Suppose there is a good for which the private marginal cost curve (the supply curve) is given by the equation P(Q) = Q + 4

Suppose there is a good for which the private marginal cost curve (the supply curve) is given by the equation P(Q) = Q + 4. The production of this good also causes a negative externalities on third parties. The dollar value of these externalities is $4 per unit at all production levels. The (inverse) demand for this good is given by the equation P(Q) = 20 - Q.

(a) Write down the equation that gives the social marginal cost curve. In a graph, draw supply, demand and social marginal cost curves.

(b) Calculate equilibrium price P and quantity Q of this market. Calculate the total externality and the dead-weight loss caused by the externality.

(c) To get rid of the dead-weight loss resulting from the negative externalities, the government imposes a tax. Now a $4 tax is imposed in every unit sold. Find the new equilibrium price and quantity. Calculate the changes in consumer surplus, producer surplus, government surplus and third party surplus (externality).

(d) Calculate net social benefit of this policy (that is, the change in total surplus).