Question

Suppose there are a two different types of travellers. The safe ones and the unsafe ones. No matter the type of travellers, they all own $20,000 in the good state of the world. If they get into an accident while travelling they lose $15,000. The utility of a traveller is u(y)= y^(1/2) . Consider the competitive market for travel insurance in answering the following questions. Whenever I refer to the state contingent space, put money in the good state on the horizontal axis and money in the bad state on the vertical axis.

1. Suppose the insurance company cannot observe the type of their clients. What kind of information asymmetry does this situation describe?

A Hidden action

B Moral selection

C Adverse selection

D Averse selection

E Risk aversion

F Moral Hazard

2. Suppose the safe type has a probability of 10% to get into an accident while travelling, but the unsafe type has a probability of 25%. What is the absolute value of the slope of the indifference curve in the state contingent space at the 45 degree line for the safe type?

3. Suppose the safe type has a probability of 10% to get into an accident while travelling, but the unsafe type has a probability of 25%. What is the absolute value of the slope of the indifference curve in the state contingent space at the 45 degree line for the unsafe type?

4. Suppose there are 80% safe types and 20% unsafe types in the population. What is the pooled risk of getting into an accident? Use an integer to provide the percentage.

5. Suppose there is only one insurance contract offered to both types, that provides full coverage and charges the actuarially fair premium for the the pooled risk. What is the expected utility of such a contract for the safe type? Use two decimals.

Answer 1