4. A small business owner has a log utility function,() = ln (). She faces a 10% chance of having a fire that will reduce her net worth to $1.00, a 10% chance that a fire will reduce her net worth to $50,000, and an 80% chance that her business will retain its value of $100,000. a. What is the business owner's expected wealth? b. What is the utility of expected wealth in this scenario? c. What is the expected utility of wealth in this scenario? d. Is this person risk averse? Explain. e. What is the certainty equivalent of wealth in this scenario and what does this mean? f. What are the risk premium and cost associated with this gamble? g. What is the maximum amount she would pay for insurance that ensures her wealth is not affected?

5. Uncertainty and initial wealth: a. Explain why it may be important to consider an individual's initial wealth when analyzing how that person will react to uncertainty (Hint: think about expected utility). b. Under what circumstances will initial wealth be irrelevant to a person's choice when faced with uncertainty?

6. Pure securities and asset pricing under uncertainty: a. What is a "pure security" and why are they important? We have derived the price of the pure security as (this is also in your book): = ( 1 1 + ) (1 () 1 + ()). b. Explain the elements that define pure security prices in terms of what economic factors will influence them. c. What are the assumptions that need to hold in order for this price to be unique? d. What implications does this pricing equation for pure securities imply about other, more realistic, securities that might trade in the market?