哈佛大学：《中级微观经济学》（英文版）Lecture 6 Choice Under Uncertainty

K K K ∑a4)=∑a∑mn-∑∑a6|m k=1n=1 n=1k=1 K ∑ akLk k=1 so linearity holds More surprisingly, if K K ∑ akLk ∑aU(LA) then we can write N Lk=(,N)=∑pnLn Where In places a probability of 1 on state n and zero on all other states

 k1 K kULk   k1 K k  n1 N unpn k   n1 N  k1 K kpn k un  U  k1 K kLk so linearity holds. More surprisingly, if U  k1 K kLk   k1 K kULk then we can write Lk  p1 k ,...pN k    n1 N pnLn where Ln places a probability of 1 on state n and zero on all other states

We have then UL)=∑pln=∑p(n)=∑ nun which has the expected utility form

We have then ULk  U  n1 N pnLn   n1 N pnULn   n1 N pnun which has the expected utility form