※ 引述《chris1 (小刀)》之铭言： : 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? : 解答是写 : 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 : 我不懂如果真的要极大化效用，Z=0怎麽会是最大的，应该是最小的吧，在这样的 : 式子下，Z越大应该效用就越大呀，因为P、Q都介於0、1之间呀，请高手指教.. 我觉得是要考虑要不要投保的问题 如果不投保此人的效用为: (1-P)*I+P*0=(1-P)I 如果投保由F.O.C可知: P=1 (Q为投保的费率 保险公司不可能设为1) 所以这时的效用为: 0 因为投保的效用小於不投保的效用 0<(1-P)I 所以此人选择不投保 Z为投保的保额为0 -- 我没有你想像那麽坚强 我只是去假装没事 而你却不知道 只有在去努力的爱着你时 我才是最勇敢的 --

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