Consider driving as a market activity. The Private Marginal Cost of adding 1 driver to the roads is: PMC 12+ T = 12 + Q This is a model where travel time is given by T and this is equal to Q: is the total number of drivers on the road. To derive the external cost caused by the Qth driver, use the formula EC(Q) = AT (Q - 1) This is the increase in travel time, multiplied by the number of drivers already on the road. (a) Find the equation for the Social Marginal Cost (SMC) as a function of Q The marginal benefit of adding 1 more driver is given by PMB = SMB = 36 3Q. (b) What is the free-market equilibrium number of drivers Q*? (c) What is the socially optimal number of drivers QB? (d) What road usage charge (tax) would lead to QB drivers on the road?