it is economics

(2) Externalities {10 pts) Like under Question (1), assume the private demand curve (private marginal utility) for WWW-3W W P stands for the price of gasoline and Q for vehicles miles driven. a) Calculate the private equilibrium b) Now assume the external cost instead of being constantly 50 per unit, it always equals 20% of the private MC. What is the socially optimal quantity? c) What is the DWL of the private solution? d) Assume the city were to impose a Pigou Tax on the supply side. What is the tax (ES/unit) at the privately optimal quantity? What is the tax ($lunit) at the socially optimal quantity