Suppose an economic agent has a utility function U = Ln (R). Assume R is the return on investment and utility is the natural log of investment. If the investment is highly successful then the agent earns $10000. If the investment is modestly successful then the agent earns $5000. Assume the probability of a highly successful outcome is Prob=0.70 and .30 for a modest outcome.
1. Answer the following questions. Show all of your work!
a. Derive the expected value of the investment opportunity.
b. Calculate the expected utility of the investment opportunity.
c. Calculate the level of utility if expected value of the investment opportunity was guaranteed.
d. Calculate the certainty equivalent level of return associated with the risky investment opportunity? Interpret your answer!
e. Given your answers in (a) and (d), calculate the risk premium and RAC coefficient.
f. Provide a graph highlighting your answers to questions above.