Assume there are two auto$-$insurers in the market. Company A charges risk$-$based premiums

and company B charges average premiums. Men have a higher accident probability than women

$(0\mathrm{.}15$ versus $0\mathrm{.}1).$ An accident has loss size L $=$ $$1,000.$ Company A has $650$ women and $350$ men

in the portfolio; company B has $200$ women and $800$ men in the portfolio. No transaction costs

and full information on the market.

a$)$ Calculate each insurer$$s premiums, assuming there is no loading and premiums are

actuarially fair

b$)$ What will happen if one policyholder from company B decides to switch $($and there are

no switching costs$)?$

c$)$ What happens if more policyholders switch?