The derivative of insurance w.r.t. c or p, for c=becomes -U(r-TD -(1-m)p2+m(1-p)2)U"(Y-D U(Y-TD -(p2+x-2p)"(Y-D which is negative and inversely proportional to the coefficient of absolute risk aversion at y-丌l.The derivative of insurance w.r.t. c or p, for c  0 becomes I p  U Y  I 1  p2  1  p2 UY  I  U Y  I p2    2pUY  I which is negative and inversely proportional to the coefficient of absolute risk aversion at Y  I