Part 1: RISK PREFERENCES AND CONVENTIONAL INSURANCE
Kelly, Isaac and Daniel 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 50% probability of having a GOOD harvest
and a 50% change of having a BAD harvest. If the harvest is GOOD, the farmer earns an income of $150. If the
harvest is BAD, the farmer earns an income of only $50.
Activity 2: Full time construction work. This activity has no risk. An individual who decides to work full time in
construction earns $95 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 $150 drops to 25%, and the probability of having a BAD harvest and earning
only $50 increases to 75%. The individual also earns $20 with certainty as a construction worker (the person earns
this $20 from construction
in addition to
her farm income under both a GOOD and BAD harvest).
- What is the expected value of consumption for each activity?
2.
Kelly, Isaac, and Daniel view risk differently, and that is why they have different utility functions (listed below).
Using those utility function, compute the certainty equivalent (CE), the risk premium (RP) and expected utility (EU)
Sample Solution
