Which type of smoke detector, there are 2, one causing more harm than good. Unforunately most people have the wrong one, the cheap one.
This sort of dangerous, ill-informed comment can cost lives. It's easy to read as 'if you can't afford an expensive smoke alarm, don't bother.' That is very wrong.
There are two types of smoke alarm. The expensive ones, photoelectric alarms, are better at detecting smoldering fires that emit lots of smoke without bursting into flames. They're great for sites near your kitchen as you're less likely to be bothered by a false alarm from cooking, or a bedroom where there might be a large piece of furniture that could smolder. You should also be careful to keep these alarms clean for proper functioning.
The cheaper ionization alarms detect actual fires more quickly. They're ideal for areas with lots of combustible materials. I've read about several trailer fires on NBC29 over the past years where the entire unit has been ablaze by the time the emergency services arrived on scene. Those fast moving fires are exactly what the cheaper alarms are good at detecting.
If you can afford to, it's better to use a mix of alarms. There are also some dual technology alarms available.
However, if you can only afford a cheaper alarm, buy it, install it and change the battery twice a year. It could easily save your life.