1. Uncertainty Assume the business-as-usual level of pollution from a group of firms is E = 15 (and this is known with certainty). In addition, assume it is known that the marginal social benefit of reducing X units of pollution from the business-as-usual level is given by MSB (X() = 30 - 2X In contrast to the known marginal benefits of abatement, the market marginal abatement costs are unknown. Assume that 50% of the time, the true marginal abatement costs will be MAC low (X() = X Assume that the other 50% of the time, the true marginal abatement costs will be MAC high (X() = 6+X a) If it turns out the low marginal abatement cost (MAC_low) is the true MAC cost, what per unit pollution tax (t_low) would result into the optimal level of abatement? b) If it turns out that the high marginal abatement cost is the true MAC cost, what per unit pollution tax (thigh) would result in the optimal level of abatement? ") Assuming that the true marginal abatement cost is MAC low, what is the DWL of using thigh (from Part B) instead of using the optimal pollution tax (t_low) from Part A? Hint: Find the abatement level (x) that T_high would generate under MAC low. d) Assume for a second that the true marginal abatement cost is MAC low. For any arbitrary pollution tax t, where t low