Problem 3: Risk Preferences and Insurance Steve, Clark, and Drew are sunflower farmers in the village of Gold. 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. Sunflower 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: Part-time farming. In this third activity, the farmer works during the week as a sunflower 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? Expected value of consumption for each activity Activity 1 Activity 2 Activity 3 Steve, Clark and Drew 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 (Round your answers to two decimal places). Steve: U(C) = 0.05C2 Clark: U(C) = 25C - 0.05C2 Drew: U(C) = 0.5C (b) Table 1. Certainty Equivalent, Risk Premium and Expected Utility for 3 Activities (Note: When you are calculating CE for Clark (for all activities), you would find two roots for the quadratic equations you derived. Report the smaller one between the two.) Full time farming Full Time Part Time Work Construction Work EU Steve EU Clark EU Drew RP Steve RP Clark RP Drew CE Steve CE Clark CE Drew