b) Solve for the socially efficient solution. In other words, assume that a social planner owns both businesses. Similar to part a), find quantities, prices, and the joint profit level. Specify how much each business contributes towards joint profits. [7 points] c) Compare the firm/joint profit levels between parts a) and b). [2 points] d) You work for the environmental agency regulating pollution in the lake. If you want to implement a quota, on which business would you impose the quota, and at what level would you set it? In terms of quantities, prices and profit levels, for both firms, what are the new equilibrium levels? (Hint: you need no further calculations) [3 points] e) Instead, consider now imposing a Pigouvian tax on the steel plant. Solve the new profit maximization problem for the steel plant, and find the equilibrium tax rate T* that achieves the socially efficient outcome. (Hint: different to what we did in class, the tax rate T is imposed on units of S) [6 points]