Let E represent global emissions of CO2 from fossil fuel burning and cement. Suppose that the marginal private surplus from emissions (the private surplus from each additional small unit of emissions) is described by the following function where E is the argument. MS Private (E) = 864 24*E The marginal external cost (the cost of an additional small unit of emissions) to the third parties is described by the following function. MCExternal (E) = 216 Units for MS Gt/y where Gt represents metric gigatonnes (billions of tonnes) and 1 tonne = 1000 kg. Private and MC External are $/t CO2 (where t represents a metric tonne) and units for emissions are a) Plot and label the marginal private surplus and the marginal external cost on a graph with emissions in Gt/y on the x-axis and $/t CO2 on the y-axis. b) If private parties are selfish or ignorant of global warming damages such that they are unconcerned about damages to third parties, they will add emissions as long as the marginal private surplus is positive. How many emissions will they add? Hint: Set MPS = 0 and solve for E. Call this level of emissions "EBAU where BAU represents "business as usual" and label on your graph on the x-axis. c) At the BAU level of emissions, calculate: i) total external costs (area under the marginal external cost curve from E = 0 to EBAU). ii) total private surplus (area under the marginal private surplus curve from E = 0 to EBAU). iii) total social surplus (= total private surplus total external costs). Label these on your graph using letters like A, B, C, D to represent areas and colour them in. d) Find the socially efficient level of emissions by setting MCExternal = MSPrivate and solving for E and call this ESE e) If the world abates (reduces emissions) from EBAU to EE, find the following and label on your graph. i) total external costs saved ii) total private surplus forgone iii) total social surplus gained. f) Find the marginal tax on emissions that would induce the world to abate from EBAU to ESE. Find the total tax collected and label on your graph. * Note: the MSnvate forgone also called the marginal abatement costs (MAC) as it is the amount the private parties forgo by abating each unit of emissions while the marginal external cost is also called the marginal damages.