A farmer has a von Neumann-Morgenstern utility function over corn consumption and effort of the form...

 

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A farmer has a von Neumann-Morgenstern utility function over corn consumption and effort of the form u(x,e) = x-ye² 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 = ae and under good weather condition, it will be x = ße, with ß> a. a) Find the farmer's optimal effort as a function of (p,a,B,y). A farmer has a von Neumann-Morgenstern utility function over corn consumption and effort of the form u(x,e) = x-ye² 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 = ae and under good weather condition, it will be x = ße, with ß> a. a) Find the farmer's optimal effort as a function of (p,a,B,y).

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