Please try to use mathematical notation as much as you can to demonstrate your answer, but don't forget to carefully define each step you make.
Question:
Q1. Define "risk averse".
Q2. Why does a risk averse agent offered actuarially fair insurance choose to insure fully?
Q3. What does the agent choose if the terms are worse than actuarially fair?
Q4. Show there are either one or two kinds of equilibrium in competitive insurance markets, depending on how equilibrium is defined.
Q5. Explain, in the context of competitive insurance markets, what is meant by: "Separating equilibrium" and "Pooling equilibrium". What assumptions are required for each of these types of equilibrium, in turn, to exist?