Suppose the consumer demand for a product is given by p = 12 - x, where p is the price of the good and x is the quantity. The supply curve for this good is given by p = 2 + x. 2.1 Find the market equilibrium price and quantity, consumer surplus (CS) and producer surplus (PS). 2.2 Suppose the supply curve, which reflects private costs, does not reflect the marginal social cost. Specifically, suppose that production of this product creates an additional marginal cost of $2 per unit of output. What is the marginal social cost (MSC) function? If there is no intervention in the private market, in the presence of the marginal social cost, what is the total externality, and total surplus produced in this market? What is the deadweight loss? 2.3 Given the marginal social cost above, what is the socially optimal output and price for this good? What are the consumer surplus, producer surplus, total externality, and total surplus at this socially optimal output? 2.4 If a government want to use a Pigouvian tax to correct for the social cost problem, how much a tax per unit should be imposed? If another government wants to solve the same problem by setting a limit to the production of this good, what should be the quantity quota?