There are three firms in an industry. Firm 1's emissions equal e1, firm 2's missions equal e2, firm 3 's emissions equal e3. Firm 1's MAC equals MAC1(e1)=42e1, for e12 Firm 2's MAC equals MAC2(e2)=5e2, for e25. Firm 3's MAC equals MAC3(e3)=7, for e26. Marginal damages from pollution equal MD(E)=2E, where E=e1+e2+e3. 1. (9 pts) Derive and plot the aggregate marginal abatement cost curve for the industry. (Also plot the MAC for each individual firm.) Explain briefly how you derived the AMAC. 2. (4 pts) Plot the marginal damage function and aggregate marginal abatement cost curve (either on the same picture as before, or in a different picture). What is the socially efficient emissions level (i) for the industry (ii) for each firm? Illustrate this on the diagram. 3. (4 pts) Suppose we were to impose a uniform emissions standard. We set a maximum emissions level of e for each firm, which they each cannot exceed. What e should we set to achieve the socially efficient total emissions level? Is the resulting outcome socially efficient? Explain the reasoning behind your answer. 4. (4 pts) Suppose we were to impose a tax on emissions, t per unit emitted. What tax rate should we charge to achieve the socially efficient emissions level