Hi,

I tried solving but I still couldn't get how to solve the certainty equivalent income. Is it possible to help me solve for this exercise question (specifically #6 in the posted picture). My guess is that I am getting confused on how to do the log() and ln() function. Thank you.

1. Suppose a person has the utility function, U(1)=log(1), where I is income. He has income 12 ($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 II and 12, 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