Lucy, from Problem 4, spends all her income on lemonade, which costs $1 per pint. She earns $300 per month, but is robbed with 25 percent probability, in which case she is left with only $100. She can buy theft insurance to protect herself against that potential loss. The insurance costs 30 cents for each dollar of promised benefits. We can represent Lucy's preferences with an expected utility function, with the benefit function W(L) = - 1/L.
Lucy's utility function is then U(LN, LR) = - 3/4LN - 1/4LR.Her marginal utility of lemonade if not robbed is MUN = ¾ LN-2 and her marginal utility of lemonade if robbed is MUR = ¼ LR-2Solve for Lucy's budget line. Does she buy insurance? What is the value of that insurance to Lucy?