The value of your real estate property is \(\$ 100,000\). In case of a fire, your property may be lost or damaged, depending on how severe the accident is. Let us assume that the following scenarios give the residual value of your property in the future, depending on the possible occurrence of a fire:

State ω1 means that no accident occurred. Assume that your preferences are represented by a logarithmic utility depending on wealth, which is why we do not consider a residual value of \(\$ 0\), but \(\$ 1\). What is the maximum price that you would be willing to pay for an insurance guaranteeing coverage of any loss? In the three states, the insurance will pay \(\$ 0, \$ 50,000\), and \(\$ 99,999\), respectively, so that the value of your property is preserved.

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State Residual value Probability W1 $100,000 0.95 W2 $50,000 0.04 W3 $1 0.01