Is there a way to propose a consumer-psychology study (as a business) and work with the university for the benefit of all people. Or do they only do studies around current subjects or select them internally?
There are two factors at work in what is being researched: interest and money.
Researchers research what they find interesting. So if you can interest someone in your idea, then chances are that they will want to research it. But wether they will actually do that research will depend on wether it seems more interesting to them than what they are currently doing, have been investing a lot of time and effort into, and have already employed a team to research. So, your topic has to be really, really interesting to an advanced researcher to pick it up, which is unlikely. If it were so interesting to them, they would have thought of it themselves.
Researchers usually depend on third party funds. Those third parties only finance what they find relevant. There is research on how topics that are currently considered important by the media and populace are more researched. A good example is research on video game violence which was intensely researched after the Columbine shooting. Much relevant research is not done, because it is not currently politically opportune. Many researchers report how they were unable to continue research, because there was no funding. So if your topic is of current popular interest, and politicians can get voted if they care for it, chances are someone is going to research it. If not, not.
If, on the other hand, you pay for the labs and the people, you will have no problem finding researchers, and you can approach any expert in the relevant field. With money being notoriously scarce at many universities, and many young researchers working in underpaid, short-term positions, it is highly likely that someone will be happy to hear from you and make your research happen.
Practical real world example:
A company produces a biofeedback device for a certain condition. To better sell their product, they want scientific research proving its therapeutic effectiveness. They approached my professor (who is a clinical psychologist, but does not do research in that field). Another psychologist, who had earned his doctorate with my professor and is now working in a relevant clinic, was found and conducted a study, the pracical side carried out by student interns. My professor appointed me, one of his student assistants, to do the statistical analysis of the data. The resulting article, which was written by the aforementioned psychologist, his students, and myself (I wrote the results section), has been peer reviewed for publication and the feedback is currently being worked into the paper. If all goes well (which I expect), a year from now the company will quote this paper on their website to emphasize the effectiveness of their device. All my professor did is write some emails and find some people, and now he has another publication under his belt. No money was involved.