Michelle owns a house in which she keeps valuables worth 100,000 which can get stolen with probability 1%. She can purchase coverage C of the amount C ∈ [0; 100,000] at premium π = 0.05 dollars for each dollar covered. Her Bernouilli utility function is u(w) = ln(w). Assume she has no other assets. 1. Set up her maximization problem. 2. How much insurance will she choose to buy? 3. How much profits does the insurance company earn on insuring Michelle? 4. Does the fact that the insurance company earn profits mean that Michelle is worse off com-pared to the situation in which she is not insured? Explain what is happening. 5. How much insurance will she buy if insurance companies charge an actuarially fair insurance rate?
Michelle owns a house in which she keeps valuables worth 100,000 which can get stolen with probability 1%. She can purchase coverage C of the amount C ∈ [0; 100,000] at premium π = 0.05 dollars for each dollar covered. Her Bernouilli utility function is u(w) = ln(w). Assume she has no other assets.
1. Set up her maximization problem.
2. How much insurance will she choose to buy?
3. How much profits does the insurance company earn on insuring Michelle?
4. Does the fact that the insurance company earn profits mean that Michelle is worse off com-pared to the situation in which she is not insured? Explain what is happening.
5. How much insurance will she buy if insurance companies charge an actuarially fair insurance rate?
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