QUESTION 3 [30 marks] A factory is producing steel, s. Its production creates a negative externality by polluting water. Denote by x the amount of water pollution. The pollution harms a nearby fish farm, producing fish, f. Both the steel factory and the fish farm are price- takers. The price of a tonne of steel is ps = 40, and the market price of a tonne of fish is pp = 30. The steel factory's cost function for producing s tonnes of steel jointly with x units of water pollution is given by cs(s,x) = s+(x-15). The fish farm's cost of producing f tonnes of fish, given that the steel factory emits x units of water pollution is given by c, (f,x) = f+xf. market a) (10 marks) How much output will the steel factory produce if pollution does not impose any external costs on the factory? What will its profits be? How much will the fish farm produce and what are its profits? b) (6 marks) How would the situation change if the two firms merged? c) (6 marks) Calculate the level of profit and for the level of pollution emitted overall if the firms merged. Would the result be efficient? d) (8 marks) Explain in words how free-riding can occur in public goods provision. Include a diagram relevant for the case of continuous public goods provision.