As(1-U(n+U(Y-Z is monotonically decreasing in丌, and as U(n>U(Y-p2>U(r-Z for any positive z,p there exists a marginal consumer, denoted with z* for whom U(Y-p2)=(1-丌*)U(Y)+m*U(y-Z) So everyone with more risk than that takes the insurance, and everyone with less risk does not This is adverse selectionAs 1  UY  UY  Z is monotonically decreasing in , and as UY  UY  pZ  UY  Z for any positive Z, p there exists a marginal consumer, denoted with  for whom UY  pZ  1  UY  UY  Z So everyone with more risk than that takes the insurance, and everyone with less risk does not. This is adverse selection