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

Citcn, the wovtd While卞auelling they loss"s15,000 Expeekd losso an oaudent do ouste da formula *15,000 ,a5 x 15000 〈25 24,15,000 ヤー×15D00 loo a O25 15,000 $31750 expected loss for a arelu, douơ 6% 5000 x45000 (oO 4150do purchase the însurance only the ual -to o, les Each fum is loss from -the aceide than -the [, The (bst

is $5000 to be u (areful diva$ coit proffake to puches the thiS l Jead-to Drolblem adlucise. not find t fnsurana Total eVenuce c the nSune m 5000 50 315000 st expected oss to the ampan 0-1x7500 x4 - 12500o expeted les to the Campa ny 125000-3500 ーキ2625000 The Cam is making an expected loss uslt ctase clown ard -the mahus for insurance not cst