Suppose we have a perfectly competitive coal market and suppose that demand and supply in this market are given by the following functions: Qa=18. 8-1/P 1 Q = 6+ = P a. Determine the equilibrium price per ton of coal in this market (P) and the quantity sold at this price (Q.). b. Calculate the consumer surplus, producer surplus, and social welfare for this market (NOTE: don't forget to calculate social welfare after deriving consumer and producer surplus). c. A unit tax of $6/ton is imposed on the producers of coal. Determine the new equilibrium quantity (Q), the effective price paid by the consumers (Pa), and the effective price received by the producers in this market (P). d. Calculate the share of this tax that is paid by the consumers and the share paid by the producers (in dollars per ton). e. Calculate the consumer surplus, producer surplus, tax revenue, and social welfare under the tax (NOTE: don't forget to calculate social welfare after deriving consumer and producer surplus and tax revenue). f. Calculate the deadweight loss resulting from this tax. g. Now suppose that, instead of a $6/ton tax on coal producers, the government imposes a $6/ton tax on coal consumers. What is the deadweight loss resulting from this tax?