LoJack and Insurance Companies. Consider the application External Benefits from LoJack. Suppose all vehicles in a state carry theft insurance. The benefit from reduced vehicle theft goes to insurance companies because they replace fewer stolen vehicles. Insurance companies do not offer any discounts for customers who install LoJack. The cost of LoJack is $100 per vehicle per year. To simplify matters, assume that the private benefit of LoJack is zero, so the social benefit equals the external benefit. (Related to Application 3 on page 650.)
a. Suppose a single insurance company provides automobile insurance to all vehicles in the state. Will the insurance company provide free LoJacks to at least some of its customers? Explain.
b. Suppose that there are 20 companies in the state, each with a market share of 5 percent. Will the insurance company provide free LoJacks?
c. What is the threshold number of insurance companies the number at which each insurance company will be indifferent about providing free LoJack systems?