Andres is a homeowner with an expected utility function u(x) = 1- e^(-x) where x is his wealthmeasured in million USD and u(x) satisfy the expected utility hypothesis. Andres' entire wealth is his house worth 1 (million USD). However, his house can be destroyed by a tsunami that will reduce its value to 0. The probability of a tsunami destroying house and reducing its value to 0 equals with range (0,1).

1. Is Andres risk-averse, risk-lover or risk-neutral?What is the larges premium P that Andres is willing to pay for full insurance?
2. Suppose that a local insurance company, InsLocal has insured n identical houses, all in the neighborhood of Andres, for a premium P per house. Suppose that the probability represents the tsunami destroying all houses (i.e., either all houses are destroyed or none of them is destroyed). Suppose that P is small enough that Andres has fully insured his house. Having insured his house, a new business opportunity arises for Andres. He is offered to buy 1/n of the insurance company InsLocal at price Q. What is the largest Q that Andres is willing to pay to get I/n of InsLocal? (The expected value of InsLocal is the total premiums it collects minus the payments to insured homeowners in case of a tsunami).
3. Answer part 2 for an insurance company that is called Ins Global that maintain global operations. InsGlobal insures n identical houses across the globe, all in different neighborhoods outside of Andres' neighborhood, so that the destruction of houses by tsunamis are independent events (i.e., the probability of a tsunami in one house is independent of how many other houses have been destroyed). Discuss briefly why your answers in parts 2 and 3 differ.
4. Is there an expected utility function u(x) for Andres where the answers for parts 2 and 3 coincide? Justify your answer.