I'm in Houston. I do know of one theater (if it's still there) in Texas City that's rather old where I could get tickets for about $6 in the middle of a weekday while everyone else was at work, otherwise they were about $9 which was still cheaper than everything else. $3.50 isn't going to happen around here on anything that's not about to come out on DVD in a week or two anyways. The Texas City theater was old enough to have non-reclining old-fashioned narrow chairs, older sound systems, etc. My parents tagged along to that one when I took my daughter to see a cartoon one time and they said they never wanted to go back to that one, they would rather spend the money. I worked overnight a lot when Texas City was in range so it was one of my preferred places to go in the summer because I could watch a movie in the morning then get home in time for my noon bedtime, or shortly after. Generally I would go to the dollar theater that was about a half mile away from my apartment and watch whatever was showing that seemed interesting, but in both cases only in the summer. I found out from working the night shift a lot that theaters tend to open earlier in the summer and near holidays than they do during a normal work week.
I have observer that normal rules of supply and demand don't apply to movie theaters. The newer and more advanced a theater is the more they can charge for a ticket, and they're likely to get it. The older but still nice ones can charge a bit less and stay full. Really old theaters -especially the kind that are in shopping centers - must be renovated into either a dollar cinema or a restaurant theater to stay in business. I don't know of any that currently fit the description of old and open that are still operating in their original build-out or purpose.
Another observation I've made - the population density has more to do with ticket pricing and theater quality than anything.