Question

Suppose that a drug dealer can earn $1,000 from selling drugs illegally and that the probability of apprehension is .25.

a. Show that a penalty requiring drug dealers to surrender their profits in the event of conviction will fail to deter them.

b. What is the lowest fine that will just deter the drug dealer?

Answer 1

a) By selling drugs and having to return the profits in case of conviction, the drug dealer makes 1000 for sure and has to pay 1000 with probability 0.25. Therefore, his expected gain is 1000-0.25*1000=750. Since the expected gain is positive, the penalty is not good enough to deter him from selling drugs.

b) Suppose he is asked to pay a fine of x if he is caught. Then, his expected gain is 1000-0.25x. To deter him, we need x to be large enough so that the expected gain is <0. Therefore, we get 1000-0.25x <0 or x>4000. Therefore, a fine of 4000 on getting caught is the lowest fine that will just deter the drug dealer.