A farmer has a von Neumann-Morgenstern utility function over corn consumption and effort of the form u(x,e)=xe2 where x is corn consumption and e is effort. He must exert effort to grow corn. After exerting his effort in the fields, there will be either drought, with probability p, or good weather with probability 1- p. Under drought conditions, the corn yield will be x=e and under good weather condition, it will be x=e, with >. a) Find the farmer's optimal effort as a function of (p,,,). b) What happens to the farmer's effort if a new fertilizer is introduced such that the values of and increase by 50 percent