Crime and Punishment – A Thought Experiment

Imagine two neighborhoods in the same city subject to the same laws. Assume the crime rate is the same. Then you would expect arrest and prosecution rates to be the same.

Now, assume two other neighborhoods, also in the same city and subject to the same laws. Call them A and B. Assume the arrest and prosecution rate is X times higher in A than in B. Assume that has been the case for a long time.

Given this scenario, under what conditions do you expect crime in Neighborhood A to exceed crime in Neighborhood B? Under what conditions would you expect the reverse to be true?

Note. A good answer is generalizable.