2. Suppose there is a good for which the private marginal cost curve (the supply curve) is given by the equation P = X/2 + 4. The production of this good also causes a negative externality on third parties. The dollar value of these externalities is $2 at all production levels. The demand for this good is given by the equation P=10 - X.

a) Write down the equation that gives the social marginal cost curve.

b) In a graph, draw supply, demand and social marginal cost curves.

c) Calculate the equilibrium of this market. Then, calculate the dead-weight loss that is caused by the externality.

d) To get rid of the dead-weight loss resulting from the negative externality, the government imposes taxes. Now the suppliers of the good are required to pay a $2 tax on each unit they sell. Write down the equation for the supply curve that arises after this policy. Calculate the changes in consumer surplus, producer surplus, government revenue and third party surplus. Also, show these changes on a graph.

e) Finally, calculate social benefit from this public policy. What are the net social benefits from this policy?