Consumers face a choice between two types of home insurance: high-quality insurers cover all damages, low-quality insurers have a number of exclusions which are hidden in the terms and conditions and difficult for consumers to identify. The value of high-quality insurance to consumers is 200 while low-quality insurance is valued at 50. The cost to insurers from offering high-quality insurance is 100 whereas low-quality insurance costs 10.

1. (a) [25%] Suppose consumers are able to differentiate between the two types of insurance. Find prices for high and low-quality insurance that may arise in a market equilibrium.

1. (b) [25%] Consider the case in which quality is unobservable, and the share of high-quality insurers in the market is . What is the smallest value of such that there is a market equilibrium in which high-quality insurance is purchased by consumers?

1. (c) [25%] Show that when insurance companies choose the quality of their policies, and quality is unobservable to consumers, then in equilibrium only low-quality insurance is sold. What is the range of prices in this case?

1. (d) [25%] It turns out that a share (0,1) of consumers is, in fact, sophisticated and actually reads the terms and conditions that reveal whether insurance is of high or low quality (that is, they know how much insurance is worth to them). Suppose the profit function for insurance companies is =100 for high-quality insurance, and =(1)+5010 for low quality insurance, where is the market price (for unsophisticated buyers). Show that when >3/5, there exists a market equilibrium in which only high quality insurance is sold, and the price is =200.