Tom Cruiser\'s car is worth $100,000. But Tom is careless and leaves the top dow

Question

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 own 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?

Write out two equations for his wealth if a) his car isn’t stolen, and b) it is stolen

Explanation / Answer

There are two states of nature : car stolen and car not stolen .

Let w1 be Tom's wealth if his car is not stolen and w2 be Tom's wealth if his car is stolen.

w1 = 100000 + 100000 - 0.6K (Tom pays the insurance premium and car is still there),

w2 = 100000 +K -0.6K (car was stolen , now Tom get the insurance money K and pays the insurance premium).

Now, from this , K= (w2 - 100000 )/0.4

Now, put this into w1 equation we get, w1 = 200000 - 0.6(w2 - 100000)/0.4

By rearraging this ,we get, w1 + (3/2)w2 = 350000.

Expected utility of Tom is U(w1,w2) = 0.5 ln (w1) + 0.5 ln(w2) .

So, at an optimum , the insurance will Tom buy is more than $0 and less than $50000.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects