Pollution that increases firm costs-Policy Solutions: This exercise continues to build on exercises 21.9 and 21.10. Assume the same basic setup of firms located around a lake producing pollution that causes the fixed costs of all firms to increase.
A. Continue to assume that each output unit that is produced results in an increase of fixed costs of δ for all firms in the industry.
(a) Begin by illustrating the market demand and long run industry supply curves, labeling the market equilibrium as A.
(b) Next, without drawing any additional curves, indicate the point B in your graph where the market would be producing if firms were taking the full cost of the pollution they emit into account.
(c) Illustrate the Pigouvian tax that would be necessary to get the market to move to equilibrium B.
(d) Suppose N∗ is the number of firms in the industry in the market outcome, Nopt is the optimal number of firms and δ continues to be as defined throughout. What does the government have to know in order to implement this Pigouvian tax? Is what the government needs to know easily observable prior to the tax?
(e) Where in your graph does consumer surplus before and after the tax lie?
(f) Keeping in mind what you concluded in exercise 21.9, has (long run) producer surplus- or long run industry profit-changed as a result of the tax?
(g) True or False: The pollution cost under the Pigouvian tax is, in this example, equal to the tax revenue that is raised under the tax.
(h) Is there additional pollution damage under the market outcome (in the absence of the tax)?
(i) Is there a deadweight loss from not using the tax?
(j) Suppose the government instead wanted to impose a cap-and-trade system on this lake - with pollution permits that allow a producer to produce the amount of pollution necessary to produce one unit of output. What is the "cap" on pollution permits the government would want to impose to achieve the efficient outcome? What would be the rental rate of such a permit when it is traded?
(k) What would the government have to know to set the optimal cap on the number of pollution permits?
B. Continue with the functional forms for costs and demand as given in exercises 21.9 and 21.10. Suppose, as you did in parts of the previous exercises, that β= 1, δ = 0.1 and A = 10,580 throughout this exercise.
(a) If you have not already done so in part (f ) of exercise 21.9, determine the Pigouvian tax that would cause producers to behave the way the social planner would wish for them to behave. What price will consumers end up paying and what price will firms end up keeping under this tax?
(b) Calculate (for our numerical example) consumer surplus with and without the Pigouvian tax. (Skip this if you are not comfortable with integral calculus.) Why is (long run) producer surplus-or long run profit in the industry-unchanged by the tax?
(c) Determine the total cost of pollution before and after the tax is imposed.
(d) Determine tax revenue from the Pigouvian tax.
(e) What is the total surplus before and after the tax-and how much deadweight loss does this imply in the absence of the tax?
(f) Suppose next that the government instead creates a tradable pollution permits-or voucher - system in which one voucher allows a firm to produce the amount of pollution that gets emitted from the production of 1 unit of output. Derive the demand curve for such vouchers.
(g)What is the optimal level of vouchers for the government to sell-and what will be the rental rate of the vouchers if the government does this?