10. Suppose all insurance buyers have the same utility function U(W)=lnW, and the same initial wealth of $10,001. Assume there are 2 types of potential insurance buyers (same proportion).

An insurance company cannot differentiate high-risk and low-risk buyers, and decides to offer full coverage insurance at a price of $1000. Will the company be able to make a profit? Explain using your calculations.

High Risk (50%)		Low Risk (50%)
Probability	Loss	Probability	Loss
10%	$10,000	2%	$10,000
90%	0	98%	0