Calculate the competitive price and quantity when there is

Question

The market for electricity in a particular region has the following supply and demand curves: QD=200,000-4,000P, QS=50,000+2,000P.

Electricity generation results in carbon emissions that have a marginal external cost (MEC) given by MEC=0.00005Q.

1. Calculate the competitive price and quantity when there is no regulation.
2. What is the socially efficient price and quantity of electricity?
3. Display graphically the costs and benefits to society of allowing the market to operate in an unregulated manner.
4. On the same graph, show the Pigouvian tax that would lead to the socially efficient quantity of electricity.