Homework SourseA farmer has the utility function UC05 and faces a choice be
A farmer has the utility function U=C^0.5 and faces a choice between planting a risky high yield variety of maize or planting the traditional variety. The outcomes and probabilities are summarized in the table below:
Different from the example in class, the farmer is now endowed with an initial wealth level of 500. So his/her consumption is the amount that they get from the Maize planted +500. (e.g., if a farmer gets 1444 income from maize planting, their consumption is 1444+500=1944).
Q4. What is the Certainty Equivalent (CE) of the Traditional Variety of maize?(Hint: Recall the CE is the fixed amount of money, given with certainty, that makes the farmer indifferent between taking the CE and planting High-Yield Maize. Don\'t forget the farmer has an initial wealth level!)
[Note: No need for decimal places here]
| Variety | Probability of Good outcome | Income in Good outcome | Probability of Bad outcome | Income in Bad outcome |
| High-Yield Maize | 0.5 | 1444 | 0.5 | 100 |
| Traditional Maize | 0.5 | 625 | 0.5 | 625 |
Solution
E(U) when Traditional Variety of Maize is used
E(U)=0.5(1125)^0.5+0.5(1125)^0.5=33.54
EMV =Expected Income=625+500=1125
CE=U^-1(33.54)=1125
Risk Premium=EMV-CE=1125-1125=0
