Problem: Thinking about Insurance
Consider a one-period model in which an individual's probability of becoming disabled is equal to 0.1. If he/she becomes disabled, then earnings will be equal to 100. In the absence of disability, earnings will be equal to 200. Assume the individual has utility equal to U = ln Y, where Y is earnings. a) a. Assuming that the person cannot purchase insurance, write down the expression for this person's expected utility. b) b. Now assume that the person can purchase insurance at a price of q cents per dollar of insurance. Write down the expression for expected utility assuming that this person purchases $X of insurance. c) c. Solve for this person's optimal level of insurance (i.e., solve for X) assuming that q = .10. d) d. Suppose there are two types of individuals - those with P = .05 and those with P = .25. Explain the adverse selection problem (assuming type is unobservable) if a private insurance company decides to serve this market.