Lukas is a risk averse farmer. He grows barley on his 1000 acre farm. In a typical year his farm yields 100 bushels of barley per acre. However, in a wet season, the farm only yields 40 bushels per acre. The probability of a typical season is 0.8 and of a wet season is 0.2. Regardless of the productivity of his farm, he expects to earn $3 per bushel (net of all costs of farming). Assume that Lukas has no other income. This information is summarized in the following table: Probability Bushels per Acre $ Earned per Acre Total $ Income Typical Season 0.8 100 300 $300,000 Wet Season 0.2 40 120 $120,000 a) What is Lukas's expected income? Write an expression for Lukas's expected utility. Illustrate Lukas's expected utility in a diagram. Before the season begins, Lukas would be just willing to forego planting his barley in exchange for a sure payment of $220,000