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So while I am sure the expense per person is more. Expense for rich murders vs poor murders is probably the opposite simply because of the difference in quantity.
I think the point is that "rich vs poor" should not be a distinction that matters when considering what resources to expend on the investigation.
If you start from that premise, there's really no reason to compare what is spent collectively on the murder of wealthy people to what is spent collectively on the murder of poor people.
The comparison itself assumes as given that there is some reason to divide the victims in that way.
The reality is that it isn't rich vs poor. It's media attention. Most of the time a rich murder gets more media attention which causes higher ups to commit more resources. But if the murder of a poor person got the same media attention, it would get more resources too. The issue is they don't have the funding to commit the reasources to investigate all murders at what you and I would consider a reasonable amount. So they have to hold back until it is a high profile case.
So while the overall effect is the same. The root cause is different. It's really that the people accept it and don't vote for decision makers who will fix the funding issue. Of course it would take more than funding to convert the police force into something that could perform at a level where they were thoroughly investigating all crimes. But noone has the stomach for the bill, so it doesn't matter.
Jesus Christ. Did you literally just sit there and value life quantitatively and actually hit send? Maybe you should get in line.
If you think we collectively don't put a price on life consider speed limits. Nearly no one dies in accidents where cars are going less than 30mph. Yet there is no law limiting the building of cars that can go faster than 30. The reason... commerce. The current speed limits on the roads are based on the point where deaths cross over a line of acceptable vs the impact of commerce.