Congestion pricing on a highway

Suppose that a given highway is designed to carry 10,000 cars per hour. When fewer cars are using it, everyone can travel at the speed limit and the road is completely uncongested. Above 10,000 cars per hour, however, the road becomes congested and every car’s travel time increases. Suppose that the amount of extra time, T, taken by every vehicle is related to the total number of cars on the road, Q, as follows: T = (Q-10,000)/40,000. (In other words, when there are 12,000 cars on the road, each one is taking 0.05 hours extra, or an additional 3 minutes, to get to its destination.) In addition, suppose that car drivers value their time at $20 per hour and that the total demand for rush hour trips on the highway is given by P = 10 – Q/2000.

1. In the absence of any kind of government intervention, how many cars will use the road at rush hour? Is this efficient? Explain. Use an appropriate graph if it would help. Please note that if the time cost of using the highway is T, the private marginal cost faced by a driver will be MC = $20*T.
2. The marginal social cost of adding a vehicle to the highway when it is congested can be shown to be given by MSC = (2Q-10,000)/2000. What is the efficient number of vehicles on the highway during rush hour? If you could impose a fee for the use of the highway, what would it be?
   
3. What is the total value of time wasted at the market equilibrium in (1)?