2. (30 points)Private and Social Costs.

A natural gas company in San Francisco owns many pipelines running underneath what are now populated areas. The company can invest atotalof$uin pipe maintenance, which affects two things:

First, more maintenance means that the gas company will lose less gas in the pipes. Assume that thetotalvalue of lost gas is$1/u. That is, the more maintenance, the less gas loss to the company.

Second, more maintenance means less damage to the land above the pipes. Assume that thetotal value of land damage is$3/u. Again, the more maintenance, the less land damage to the residents.

Remember:

Benefits can be negative.

QUESTION: We knew from above the total costs and benefits of maintenance. Derive the marginal private cost (MPC), marginal social cost (MSC), marginal private benefit (MPB), and marginal social benefit (MSB) of maintenance, as functions of u.