Question 3: Risk Preferences and Insurance

Miki, Jiting and Kelly are sunflower 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. 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 60% probability of having a GOOD harvest and a 40% 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 $20.

Activity 2: Full time construction work. This activity has no risk. An individual who decides to work full time in construction earns $60 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 35%, and the probability of having a BAD harvest and earning only $20 increases to 65%. 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)?

• Activity 1: Full time farming ?0.6*200+0.4*20= $128
• Activity 2: Full time construction work: $60
• Activity 3: Part time farming: 0.35*200+0.65*20+30= $113

Please help with the following table:

Miki, Jiting and Kelly 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. Please answers in Table 1 below.

• Miki: ?(C)=0.5?
• Jiting: U(C)=5*sqrt(?)
• Kelly: U(C)=0.05C²

preview=8940295 Page 14 > of 16 O Jiting: U(C) = 5VC Kelly: U(C) = 0.05C2 Table 1. CE/RP/EU for 3 Activities Full Time Full Time Part Time Farming Farming Construction Work Miki EU Miki CE Miki RP Miki Jiting EU Jiting CE Jiting RP Jiting Kelly EU Kelly CE Kelly RP Kelly