Demeter has 100 acres of land on which she can plant wheat or rice. The following table shows the income per acre that each crop will produce, both for a wet growing season and a dry growing season. Wet Dry Wheat 200 700 Rice 700 200 The probability of a wet growing season is 3 and the probability of a dry growing season is . Demeter's utility function over income is U(W) = In W. What is Demeter's contingent income bundle if she plants only wheat? If she plants only rice? If she plants 50 acres of wheat and 50 acres of rice? (Note: A contingent income bundle is (Ww, Wa), where the “w" subscript indicates "wet" and the “d" subscript indicates "dry".) а.
Demeter has 100 acres of land on which she can plant wheat or rice. The following table shows the income per acre that each crop will produce, both for a wet growing season and a dry growing season. Wet Dry Wheat 200 700 Rice 700 200 The probability of a wet growing season is 3 and the probability of a dry growing season is . Demeter's utility function over income is U(W) = In W. What is Demeter's contingent income bundle if she plants only wheat? If she plants only rice? If she plants 50 acres of wheat and 50 acres of rice? (Note: A contingent income bundle is (Ww, Wa), where the “w" subscript indicates "wet" and the “d" subscript indicates "dry".) а.
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
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Transcribed Image Text:3. Demeter has 100 acres of land on which she can plant wheat or rice. The following table shows
the income per acre that each crop will produce, both for a wet growing season and a dry growing
season.
Wet
Dry
Wheat
200
700
Rice
700
200
1
2
The probability of a wet growing season is ; and the probability of a dry growing season is
3
Demeter's utility function over income is U(W) = In W.
What is Demeter's contingent income bundle if she plants only wheat? If she plants only
rice? If she plants 50 acres of wheat and 50 acres of rice? (Note: A contingent income
bundle is (Ww, Wa), where the "w" subscript indicates "wet" and the "d" subscript
indicates "dry".)
b. Use your answers in (a) to find an algebraic expression for Demeter's budget constraint
over contingent income bundles.
What is Demeter's expected utility function? What is her MRS function?
а.
с.
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