Whilst it's not a rule set in stone, there is evidence across the software world to show that competition does not drive down prices.
The most obvious example is Microsoft, whose various Windows operating systems have been crushing competition for years, despite a price that has been constantly held high. The price is such that in entry level computers, the operating system is the single most expensive item.
Unlike, lets say, potatoes or milk, operating systems, or any other software, are not created equal.
Once you start using a particular piece of software, and have learnt it well, the sheer amount of effort needed to relearn a different application means that a huge number of people would rather stay with their current software than take the chance of trying something else. This distorts the very real reason why competition should exist.
Software firms also build in “features”, that trap users into using their technology (e.g. proprietary file formats), essentially locking in users and keeping them away from the competition.
All this goes to prove that competition is often a meaningless word as far as software is concerned.
You can read about the ten other myths of commercial and proprietary software here.