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A risk averse agent with vNM utility u is offered two lotteries. The payoffs of lottery 1 , x, are distributed according to cumulated distribution

A risk averse agent with vNM utility u is offered two lotteries. The payoffs of lottery 1 , x, are distributed according to cumulated distribution function F. Lottery 2 is obtained by randomizing payoff x further so that the final payoff is y=x+ , where H and dH()=0 . Show that the agent prefers lottery 1 to lottery 2.

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