a. The marginal private benefit (MPB) for commodity X is given by MPB = 20 – X, where X is the number of units consumed. The marginal private cost (MPC) of producing X is 2X (MPC = 2X). For each unit of X produced, the marginal external cost (MEC) of producing X is X imposed on bystanders (MEC = X). In the absence of any government intervention how much is X produced? What is the efficient level of production of X? What is the gain to society involved in moving from the inefficient to the efficient level of production? For a large numbers case, suggest a Pigouvian tax that would lead to the efficient level. How much revenue would the tax raise? Would a welfare loss or welfare gain result from imposing the Pigouvian tax? Calculate it and show your findings diagrammatically on a per unit diagram as well as a couple of total diagrams one stacked upon another. Give an economic intuition of your findings. b. Imagine instead that there were only two neighbors involved in the above case, a perpetrator and a victim. How would an efficient solution be achieved? Hint: Use the strips of areas arrived at above.