Question 2. (16 marks) Consider a competitive market for some commodity x in which some firms are polluters. Firm A: Clx,) = (x,2) and the external cost to society is E(x,) = 100x,. Firm B: C(xg) = 240xg and the external cost to society is E(xg) = 0. Assume initially that a competitive market operates that ignores external costs. i) (2 marks) Find the supply function for Firm A. i} (3 marks) Determine for what prices Firm B will provide the good. Does it matter to firm B what quantity is supplied? Explain. Pagelof2 Assume the market demand for the commaodity is given by X (p) = = iii) (3 marks) Find the competitive market equilibrium price and quantity using your answers in i) and ii) when the firm supplies reflect their ability to compete at a given price. iv) (3 marks) Suppose a planner uses the representative consumer's utility function, to find the socially optimal allocation of resources to the two firms. Choose (x4, xg, ) to solve max U(x, y) = (40000)In(x) + Subject to X=Xx,+Xxg, X, =z0andxg = 0 and C(x,) + C(xg) + E(x,) + v = 100,000 When the planner decides, what will be the aggregate production level, and how much will each firm supply? ) (5 marks) Use a pair of sketches of the market and planner allocations (using the market demand/marginal benefit curve and cost curves of the firms) to compare the net benefit to society from the outcomes in iii) and iv)