A natural gas company in Hartford owns many pipelines running under heavily developed areas. The company can invest $x in maintenance of the pipes which means that the gas company will lose less gas leaking from the pipes and there will be less damage to the property above the pipes. Assume that the value of lost gas is and the value of damage to the property above the pipes is a. What is the socially optimal level of maintenance x? What is the value of gas lost? What is the value of land damaged? b. What is the level of x chosen by the gas company if it is not held responsible for property damage? What is the value of lost gas? What is the value of land damage? What is the deadweight loss? C. Suppose the gas company owns the land above the pipes. What level of x will it choose now? Is this optimal? What is the deadweight loss? d. Suppose that Roger owns the property above the pipes and can costlessly sue the natural gas company for damage to his property. What level of x will the natural gas company choose? How much will be paid from the gas company to Roger? e. No suppose that the court system is imperfect and for every $1 in actual damage only $.50 is recovered by Roger. That is, if the true damage is D the Roger receives a payment of what level of x will be chosen by the gas company? Is this efficient? What is the deadweight loss