Suppose that the market for R&D is characterized by: Demand: P = 9 Q Supply: P = 1/2Q Furthermore suppose that R&D creates hazardous waste as a byproduct of the research process. This hazardous waste has marginal damages of MD = 2. In addition, R&D creates external marginal benefits of EMB = 1. 1. What is the efficient level of R&D? Illustrate the efficient equilibrium on a graph. 2. Suppose that the regulator enacts a pollution tax equal to marginal damage. Does this lead to the efficient outcome? If not, what is the DWL associated with the tax? Illustrate the effects of a tax on a graph. 3. Now suppose that the regulator enacts a research subsidy equal to external marginal benefits. Does this lead to the efficient outcome? If not, what is the DWL associated with the subsidy? Illustrate the effects of the subsidy. 4. Finally, suppose that the regulator enacts both the pollution tax, and the research subsidy. Does this lead to the efficient outcome? Why or why not