ISyE 4803b Homework 9 1. In class we discussed the notion of adverse selection for purchasing trucking services. The following example (taken from Managerial Economics by Allen et al) illustrates the idea for insurance. Suppose there are two categories of drivers: high and low risk. Each policy-holder has an initial wealth of $125, but a loss can reduce the wealth to $25; that is, drivers can lose $100 of their wealth should the loss occur. For high-risk drivers the probability of loss is 0.75 and for low risk drivers the probability is 0.25. In addition, assume that a driver’s utility is equal to the square root of their wealth (this would be the case if a driver were risk averse). Answer the following: a. Determine the competitive premiums for the insurer (i.e., the premium based on expected losses) for each group. b. Find the utilities with and without insurance for each group. c. Now suppose that the insurer can’t distinguish between high- and low- risk drivers.
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