As part of the California High Speed Rail System, the Caltrain tracks from SJ toSF will be upgraded to support modestly higher speeds. A key question is what speed should they be upgraded to. The current speed (80 mph) is unacceptably slow, but the top speed of the trains (220 mph) may not be appropriate for a dense urban/suburban area. Suppose that train ridership is P= 100S, wherePis total daily ridership (passengers) and S is the speed that the train will run at (mph). Suppose that operating at speed S costs C= 100S+ 5S^2(note that this cost is independent of the number of passengers that ride). Further supposethat each passenger that rides has a willingness to pay equal to the train fareand that each passenger saves other highway commuters $5 in congestion costsand reduces pollution externalities by $1. Finally, suppose that higher speeds create more noise for houses located next to the tracks, and that the total cost of this noise is N= $S^2.

Caltrain is currently in the process of converting from diesel locomotivesto electrification. Electric trains are faster and have no (local) emissions.Assume that the electric trains will reduce pollution externalities by $2 perride (vs $1) and change operating costs toC= 50S+4S^2. What operating speed with Caltrain choose with electric trains (assuming it takes into account all costs and benefits)?

How much should Caltrain be willing to pay (on a daily basis) to convertfrom diesel to electric (assuming it takes into account all costs and benefits)?