Beijing and Shanghai both implemented ambitious quota schemes over vehicle licence plate, in order to curb congestion and air pollution. However, the rationing schemes in the two cities are quite different: Beijing uses a lottery system to allocate the plates to a random selection of applicants, while Shanghai adopts a hybrid lottery and auction mechanism. Now let's model the two systems using the following simplifying assumptions: Assuming each family needs the maximum 1 licence plate, we can thus approximate the family's preference over licence plate as quasilinear. Both cities face the same aggregate demand for licence plate x = 100, 000 p per year and offer the same quota Q = 10, 000 per year. The only difference is that Beijing rations the quota through lottery while Shanghai rations it through auction (the auction revenue goes to the Shanghai city government). We further assume both systems work smoothly with zero administrative cost.

1)Compute and compare the total social surplus from vehicle licence plate rationing in Beijing and Shanghai. Which city's rationing system is more efficient?

2)In a recent study, researchers observe that the average purchasing price of car in Beijing goes up substantially right after the introduction of the licence plate lottery system. After ruling out supply side factors (i.e., there was no price or quality change on the seller's side), they conclude that there must exist a black market where the license plates are traded illegally. Why?

3)How would the existence of a black market in Beijing change your discussion in part (1)?

4)Household travel survey data show that high-income households on average buy less fuel-efficient vehicles and drive more than low-income households. Therefore, the negative externality associated with vehicles is likely to be increasing in consumers' willingness to pay (WTP) for a licence plate as consumers with high WTP tend to have high income. Assume that the relation between total externality associated with vehicles and WTP for the licence plate is given by e = 0.1 W T P2 . Taking into account this negative externality, how would your discussion in part (1) change (assuming away the black market)?