Marla, a Von Neumann-Morgenstern utility maximizer, is planning a cross country trip. Her utility from the trip is a function of how much of her cash Y she spends, and is given by

U(Y) = Ln(Y) where LNis the natural log.

Assume Marla has $5,000 to spend.

1. What is her utility if she spends all of her cash?

2. Suppose there is a 25% probability she will lose $1000 during the trip. What is her expected utility?

3. Suppose Marla can buy insurance against this loss. What is the actuarially fair premium (the premium= expected loss)? Show that she will have higher utility if she buys this insurance.

4. What is the maximum she would be willing to pay for this insurance? (Assume she cannot avoid the risk).

5. Suppose Marla reads Chapter 3 in Ackert and Deaves and concludes that she needs to follow Prospect Theory to decide whether to buy the insurance. If she uses $5,000 as her reference point and has the value function v(z) = -(z)for a loss with = =.88. Assuming Marla got the probability correct, (i.e. w(.25)=.25) would Marla buy the insurance if it cost $250?