Q1: Externalities (20 points) Suppose a monopoly produces products that exhibit negative externalities. The marginal private benefit associated with a monopoly's consumption is MPB = 360-4Q and the marginal revenue associated with its production is MR = 360-8Q The marginal private cost associated with its production is MPC = 2Q The marginal external cost associated with its production is MEC = 60. Please draw all the above in one graph and answer the following questions: 1). Find the social optimum (Q* and P*) (5 points) 2). Without any government intervention, the monopoly will product at which point in your graph? Compute the associated price and quantities (Q1 and P1) (5 points) 3). Should the government intervene to correct the negative externalities? Why or why not? Explain. Should the government impose a tax T per unit or cap the price to regulate? Compute the unit tax T or the price to cap to achieve the social optimum. 4). Compute the area of net gains if there is any