Market supply in a competitive industry is p = Q. Demand is p = 100 - Q. Production creates pollution with a social cost of $1 per unit of output. In response to environmentalists, the government creates a tax of $2 per unit. Is overall welfare improved or reduced by the tax?

a) Find the total welfare when the government does not intervene. 

b) What is the socially optimal output level? And the total welfare at this level of output?

c) When the government imposes a tax of $2 per unit, calculate the DWL created by the excessive tax.