(3) Problem 2 might leave us wondering why on earth Malini would choose to sharecrop if fixed rent is better. We kind of waved our hands and said that otherwise the situation is too risky for Kumar. We are now going to try and formalize this argument in a very simple setting. In the previous problem, let us say that that when Kumar farms the land, A = B = 1 with probability 1/2, or A = B = > > 1 with probability 1/2. (Good and bad outcomes are perfectly correlated across the two plots.) In other words, A = AveA and YB # = XVeB. with probability 1/2, while YA = VeA and YB = VeB, again with probability 1/2, where I have used the signs "+" and "-" to distinguish good and bad outputs. Kumar's next-best alternative (if he does not rent) is just to farm his own plot. And total labor endowment equals 1, as before, and supplied at zero cost. Kumar's utility is strictly concave in his own income - he is risk averse. If Kumar earns r, his utility is given by In(I).(d) Now suppose that Malini offers a sharecropping contract with share o to herself and 1-o to Kumar. Using a similar logic to that in the previous question, show that (1- 0)2 eB 1+ (1-0)2 so that the expected rent that Malini receives is given by 1+x o(1-5) Sharecropping rent = 2 VIt ( 1 - 0) (e) Use part (c) and the formula in part (d) to show that if A is large enough, a risk-neutral Malini prefers sharecropping to fixed rent tenancy. Intuitively explain your