offer such a scheme and the farmer would want to accept it? (Just write down the conditions, that is, the mathematical inequalities that B and D should satisfy; don’t try to solve these equations !) (c) For which set of (B,D) values: (i) (19,96) or (ii) (36,56) or (iii) (19,75) the friend would offer and the farmer would accept the scheme? (Plug the values into the inequalities you found in (b) to check) PLEASE ANSWER ALL THE PARTS!
PROBLEM (6) A farmer with expected utility preferences with u(x) = sqaure root(x) can experience a Bountiful or a Dry year with probabilities %80 and %20, and with $100 and $25 worth of crops, respectively.
(a) Calculate the expected value and expected utility of the “lottery” the farmer is facing. What is the certainty equivalent and risk premium of this lottery for the farmer?
(b) The farmer’s risk-neutral friend offers him the following “insurance” scheme:
“Give me $B if the year is bountiful and I will compensate you with $D if the year is dry”
What should the numbers B and D be so that the friend would be willing to offer such a scheme and the farmer would want to accept it? (Just write down the conditions, that is, the mathematical inequalities that B and D should satisfy; don’t try to solve these equations !)
(c) For which set of (B,D) values: (i) (19,96) or (ii) (36,56) or (iii) (19,75) the friend would offer and the farmer would accept the scheme? (Plug the values into the inequalities you found in (b) to check)
PLEASE ANSWER ALL THE PARTS!
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