Problem 4 [5] : A chemical factory produces a product that is sold at 10/- per ton (1 ton = 1000kg). The cost of production is () = 0.5 where is the number of tons of production. For every ton of production, the factory produces 1 kg of a pollutant that is either dispersed into the atmosphere at no cost to the firm or stored away at a cost of 2/- for each kg of pollutant. Let denote the amount of pollutant that is dispersed in the atmosphere. The pollution causes the nearby textile firm (producing output m) to have to wash its products twice with an additional cost of = 0.5

which does not depend on the amount of output produced. The unit price of the output of the textile firm is 5/- and the cost of production is () = 0.02.

a. Determine the values of , , in the competitive equilibrium.

[b. What is the socially optimal level of ?

c. What is level of if the externality is internalized.