Question

Optimal tax under monopoly supply. This problem asks you to solve an algebra problem for a case where there is a negative externality and a second market distortion due to market power. There are many reasons why there might be another market failure or inefficiency that interacts with the externality.

Albany-Berkeley Clinker (ABC), LLC is the monopoly provider of ready mix concrete in East Bay. The factory can produce a bag of concrete for a constant marginal cost of $2. Monthly demand for concrete is equal to LaTeX: Q^d = 20,000 - 4,000P .

Suppose that each bag of concrete causes $2 worth of social damages due to air pollution from the ABC plant.

1) Write out an equation for the monopolist's marginal revenue curve (LaTeX: MR M R as a function of Q).

2) Assuming there is no policy, what price does the monopolist charge when maximizing profits?

3) Draw a graph of this market labeling these six things: marginal cost, marginal social cost (=marginal cost plus marginal external damage), demand, marginal revenue, the monopoly price, and a shaded area that represents the lost consumers surplus due to monopoly pricing, a shaded area that represents the damages from the externality.*

4) Calculate total welfare (including consumer surplus, producer surplus, the externality and tax revenue—in this part, there is no tax revenue), assuming no policy.

（please help me to solve these questions by step, especially the graph.)

Answer 1

Setting a tax rate equal t o $ 3 will make ttotal welfare go down. there will be decrease in consumer surplus while an increase in tax revenue will not be suffciient to overcoem decrease in consumer surplus. Kindly look at the figure in attached photo and you will know the externality.