2. Externalities US drivers consume billions of gallons of gas every week, and with every gallon consumed harmful emissions are released into the atmosphere. The aggregate demand function for gasoline is given by P = 12 2QP, where Q is the quantity of gallons of gas per week in billions and P reflects the price per gallon in dollars. The aggregate supply function is given by P = 1+ Q. IMF economists have estimated a substantial external marginal damage of gas consumption, which we'll round to $1 per gallon. (a) Solve for the equilibrium private market price and quantity that will be generated without any government intervention. (b) What is the socially optimal demand function taking into account externalities? () Solve for the socially optimal equilibrium price and quantity. (d) Graph the market for US gasoline with a supply/demand graph. Be sure to label 8 things: PMC, SMC, PMB, SMB curves, the Marginal Damage, the DWL, the private market equilibrium and the socially optimal equilibrium. (Also pay attention to the slopes they certainly don't need to be exact, but try to consider who is the more elastic/inelastic side of the market.) (e) Calculate the dead-weight loss from the externality. (f) If the government uses a gas tax to address this externality, what is the optimal tax to offset the externality? ot (g) Calculate the revenue that would be raised by this tax. (h) Will there be deadweight loss associated with this tax? If yes, how much? If no, why not