Question: suppose a farmer is considering insuring his corn crop from from rain damage. the farmer believes there is a 10% chance it will rain. if

suppose a farmer is considering insuring his corn crop from from rain damage. the farmer believes there is a 10% chance it will rain. if it rains, his crop is only worth $10000, if it does not rain his crop is worth $50,000. the farmer can choose to purchase $x worth of insurance, so that if the crop is ruined by rain, the insurance company pays the farmer $x. the cost of insurance is equal to $.10 per dollar of insurance the farmer purchases, this is know as the premium. suppose the farmer has constant relative risk aversion (CRRA) utility, given by u(w)=W^-2/-2. show that u'>0 and u"<0 and how much insurance should the farmer purchase?

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