Richard owns a farm with 64 acres of land on which he grows wheat. Each acre...

 

 

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Richard owns a farm with 64 acres of land on which he grows wheat. Each acre of wheat, if harvested, yields a money income of £1024 at the end of the year. Richard has no other current income or financial assets. He is an expected utility maximiser with a utility function over outcomes (measured at the end of the year in money income £z) given by u(z) = 10,000log2 (z). Due to global warming, with a probability of 10 percent, his land is flooded and half of his crop is lost. (a) Write down the lottery that Richard faces, determine its expected value and Richard's expected utility. [5] [4] (c) Suppose an insurance company offers a "crop-insurance". If Richard buys this, he needs to pay £p, but receives the full amount of crop lost in case of a flooding in money value. What is the maximal price p he is willing to pay for this insurance? Compare this with his expected monetary loss and discuss what explains the difference. (b) Derive the certainty equivalent and compare to the expected value from (a). Infer Richard's risk attitude. [8] (d) Now suppose no crop-insurance is available. However, Amy is in the exact same situation, but lives in a different part of the country. In particular, the probability that Amy's land is hit by a flood is identical to and independent of the probability that Richard's land is flooded. E.g., the probability that both of their land is flooded at the same time is 0.1*0.1. Amy proposes to share the risk, i.e. proposes that if one of their land is flooded, then that person receives half the loss from the other person (provided not both lands are flooded). For instance, if Richards looses 32 acres of crop then Amy gives him the money amount equal to 16 acres of crop if her land is not flooded and vice versa. Will Richard agree to this deal? [8] Richard owns a farm with 64 acres of land on which he grows wheat. Each acre of wheat, if harvested, yields a money income of £1024 at the end of the year. Richard has no other current income or financial assets. He is an expected utility maximiser with a utility function over outcomes (measured at the end of the year in money income £z) given by u(z) = 10,000log2 (z). Due to global warming, with a probability of 10 percent, his land is flooded and half of his crop is lost. (a) Write down the lottery that Richard faces, determine its expected value and Richard's expected utility. [5] [4] (c) Suppose an insurance company offers a "crop-insurance". If Richard buys this, he needs to pay £p, but receives the full amount of crop lost in case of a flooding in money value. What is the maximal price p he is willing to pay for this insurance? Compare this with his expected monetary loss and discuss what explains the difference. (b) Derive the certainty equivalent and compare to the expected value from (a). Infer Richard's risk attitude. [8] (d) Now suppose no crop-insurance is available. However, Amy is in the exact same situation, but lives in a different part of the country. In particular, the probability that Amy's land is hit by a flood is identical to and independent of the probability that Richard's land is flooded. E.g., the probability that both of their land is flooded at the same time is 0.1*0.1. Amy proposes to share the risk, i.e. proposes that if one of their land is flooded, then that person receives half the loss from the other person (provided not both lands are flooded). For instance, if Richards looses 32 acres of crop then Amy gives him the money amount equal to 16 acres of crop if her land is not flooded and vice versa. Will Richard agree to this deal? [8]

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a Write down the lottery that Richard faces determine its expected value and Richards expected utility 4 ANSWER The lottery that Richard faces is as follows With probability 01 he will lose half of hi... View the full answer