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).

Q2. What is the farmer's Expected Utility should they plant the Traditional Variety of Maize?

[Note: Preserve 1 decimal place]

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

Solution:

Given the utility function U = C^0.5

Expected utility E (UH) from high yield maize = (probability of good outcome x utility of income from good outcome) + (probability of bad outcome x utility of income from bad outcome) + Initial wealth

E (UH) = (0.5 (1444)^0.5) + (0.5 (100) ^0.5)

=0.5 x 38 + 0.5 x 10 = 19 + 5 = 24

Expected utility E (UT) from Traditional yield maize = (probability of good outcome x utility of income from good outcome) + (probability of bad outcome x utility of income from bad outcome)

E (UT) = (0.5 (625)^0.5) + (0.5 (625) ^0.5)

=0.5 x 25 + 0.5 x 25 = 12.5 + 12.5 = 25

Yes, farmer should plant traditional variety of maize because expected utility from planting traditional variety of maize is greater than expected utility from planting high yield maize.

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