Need help with question b on filling this whole table. Anubhab, Ed and Javier ar

Question

Need help with question b on filling this whole table. Anubhab, Ed and Javier are cotton farmers in the village of Igaka in Tanzania. 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 me farming WI n 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 g 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). (b) Anubhab, Ed and Javier 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. Anubhab: U(C)=2C Ed: Javier: . U(C) = 40C-0.05 U(C) = 0.1C2 Table 1. Certainty Equivalent, Risk Premium and Expected Utility for 3 Activities Activity 2 Activity 3 EU Anubhab CE Anubhab RP Anubhab EU Ed CE Javier RP Javicr

Explanation / Answer

Given,

utility functions of Anubhab ,Ed and Javier

U(C)= 2*C

U(C)=40C-0.05*C^2

U(C)=0.1*C^2

so now calculating expected utility,certainty equivaalent and risk premium for Anubhab..

for activity1,

e(u)=0.5*(420)+0.5*(60)=240

CE=u(2C)=0.5*2*(420)+0.5*2*(60)=480

risk premium=e(u)-CE=

similarly for activity 2

since there is no risk involved

e(u)=1*210

CE=1*2*210=420

risk premium=e(U)-CE=210

for activity 3

e(U)=0.25*(420)+0.75(60)+1*(60)=210

CE=0.25*2*420+0.75*2*60+1*2*(60)=420

RP=e(U)-CE=210

calculate in the same way for Ed and Javeir

Calculating CE for Ed...

Activity 1

CE=0.5*(40*420-0.05*420^2)+0.5*(40*60-0.05*60^2)

=5100

Activity 2

CE=(40*210-0.05*210^2)

= 2190

Activity 3

CE=0.25*(40*420-0.05*420^2)+0.75*(40*60-0.05*60^2) +1*(40*60-0.05*60^2)

   = 5880

calculate risk premium accordingly

Activity 1 Activity 2 Acitivity 3 EU Anubhab 240 210 210 CE Anubhab 480 420 420 RP Anubhab 240 210 210 EU Ed 240 210 210 CE Ed 5100 6195 5880 RP Ed 4860 5985 5670 EU Javier 240 210 210 CE Javier 9000 4410 4740 RP Javier 8760 4210 4350

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