Question 2 A potential criminal enjoys a gain of g > 0 from committing an illegal act. If the potential criminal does not commit the act, he gets a gain equal to g = 0. The expected punishment upon conviction is p (e.g. number of years in prison), but there is the possibility of legal error. In particular, if the criminal commits the act, there is a probability r that he will not be punished, and if the criminal did not commit the act, there is a probability q that he will be punished regardless.
Question 2
A potential criminal enjoys a gain of g > 0 from committing an illegal act. If the potential criminal does not commit the act, he gets a gain equal to g = 0. The expected punishment upon conviction is p (e.g. number of years in prison), but there is the possibility of legal error. In particular, if the criminal commits the act, there is a probability r that he will not be punished, and if the criminal did not commit the act, there is a probability q that he will be punished regardless.
a. Derive the net gain (i.e. gain minus expected punishment) for the criminal from not committing the illegal act.
b. Use your answer in a. to derive the condition for the criminal to commit the illegal act. Show and explain every step of your calculations.
c. Lawmakers decided to further increase the standard of proof for a criminal conviction. How will this change a ect the criminal’s decision to commit the illegal act in your answer in b.?
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