Assume that an insurance company is willing to offer theft insurance coverage on a $100 bicycle. It is facing two types of consumers: those who live in a high crime area (probability of theft is 40%) and those who live in a low-crime area (probability of theft is 20%).

Both types of customers are risk-averse. The high-risk customers are willing to pay $45 for full coverage and low-risk customers are willing to pay $25 for full coverage.

1) Show both consumers on a graph with the total utility curve on the Y-axis and wealth on the X-axis (similar to Figure 12.2. in the textbook, however, assume that utility is zero at the origin). Use the example from the previous lecture on house insurance and show the expected value of the consumer wealth and willingness to pay for the insurance (the 45 and 25 dollars correspondingly).

2) what is the premium value at which the insurance company is just breaking even for each type of customer?

3) What will happen in case the insurance company cannot distinguish between the two consumers and charges the average price of $35? Show your calculations and explain.

4) Assume that the insurance company decides to use the screening technique, in which they set up two different insurance products: one for low-risk and one for high-risk consumers. It decides to offer the full coverage for the high-risk consumers and charge them $45.

The product targeted for the low-risk consumers is a partial coverage (it only covers half the value of the bicycle). The premium for this product is set at $15.

Is this a good strategy? Will the high-risk consumers purchase the $15 dollar insurance or maybe they will be drawn more to the full coverage product?