Suppose that there are two individuals: Rocky and Bullwinkle. Both of them gain utility from their...

 

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Suppose that there are two individuals: Rocky and Bullwinkle. Both of them gain utility from their income according to the following functions: UR (MR) = 5√ √mR UB (MB) = 10√mB Suppose that each individual plants different crops. Each of them has a 50% probability of receiving a good harvest (m = $400) and a 50% probability of receiving a bad harvest (m = $100). As the farmers each planted different crops, we assume that their individual probabilities of receiving a good harvest are independent of each other. 7. What is each farmer's expected utility in this case? Show your work. [2 points] Suppose that these farmers enter into an agreement, where if one farmer receives a good harvest and the other receives a bad harvest, then the farmer with the good harvest pays $100 to the farmer who receives a bad harvest. This is a common form of "informal insurance". 8. What is the probability of one of these farmers having to make a payment to the other? Show your work. [1 point] 9. What is each farmer's expected utility under this informal insurance scheme? Are the farmer's made better off under this scheme? Show your work. [2 points] Suppose that there are two individuals: Rocky and Bullwinkle. Both of them gain utility from their income according to the following functions: UR (MR) = 5√ √mR UB (MB) = 10√mB Suppose that each individual plants different crops. Each of them has a 50% probability of receiving a good harvest (m = $400) and a 50% probability of receiving a bad harvest (m = $100). As the farmers each planted different crops, we assume that their individual probabilities of receiving a good harvest are independent of each other. 7. What is each farmer's expected utility in this case? Show your work. [2 points] Suppose that these farmers enter into an agreement, where if one farmer receives a good harvest and the other receives a bad harvest, then the farmer with the good harvest pays $100 to the farmer who receives a bad harvest. This is a common form of "informal insurance". 8. What is the probability of one of these farmers having to make a payment to the other? Show your work. [1 point] 9. What is each farmer's expected utility under this informal insurance scheme? Are the farmer's made better off under this scheme? Show your work. [2 points]

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