What do the 45 degree line, the fair line of insurance, and indifference curves represent in the two-state model?
45 degree line: Perfect equality between wealth in loss and no-loss states
Fair line of insurance: Line where premium equals expected loss, i.e., actuarially fair insurance
Indifference curves: Represent combinations of wealth in both states that yield the same utility
How does loss probability p affect the shape of indifference curves?
As p increases, indifference curves become flatter, indicating that the insured values wealth in the loss-state more, reflecting higher risk
How does the shape of indifference curves relate to risk aversion?
More risk-averse individuals have steeper and more curved indifference curves, reflecting a stronger preferance for certainty
How can the certainty equivalent and risk premium classify risk preferences?
Certainty equivalent: Amount an individual would accept instead of a risky option
Risk premium: The difference between the expected value of the lottery and the certainty equivalent. A higher risk premium indicates greater risk aversion
How do you calculate the Arrow-Pratt coefficient of absoulte risk aversion?
How do insurers handle assymetric information in a pooling contract?
Insurers offer the same contract to both high-risk and low-risk individuals, leading to inefficiencies since high risks are more likely to purchase insurance
Why can’t a pooling contract be a Nash equilibrium?
A pooling contract cannot be a Nash equilibrium because insurers could offer a contract tailored to low risks that would attract them, leaving only high-risks in the pool, causing losses
What is the difference between a Wilson equilibrium and a Nash equilibrium?
In a Wilson equilibrium, insurers can withdraw unprofitable contracts, which often leads to a polling contract being an equilibrium, unlike a Nash equilibrium where such contracts cannot exist
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