A farmer has the utility function U=C^0.5 and faces a choice between planting a

Question

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).

Q5. What is the Risk Premium (RP) of the High-Yield Variety of Maize? [Hint: recall the RP is the difference between Expected consumption and the certainty equivalent]

[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

Explanation / Answer

E(U)=Probability of good outcome*U((initial ealth level+Income in good outcome))^0.5+Probability of bad outcome*U((initial ealth level+Income in bd outcome))^0.5

E(U)=0.5(1944)^0.5+0.5(600)^0.5=34.30

Ans wer is 34.30

CE =U^-1(34.30)=1176.5

Risk Premium=EMV-CE

EMV=0.5(1944)+0.5(600)=1272

Risk Premium=1272-1176.5=95.5=96

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