There are extremely high incidences of speeding in Bathlaham. The fine for speeding is currently $200, and it is estimated that the current probability of a speeding driver being caught and convicted is 5%. Studies show that most people stop speeding if the expected fine is at least $150.

(a) Provide an explanation for why speeding is so prevalent in Bathlaham.

(b) The local government of Bathlahem decides to do something to curtail speeding. Suppose the government wants to increase the probability of catching speeding. How high must the probability of being caught and convicted be to discourage speeding at the current size of fine?

(c) Suppose the government is to raise the fine while keeping the probability unchanged at 5%. How large must the fine be to discourage speeding?

(d) Suppose it costs police resources of $10, 000 for every 1% increase in the probabil- ity of catching and convicting speeding, whereas increasing the fine by every $50 costs administrative expenses of $12,000. At the same time, the court prevents local governments from charging a fine more than $500 for speeding. If the local government of Bathlaham wants to curtail speeding at the lowest cost possible and allowable, what will be the mix of fine and probability that it will choose? Explain your answer.