Tom Cruiser's Car Is Worth $100,000

Tom Cruiser's car is worth $100,000. But Tom is careless and leaves the top down and the keys in the ignition. Consequently his car will be stolen with probability .5. If it is stolen, he will never get it back. Tom has $100,000 in other wealth and his von Neumann-Morgenstern utility function for wealth is u(w) = ln(w) . Suppose that Tom can buy $K worth of insurance at a price of $.6K. How much insurance will Tom buy?

A) $0
B) $100,000
C) More than $0 but less than $50,000
D) More than $50,000 but less than $100,000
E) Exactly $50,000