Suppose that the demand curve for coal is described byP= $500Qwhere Q is tons of coal. The industry faces increasing marginal cost and has a supply curve with the equationM C= 250 + 0.5Q. Coal mining causes harmful health effects. The external marginal cost of these externalities isEMC= 0.5Q.

(a) What is the socially optimal amount of coal that should be produced? At what price?

(b) At the private market equilibrium in part (b), shade the dead weight loss due to the externality on you graph.

(f) Now suppose a tax is imposed on the producers of coal equal to the external marginal costTax= 0.5Q. Does this tax cause deadweight loss or does it increase economic surplus relative to part (b)?