High levels of automobile traffic in big cities are incredibly costly to society

The benefits of driving changes based on the time of day. During Peak (P) times of day
(morning or afternoon rush hour) the marginal social benefit is higher than at Off-Peak
times (O).
Let MSB​ P​ =.75-(1/6000)N. Let MSB​ O​ = .5-(1/1000)N. I’ve selected these numbers so that the
results work out reasonably cleanly.
Calculate the socially optimal level of traffic (N*) during P and O times of day. What is the
value of the MSB at the optimal level during these times?
Hopefully you recognized in the last part that during time O the socially optimal level and
the market level will be the same. During time P, what will the market level of traffic be
(N​ M​ )? What is the MSB at this level of traffic during time P?
What is the difference between the market level of traffic (N​ M​ ) and the optimal level (N*)?
What is the deadweight loss per mile from too much traffic?
What should the “congestion price” be per mile during time period P? (The congestion
price is effectively a per unit tax that brings the MPC and MSC into alignment at the
optimal level of traffic.)
Are there any unintended consequences possible from imposing a congestion price
during peak times? (Hint: remember what substitute goods are?) Write a paragraph of at
least 100 words clearly describing your thoughts.