Anubhab, Ed and Xinda are cotton farmers in the village of Qacha’s Nek in rural Lesotho. They each have zero wealth
(W=0), 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 with UKM08 cotton seeds: A farmer should work full time (7 days per week) on their
farm if they are cultivating UKM08 cotton. Working full time a farmer has a 50% probability of having a GOOD
harvest and earning income of $420 and a 50% chance of having a BAD harvest and earning only $60.
Activity 2: Full time farming with UK92 cotton seeds: UK92 variety is very well adapted to local weather conditions
and thus has no risk. If a farmer works full time she will earn $210 with certainty.
Activity 3: Part-time farming with UKM08 cotton seeds: In this third activity, a farmer plants UKM08 variety cotton
seeds and works Monday through Thursday on his farm and he works Friday through Sunday as a construction
worker in the nearby city of Geita. Since he is not able to work full-time on the farm, it is more likely that he suffers
damages from pests or bad weather. Specifically, the probability of having a GOOD cotton harvest and earning $420
drops to 25%, while the probability of having a BAD harvest and earning only $60 increases to 75%. The individual
also
earns $60 with certainty as a construction worker (i.e., he earns $60 in addition to his farm income under both
a GOOD and a BAD harvest).
(a) What is the expected value of consumption for each activity?
