=0, for any
: I>=0 (so money is of no use to an individual having an accident). An
: insurance company offers a contract: if a person pays the company QZ dollars
: before he knows whether he has an accident, the person will receive Z dollars
: from the company when he does not have an accident (so I=20+Z-QZ), but
: receives 0 from the company if he has an accident (so I=15-QZ). Suppose
: that each insurance company gets 0 expected profit. Suppose that each
: individual can have negative income even after an accident, what will be
: an individual's choice of Z?
: 解答是寫
: Max EU=P*U0(15-QZ)+(1-P)U1(20+Z-QZ)=P*0+(1-P)(20+Z-QZ)
: F.O.C : (1-P)(1-Q)=0 ∴Z=0
: 我不懂如果真的要極大化效用，Z=0怎麼會是最大的，應該是最小的吧，在這樣的
: 式子下，Z越大應該效用就越大呀，因為P、Q都介於0、1之間呀，請高手指教..
我覺得是要考慮要不要投保的問題
如果不投保此人的效用為: (1-P)*I+P*0=(1-P)I
如果投保由F.O.C可知: P=1 (Q為投保的費率 保險公司不可能設為1)
所以這時的效用為: 0
因為投保的效用小於不投保的效用 0<(1-P)I
所以此人選擇不投保 Z為投保的保額為0
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我沒有你想像那麼堅強 我只是去假裝沒事
而你卻不知道 只有在去努力的愛著你時 我才是最勇敢的
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