8.As the owner of a family farm whose wealth is $250,000,you must choose between sitting thiss son safe money market fund ($200,000)in ating summer corn. Planting costs S200,000,with a six-month time to harvest.If there is rain,planting summer corn will yield $500,000 in revenues at harvest.If there is a drought,planting will yield $50,000 in revenues at harvest.As a third choice,you can purchase AgriCorp drought-resistant summer corn at a cost of $250,000 that will yield s500,000im revenues at harvest if there is rain ,and$350, 000 in reven harvest if there is a drought.You are risk averse and your preferences for family wealth (W)are specified by the relationship U(W)=W.The probability of a summer drought is 0.30 and the probability of summer rain is0.70.Which of the three options should you cho te? Explain. ected utility of wealth under the three option ceadhhieatnentals250bw0pl咖grhatereriermedomgoiag investing in the safe financial asset.Expected utility under the safe option allowing for the fact that your initial wealth is S250,000 is: EU)=(250,000+200,000(1+.05-5=678.23. Expected utility with regular corn,again including your initial wealth: EU=.7(250,000+500.000-200.000》5+.3250,000+60,.000- 200,0005=519.13+94.87=614 Expected utility with drought-resistant corn,again including your initial wealth: EU)=.7250,000+(600,000 .250,000)5+.3250,000+(350,000 250,00005=494.975+177.482=672.46. You should choose the option with the highest expected utility,which is the safe option of not planting corn. 9.Draw a utility function over income u(D)that has the property that a man is a risk lover when his income is low but a risk averter when his income is high. Can you explain why such a utility function might reasonably deseribe a person's Preferences? Consider an individual who needs a cer ain level of incom e,in order to stay alive.An increase in income abovewill have a diminishing marginal utility. Below I,the individual will be a risk bver and will take unfair gambles in an effort to make large gains in income.Above the individual will purchase insurance against losses. 8. As the owner of a family farm whose wealth is $250,000, you must choose between sitting this season out and investing last year’s earnings ($200,000) in a safe money market fund paying 5.0% or planting summer corn. Planting costs $200,000, with a six-month time to harvest. If there is rain, planting summer corn will yield $500,000 in revenues at harvest. If there is a drought, planting will yield $50,000 in revenues at harvest. As a third choice, you can purchase AgriCorp drought-resistant summer corn at a cost of $250,000 that will yield $500,000 in revenues at harvest if there is rain, and $350,000 in revenues at harvest if there is a drought. You are risk averse and your preferences for family wealth (W) are specified by the relationship  U(W ) = W . The probability of a summer drought is 0.30 and the probability of summer rain is 0.70. Which of the three options should you choose? Explain. You need to calculate expected utility of wealth under the three options. Wealth is equal to the initial $250,000 plus whatever is earned on growing corn, or investing in the safe financial asset. Expected utility under the safe option allowing for the fact that your initial wealth is $250,000 is: E(U) = (250,000 + 200,000(1 + .05)).5 = 678.23. Expected utility with regular corn, again including your initial wealth: E(U) = .7(250,000 + (500,000 -200,000)).5 + .3(250,000 + (50,000 - 200,000)).5 = 519.13 + 94.87 = 614. Expected utility with drought-resistant corn, again including your initial wealth: E(U) = .7(250,000 + (500,000 - 250,000)).5 + .3(250,000 + (350,000 - 250,000)).5 = 494.975 + 177.482 = 672.46. You should choose the option with the highest expected utility, which is the safe option of not planting corn. 9. Draw a utility function over income u(I) that has the property that a man is a risk lover when his income is low but a risk averter when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences? Consider an individual who needs a certain level of income, I*, in order to stay alive. An increase in income above I* will have a diminishing marginal utility. Below I*, the individual will be a risk lover and will take unfair gambles in an effort to make large gains in income. Above I*, the individual will purchase insurance against losses