A. Find the amount of steel and fish in the

a. Find the amount of steel and fish in the equilibrium. 

b.  What is the optimum level of steel, fish, and pollution? 

C. What is the Pigovian tax (for each level of pollution) necessary to achieve Pareto Optimal allocation

There are two firms in a village: steel firm (S) and fishery (F). Firm S produces some amount of steel, s, and also produces a certain amount of pollution, x, which it dumps into a river. Firm F, a fishery, is located downstream and is adversely affected by S’s pollution. Suppose that firm S’s cost function is given by Cs(s,x) = 52 – 4x + x2, where s is the amount of steel produced and x is the amount of pollution produced. Firm F’s cost function is given by Cf(f,x) = 2 + 2x, where f indicates the production of fish. Price of steel, Ps is 4 dollars and price of fish, pf is 2 dollars.