Consider a village of a large number of identical farmers. All farmers are ownercultivators; i.e., they own and work their own land. They can choose how much effort p to apply to their land, where p is either pL or pH (pL < pH). With probability p their crop is a success, and their output is H; with probability (1 p) their crop is a failure, and their output is L < H. For consumption equal to y, utility over consumption and effort is given by u(y) C(p). C(p) is the cost of effort; assume that C(pL) = 0 and C(pH) = K, a positive constant. Farmers are risk-averse.

i. Assume there is no insurance. What condition must be satisfied for farmers to choose effort level pH? For the remainder of this problem, assume that this condition is satisfied. What is each farmer's expected consumption under this choice of effort? What is their expected utility?