Q. In 1950s, Mahjong was illegal in Taiwan. Given the enjoyment of playing such a fun game, this is surely inefficient. Assume the social cost of playing Mahjong is zero. (g, p, c, f, t) are defined as in the lecture notes. p = 0.2, c = 1000, t = 2, f = 0. (g=gain from criminal, p=probability of punishment, c=opportunity cost from prison per unit time, f=fine to criminal, t=time in prison)
a) Assume using prisons is costless. Under what condition does the law lead to an inefficient result?
b) Assume that g can take integer value from 1 to 500, each with probability 1/500. Calculate the social welfare loss caused by the law. Remember that the law will be enforced only if a player is found playing as well as actually arrested by the policeman (what actually happened was that people would bribe the police officer as well as would avoid prison in that way).
c) Now Assume the police officer can set a single bribe cost, as well as people who get caught can choose to pay that bribe or not. What is the bribe cost that maximizes the police officer revenue? Compare social welfare under the bribe with social welfare in the case where the police officer always abides by the law.
d) Assume that people can pay a "protection fee" to the police officer in advance (like buying insurance), as well as the police officer commits not to arrest people who paid the protection fee even when they are found playing Mahjong. What will the maximum protection fee be? Show that more people will choose to play Mahjong than in the case of (c).