Question

In: Economics

Q2. Consider the ase of a risk neutral automobile insuran e ompany that insures ar drivers...

Q2. Consider the ase of a risk neutral automobile insuran e ompany that insures ar drivers for damages from a idents. For simpli ity let's assume that all a idents result in $12,000 of damages for all drivers and the insuran e ompany pays an insured driver this amount for ea h a ident. Now suppose that drivers are of three types: safe drivers whose probability of an a ident is 0.005 per year, risky drivers whose probability of an a ident is 0.01 per year and dangerous drivers whose probability of an a ident is 0.05 per year. While the drivers know their own type, the insuran e ompany only knows that 25% of al l drivers are safe, 50% are risky and 25% are dangerous. Finally assume that the likelihood of a idents for ea h type of drivers mentioned earlier is ommon knowledge. (18 marks )

(b) Suppose that all drivers are equally risk-averse, su h that they are willing to pay as yearly insuran e premium double the amount of their own expe ted damages. Based on your answer to part (a) above, whi h type(s) of drivers will buy insuran e? Please explain your answer. (4 marks )

Solutions

Expert Solution

Expected loss in case of safe drivers=probability of accident*Loss amount=0.005*12000=$60

Expected loss in case of risky drivers=probability of accident*Loss amount=0.01*12000=$120

Expected loss in case of dangerous drivers= probability of accident*Loss amount

=0.05*12000=$600

Firm's weighted payout based upon given distrubution of drivers is given as

Weighted payout=0.25*60+0.50*120+0.25*600=$225 per customer

Insurance premium=Weighted payout=$225 per customer

Now

Each drivers is ready to pay twice the amount of expected loss. So,

In case of safe drivers, willingness to pay for insurance (WTP)=2*60=$120

In case of risky drivers, willingness to pay for insurance (WTP)=2*120=$240

In case of dangerous drivers, willingness to pay for insurance (WTP)=2*600=$1200

We can see that WTP is higher than the insurance premium of $225 in case of risky and dangerous drivers. So, Only Risky and dangerous drivers will buy the insurance in this case.

Rahul Sunny answered 2 years ago
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