3) The hog farms in NC that produce pork products generate hog waste as a byproduct, storing tons of waste in open ponds until bacteria can break it down for safe use as fertilizer. Those who live near hog farms complain about the odor, health problems (increased respiratory problems and bacterial infections), and contamination of drinking water after flooding occurs. Suppose the market (inverse) demand and supply of pork are given by these equations: (Demand) P = 14.3 - 0.05Q and (Supply) P = -2.2 + 0.025Q The marginal external cost of the hog production is MEC(Q) = 0.008Q, where Q is quantity of pork (millions of kilograms) and P is the price of pork in dollars per kilogram. a. Solve for the competitive market price and quantity of pork produced, and show it on a diagram. [10] b. Derive the marginal social cost equation for pork, and use it to solve for the socially optimal price and quantity of pork. Explain why it differs from the competitive equilibrium found in part a. Show this on the diagram, too. c. If no intervention occurs, what will be the social loss from the hog waste pollution? Calculate the social loss and show it on the diagram. [8] d. Discuss at least two kinds of government interventions that could lead to the socially optimal solution being achieved. Be sure to explain each policy and how it would work to address the