Suppose a person has the utility function, U(I)=log(I), where I is income. He has income I2 ($4,000)

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Question:

Suppose a person has the utility function, U(I)=log(I), where I is income. He has income I2 ($4,000) with the probability of p, but knows that some externally generated risk may reduce his income to I1 ($1,000) with probability of 1-p. Suppose p=0.8.

1) Is this person risk-averse? If so, why?

2) What is the expected income of this person?

3) What is the utility of expected income for this person?

4) What is the expected utility of this person?

5) Compare 3) and 4). Which is larger? Why?

6) What is the certainty equivalent income in this case?

7) What is the risk premium in this case?

8) Graphically show the risk premium with this utility function. Make sure to label each number of I1 and I2, expected income, expected utility, certainty equivalent income, together with the risk premium on the same graph.

9) Calculate the risk premium if p=0.5.

10) Is risk premium in 9) smaller or larger than the one you get in 7)? Why? Briefly summarize the intuition behind this result.