Suppose you wish to insure an asset valued at $100. Only two states of the world can occur in the future, FIRE and NO FIRE, with probabilities .25 and .75 respectively. In the FIRE state, the asset is completely destroyed. Your initial wealth (including this asset) is $120, and your utility U(W)= ln W.
A. Suppose an insurer offers to fully insure your fire risk for a premium of $25. Should you purchase this insurance policy? Why or why not?
B. If the premium for full coverage is $35, should you fully insure? Why or why not?
C. What is the maximum premium you are willing to pay to fully insure this risk? Explain how you determined the answer to this question.