I mentioned (and posted a link to) cities with a population of 50,000 or greater. I didn't compare apples to apples because you're talking about the wrong fruit. But let's compare some apples...
Look at San Francisco they're ranked 18th in the world and 9th in the US which puts them above Houston, Miami , Detroit. San Francisco is less than 8% black, about 50% white and 30% Asian; their murder rate is much less than those three cities I mentioned despite Seattle having a higher total GDP.
Then look at the next city right behind Detroit - Seattle. Seattle is 70% white and their murder rate is even lower than the national average.
So if you look at these wealthy cities and go down the list some have very high murder rates and some have low murder rates and the relationship is not a linear one with murder rates and total GDP. However, one thing that is always true, is if the city is largely black the murder rate is really high regardless of total GDP.
Four is not a large sample size now is it.
List of cities by GDP - Wikipedia, the free encyclopedia
GDP has nothing to do with income as it depends how much of that income goes to labor and capital. any area/city/country that has a high degree of income/wealth inequality has a high crime rate and murder rate, race has nothing to do with it this is seen across the globe. In terms of just the OECD you can compare the violent crime/murder rate and it is directly correlated with income/wealthy inequality as is seen in the 2011 OECD Social Justice report where the US ranks #27 out of #31 member country's with only Greece, Mexico, Turkey and Chile scoring lower.