A factory (F) produces a product that is sold at the price of 10$ per ton. The total cost of

production is:

(y) = 0.52

where y is the number of tonnes of production. For each tonne of production, the factory

produces 1kg of pollutants. The pollutants are either dispersed into the atmosphere at a cost

of 0$ or captured and stored at a cost of $2 for each kg of pollutant. Dispersion of e

pollutants into the atmosphere causes a nearby textile firm to wash its textiles twice at an

additional cost of:

= 0.52

which does not depend on the amount of output, m, produced by the textile firm. The unit

price of the output of the textile firm is 5$, and the total cost of production is:

= 0.52.

Note [1tonne = 1000kg].

a. Determine the values of y, m, and e in a competitive equilibrium (i.e., when the

factory acts independently from the textile firm).

b. In the competitive equilibrium, what is the cost of the externality imposed on the

textile firm by the factory?

c. Why is the competitive equilibrium inefficient from a social perspective?

d. Now, assume that the externality is internalized such that the amount of the pollutant

that is dispersed into the atmosphere is = where s is the amount of the

pollutant that is captured and stored by the factory. Determine the values of y, m

and e, the expenditure on capturing and storing s pollutants, and the additional cost for

the textile firm caused by pollution