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Farm diversification and insurance using expected utility theory

In this assignment you are asked to solve some problems using expected utility theory. The theoretical approach, as we discussed in the notes, is viewed as out of date by many economists.

Part A
Smith has an expected utility function, E(U), that looks like:

E(U)= E(log10(outcome))

where ‘outcome’ is income in dollars. She expects the following income distribution:

probability income

0.25 $20,000

0.50 $40,000

0.25 $45,000

1.What is the expected monetary value of Smith’s enterprise?
2.What is Smith’s certainty equivalent income? How is ‘certainty equivalent’ interpreted in this context?
3.What is Smith’s risk premium associated with this income distribution? How do you interpret it?
(Note: Log(20,000) = 4.30103, Log(40,000) = 4.60206 and Log(45,000) = 4.65321 . The anti-log of 4.54 is 34,674 ie 104.54 = 34,674.)

Part B
Read Appendix A before attempting this question.

A farmer intends to sow all of her 1000 hectares to Barley (B) and Wheat (W). The expected gross margins for barley and wheat are $150/ha and $100/ha and their associated variances are $10,000 and $3,600 respectively. In addition, the returns from the two crops are expected to be correlated with a correlation coefficient (pxy) of 0.25.

The farmer’s expected utility function looks like:

E(U) = E(Y) – 0.0001Var(y).

1.What is the optimal amount of barley for the farmer to grow? Show all your workings

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