(solution) The Fireyear and Goodstone Rubber companies are firms located in

(solution) The Fireyear and Goodstone Rubber companies are firms located in

The Fireyear and Goodstone Rubber companies are firms located in the rubber capital of the world. These factories produce finished rubber and sell that rubber into a highly competitive world market at the fixed price of £ 60 per ton. The process of producing a ton of rubber output results in a ton of air pollution that affects the rubber capital of the world.  This 1:1 relationship between rubber output and pollution is fixed and immutable at both factories. Consider the following information regarding the costs (in £) of producing rubber at the two factories (QF and QG):

Fireyear: Costs: 300 + 2 QF^2 Marginal costs: 4QF

Goodstone: Costs: 500 + QG^2 Marginal costs: 2QG

Total pollution emissions generated are EF + EG = QF + QG . Marginal damage from pollution is equal to £12 per ton of pollution.

Question:

a. In the absence of regulation, how much rubber would be produced by each firm? what is the profit for each firm?

b.The local government decide to impose a Pigovian tax on pollution in the community. What is the proper amount of such a tax per unit of emissions? what are the postregulation levels of rubber output and profits for each firm?

c.Suppose instead of the emission tax, the government observes the outcome in part(a) and decides to offer a subsidy to each firm

for each unit of pollution abated. What is the efficient per unit amount of such a subsidy? Again calculate the the level of output and profit for each firm.

d.Compare the output and profit for the two firms in part (a) through (c). Comment on the differences, if any, and the possibility of one or both of the firms dropping out of the market.