Lucille is considering the purchase of insurance coverage on a family heirloom diamond necklace. The necklace is value at $500,000 and Lucilles net wealth is $900,000. She estimates the probability that the necklace is lost or stolen to be = 0.15. Furthermore, Lucilles utility function over final wealth is given by

u(x) = x0.5 Suppose that the insurance company offers Lucille any amount of coverage C at a premium rate p = 0.16.

1. WhatdoesyourintuitionsuggestabouttheamountofcoverageLucillewouldchoosetopurchase?FindtheoptimalamountofcoveragethatLucillewillpurchase.
2. Nowsupposethat,theprobabilitythatthelossoccurs,increasesto0.155.WhatdoyouexpectwillhappentoLucillesoptimalamountofcoveragecomparedtopart(b)(increase,decrease,orstaythesame)?
3. Find the new optimal amount of coverage that Lucille will purchase if = 0.155.