Consider an individual who owns a warehouse
3. Consider an individual who owns a warehouse that is subject to fire damage. The warehouse is worth $1,000,000 and .re can result in a damage of $910,000. The owner of this warehouse can take precautions against fire. For simplicity, we assume that he can be negligent, .moderately cautious, or .very cautious. The owner’s choice affects the probability with which the warehouse gets burnt. These probabilities together with the disutilities of efforts are given in the following table.
|
Outcomes and probabilities |
disutilities |
|||
|
$1,000,000 |
$90,000 |
|
||
|
Efforts |
|
0.8 |
0.2 |
0 |
|
|
0.9 |
0.1 |
20 |
|
|
|
0.95 |
0.05 |
45 |
: negligent
: moderately cautious
: very cautiousThe owner’s preferences are described by a
von Neumann and Morgenstern utility function
wherewis his net wealth and
is his disutility of taking action
.
Suppose that the warehouse owner can buy insurance from a risk-neutral monopolist.
(1) If the insurance monopolist can observe the actions of the warehouse owner, what insurance contract will the monopolist offer? Which action is the warehouse owner going to take? What are the profits of the insurance monopolist?
(2) Suppose that the insurance monopolistcannotobserve the warehouse owner’s actions. Set up the insurance monopolist’s problem of designing the optimal insurance policy. Find the optimal insurance contract. What are the profits of the insurance monopolist? Compare this optimal contract with the one you found in (1).
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Solution: Consider an individual who owns a warehouse