Old MacDonald, a farmer, owns a wheat ?eld, and its crop is valued at 9 dollars. With probability %, however, a swarm of locusts will attack, reducing the value of the cr0p to 6 dollars. Suppose that the farmer can self insure against this loss by investing in pesticides. If she spends :1; dollars on pesticides, the value of the crop if the locusts attack becomes 6 + J5 (not including the cost). (6%) Suppose that Old MacDonald is risk neutral. Let the arc—axis be his wealth wg if there is no locust attack, and the y—axis be his wealth wb if there is a locust attack. Draw an indifference curve and the budget set for John. Show your work and explain why your graphs look this way. Hint: you are working with the space of (tug, wb). Here it would be really helpful to understand what indifference curve and budget set mean. Find the Optimal choice of pesticide use when Old MacDonald is risk neutral. Now suppose that Old MacDonald is risk averse with vNM utility u(:c) = ?. What is her optimal choice of pesticide use now? Is it more or less than if he was risk neutral. Give an intuitive explanation of this result. Can you relate your solution to your graphs in part (a)?

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