6. There are 4 firms in the industry that have the total costs of eliminating pollution given by P/4, P2/3, P/2 and P2 respectively. (a) Suppose that we want to reduce aggregate pollution in a way that minimizes the overall cost. Derive the marginal cost of doing so as a function of the overall reduction in pollution P* (b) Suppose we want to reduce the overall pollution by 100 units. How much should each of the firms reduce pollution by in order to minimize the overall cost of doing so? (c) Suppose that we require each firm to reduce pollution by 30 units. Firms are allowed to trade obligations to lower their pollution reduction requirements. What will be the competitive market price of a unit of pollution reduction and how many units will be traded? (d) Suppose we do not allow firms to trade in part (c). What would be the deadweight loss compared to the solution in part (c)