The cost of pollution control

Some people are good drives and others are bad drives. The former have a 10% chance of crashing their cars and the later have a 30% chance. All have a total wealth of 400 but this will fall to 100 if they crash their cars. In other words, each will lose 300 of wealth if crash. You're an insurance company who wishes to offer a pair of policies to all drivers. Each policy is designed to break even (zero profit) given the people that choose to buy that policy. The first policy has a premium of 90 and covers all losses (i.e. will pay 300 in the event of a crash). The second policy has a premium of 5 and will pay 50 in the event of a crash. Each person has a utility function of Utility = (Wealth)0.5

a. Who will buy which policy?

b. Will the insurance company make a profit, break even or lose money?

The cost of pollution (in billions of dollars) originating in the paper industry is Cp= 2P + P², where P is the quantity of pollutants emitted (in thousands of tons). The cost of pollution control (in billions of dollars) for this industry is Cc= 5-3P.

a. What is the optimal level of pollution?

b. At this level of pollution, what is the marginal cost of pollution?

c. At this level of pollution, what is the marginal cost of pollution control?