A student has a BMW that is worth $40,000. Given your driving skills, the probability of an accident is Pa = 0.7. Assume that when an accident occurs, the value of your car goes down to $20,000.

1.What's the expected wealth of this student? Let the utility function over the value of the car be given by: u(c)=(c).

What's the expected utility? What's the utility of the expected wealth? From your previous answers, is this student risk-loving or risk-averse?

2. let $ be the premium that you have to pay to insure $1. Assume that the student buys $K worth of insurance. Write down his wealth with insurance when the accident occurs (call it Wa). Write down his wealth with insurance when the accident does not occur (call it Wn). Now, combine these two into an expression for the budget constraint.

3.The expected utility function can be expressed as: U(Wa,Wn) = 0.7Wa +0.3Wn. Using the budget constraint in part (2), solve the [UMP] and state the optimality condition. (Hint: show the condition that implies that MRS is equal to the slope of the budget constraint.)

4.If = 0.7, what does the expression in part (3) reduce to? Find the amount of insurance this student would be buying, K*?