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(2) Extemalities (10 pts) Like under Question (I), assume the private demand curve (private marginal utility) for automobile trips is given by P=ZUfU-3Q. The private supply curve (private marginal cost curve) 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 ($lunit) at the privately optimal quantity? What is the tax ($lunit) at the socially optimal quantity? Max has a lot of data from stochastic process: (17 = 0.983}t_1 + (it 0.1.63-1 where 5t N N (0, 0'2) are Gaussian white noise. He tests for a unit root and mistakenly decides that the stochastic process is integrated of order 1. He then differences the data to obtain yt = A3: . A} Write out the ARMA model for 3,1,; . [2 points] B) If you were to t an ARMA model to 3;; ,what would the order of the AR and MA components be? [2 points] C) Is it; causal? [1 point] D) Is the ARMA model for y: stationary? [1 point] E} Is the ARMA model for y: invertible? [2 points] F] Knowing the ARMA model for yt = Amt , would you expect the ACF for y; , to cut off abruptly after 2 lags? Explain why. [1 point] G} Knowing the ARMA model for yt = Amt , would you expect the PACF for gt , to cut off abruptly after 1 lag? Explain why. [1 point] 1. Answer all questions: (a) ASHEEKA LTD. has annual turnover of