Question

1. there are two types of drivers. Speed racers with %5 chance of accident per year and low racers with %1 chance of accident per year. There are twice more speed racers than low racers and the cost of each accident is $12000. Assume that the pre-accident income for both types of drivers is $12,000 and that they all have utility function U(c)=√??. Also suppose, that the insurance company is offering full insurance (i.e. $12,000 payout in case of an accident).

a) suppose insurance knows the type of each rider, what premium each insurance will charge each rider?

b) due to asymmetric info, insurance does not know the type of each rider. would the insurance be sold out if (i) drivers self-reported their type of insurance? (ii) suppose there is no info related to drivers individual type, explain is there is uncertainty about selling insurance and why?

Answer 1

Answere (a) The insurance company expects to pay out $12000 in claim to 5% of speed racers it covers so it must collect at least 0.05($12,000) = $600 from each one. In similar way insurance company will collect at last 0.01($12,000) = $120 fro each lo rider.

Answere (b) (1) Every individual would claim to be a Low Rider, but if the insurance company sold insurance to everyone for $120 ,it would lose money beacuse of the presence of speed racers in the population. The insurance company would quickly increase premiums, bt if it increased them by too much the low riders would leave the market. It cannot be determined here exactly ho much more $120 the low riders would tolerate, as their risk aversion is not specified. As more low riders chose not to purchase insurance, the pool of convered drivers would include a higher and higher proportionspeed racers, requiring the insurance company to increase premiums again to cover claims.

(2) The insurance company could offer a premium that averages the expected claims. In a population of half low riders and half speed racers , the pooling premium wold be($600+$120)/2 = $360. The low riders would have to be extremely risk averse to be willing to pay $360 to cover an unexpected loss of $120. If they (low riders) opted out of the market, the insurance company would be back to the adverse selectio problem discussed above; an insured pool containing a high proportion of speed racers.