First, the good news. In law enforcement now, a degree can only help and the more advanced the more help.
Now the bad news. Never ever go into law enforcement or any public safety work (fire,ems) looking for money. Starting salaries are low, especially compared to MBA's.
Now the longer winded explanation. You do not need college to enter police work in most places. There has been a move for the past 20 years to increase the entry requirements, and some agencies have done so. You need college to join DPS for example, and you need a BA in criminal justice to join TABC if you are not an experienced officer.
With the increase in emphasis on education, a degree can get you more money. Most larger departments pay a monthly bonus for a degree, with the higher degree getting more money. TABC (and all state police jobs in Texas) pay 150/month extra for a Masters in any field. SAPD pays 350 month for the same thing.
In addition, the pressure for degrees to enter is also raising the bar for promotion. It is almost impossible to get a job at higher levels without a degree, and many departments require a masters to be a Chief or Assistant Chief.
The downside is that police work is fairly low paying. A major department, like Houston, Dallas, or San Antonio is starting people at about 2500 monthly while in the academy. Pay rises fairly quickly for the first few years, then levels off with incremental raises. There are other monthly pays that help, such as shift differential and language pay too. All told, using SAPD as a comparison, I think you would be making about 40K yearly in one year, then up to about 65K in about 5 years, if you work the midnight shift. The alternative is to work a very small town where you start at about 24K and the Chief only makes 40K or so. But there are all sort of ranges in between also.
Also, as you go up in rank, which takes time, you get more money. Chief of Police is about 60K in most decent sized towns, climbs to 90K in small cities, and up to about 150K or so in large cities.
As others said, one of your other alternatives is to work in a business field with the degree and then volunteer as a cop. It requires you to go through an academy though, and that can be a year of hight school or 4 months of full time day school. This way, you might find an acceptable job that pays and still get the police work for the fun/interest.
If you have more questions, you can call me at work: 512-206-3444. I am in charge of the TABC Enforcement training