please show all work!!

2. Tax and Welfare problem: Refer to the figure below for the following questions: (12 pts.) a. Suppose the government initially imposes no per-unit tax on this good. i. What is the equilibrium price and output without a tax? Identify this on your graph as P* and 0*. b. Calculate and show your work for the following: i. consumer surplus ii. producer surplus iii. total surplus when there is no tax. c. Suppose the government then imposes a $3 per-unit tax on this good. i. What is the new output level with the tax? Identify this on your graph as QT ii. Find the price consumers pay and label it Pc and the price sellers receive and label it PS. iii. After the tax is imposed, calculate and show your work for the following: a. tax revenue b. consumer surplus c. producer surplus iv. Calculate the dead weight loss. Show your work. d. Suppose the voters decide to increase funding for schools. Should they raise the tax to $4.50 or raise it to $6.00 to increase revenue as much as possible? Show your work to support your answer.