→ ecoHYL:怎麼會是沒意外卻有保險金領，有意外卻沒保險金 =.=" 08/14 12:24
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..
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