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How much insurance should the agent buy

Question 1- An agent, with wealth 50, faces a probability 0.2 of a loss 35. The agent is offered insurance at a premium rate of 0.25. The agent has the von Neumann-Morgenstern utility function, u=lnx, where x is wealth. How much insurance should the agent buy?

Question 2 - Show that a risk averse agent offered terms worse than actuarially fair will not choose to insure fully?

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