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Problem 3 Risk Preferences and Insurance Kayek, Meynes and Tilton are sunower farmers in the village of Girasol. They each have zero wealth, so their consumption is equal to the income they earn from their economic activity. Each of them must choose one (and only one) of the following three activities: Activity 1: Full time farming. Sunower farming is risky because of a combination of weather and pests. Under full time farming, the farmer works 7 days per week on their farm. There is a 50% probability of having a GOOD harvest and a 50% chance of having a BAD harvest. If the harvest is GOOD, the farmer earns an income of $200. If the harvest is BAD, the farmer earns an income of only $40. Activity 2: Full time construction work. This activity has no risk. An individual who decides to work full time in construction earns $80 with certainty. Activity 3: Parttime farming. In this third activity, the farmer works during the week as a sunower farmer and works in construction during the weekend. Since she is not able to work full time on the farm, the probability of having a GOOD harvest and earning $200 drops to 25%, and the probability of having a BAD harvest and earning only $40 increases to 75%. The individual also earns $30 with certainty as a construction worker (the person earns this $30 from construction in addition to her farm income under both a GOOD and BAD harvest). (a) What is the expected value of consumption for each activity? A. Activity 1: Full time farming: B. Activity 2: Full time construction work: C. Activity 3: Part time farming: Kayek, Meynes and Tilton view risk differently. This is reflected in the differences in their utility functions, which are listed below. Using those utility functions, compute the certainty equivalent (CE), the risk premium (RP) and expected utility (EU) associated with each of the three activities for each individual. Report your answers in Table 1 below. Kayek: U(C) = 0.05C2 Meynes: U(C) = 20C - 0.0502 Tilton: U(C) = 0.5C (b) Table 1. Certainty Equivalent, Risk Premium and Expected Utility for 3 Activities Note: Please put in your final answers as whole numbers or up to one decimal point wherever necessary. Full time farming Full Time Construction Part Time Work Work CE Kayek CE Meynes CE Tilton RP Kayek RP Meynes RP Tilton EU Kayek EU Meynes EU Tilton (c) Which activity each individual will choose? A. Kayek B. Meynes C. Tilton (d) Which type of risk preferences describes each individual? (Risk Neutral, Risk Averse, or Risk Loving?) A. Kayek B. Meynes C. TiltonMadam is an insurance agent who offers conventional crop insurance contracts only to full time farmers. He is not interested in offering insurance to part time farmers. The contracts are straightforward. At the beginning of the season, farmers pay a premium of $50. At the end of the season, Madam pays farmers an indemnity payment of $100 if the farmer had a BAD harvest. If the farmer had a GOOD harvest, Madam doesn't pay the farmer anything. For questions ef, assume that Madam has perfect information about the farmer's activity choice. In other words, he can write and enforce a contract that requires the farmer to choose full time farming. (e) What is Madam's expected prot li'om this contract? (Madam's prot is just the premium he collects from the farmer minus the indemnity payment he makes to the farmer). (i) What is the expected consumption for an individual who chooses hill-time farming with Madam's insurance contract? (3) What is the expected utility associated with full-time farming with an insurance contract for Kayek, Meynes and Tilton? A. Kayak: B. Moynes: C. Tilton