Final answer:
Doubling the police force size is likely to deter crime due to increased apprehension likelihood. Higher incomes from legitimate jobs for the richest can increase opportunity cost for crime; however, if criminal income also increases, crime rates may not decrease.
Step-by-step explanation:
When a city's mayor doubles the size of the police department, this can have a deterrent effect on crime by increasing the probability that criminals will be caught. This is an application of deterrence theory, where raising the costs or the probability of getting caught is meant to prevent crime.
If the richest portion of the population begins to make more money from their legitimate jobs due to technological changes, the legitimate income curve would shift upwards for this group. It is typically assumed that higher legitimate earnings would lower the incentive to engage in crime due to increasing opportunity cost; legitimate work becomes relatively more attractive compared to criminal activities.
However, if income from criminal activities also increases disproportionately as a result of changes in income distribution, this could counteract the expected reduction in crime rates by making criminal activities more lucrative, thus potentially keeping crime rates the same or even increasing them despite improvements in legitimate income.