I never undermined going rates, even when I started out. I was always a firm believer that if I am good enough to teach, I will be good enough to charge going rates. If I am not good enough to charge going rates, maybe I shouldn't teach.
I know this may sound harsh, but I firmly believe it is true (of course it doesn't mean that everybody charging the going rate is therefore necessarily a good teacher

).
I always based this idea on two reasons:
1. If I am good at what I do (of course we all keep on learning, no matter how long we've been teaching), I deserve to be paid for it. There is no reason why I should charge a quarter (or less) of going rates. Beginners earn less, yes, but how many school teachers do you know who start out and only earn 25% of what they earn after a couple of years? They start on a lower wage, but not to the extent you sometimes see with private teachers.
2. If I undermine the going rates, I destroy the prices for everyone else, because the word will spread.
Having said that - even going rates have a range you can move in. So you would start at the lower end when you begin teaching, and then you would gradually put your prices up.
To give you an example: The MU suggests the following rates for peris for the academic year 2009/2010, and this gives you a good idea of a range to move in, depending on expertise/experience etc:
1. Entry Level: £22.00 - £23.50 per hourFor newly qualified teachers on entry to the profession. This level is expected to apply for not more than two years.
2. Standard Level: £25.50 - £27.50 per hourTakes into account FHE and other relevant specialist musical qualifications and a minimum of two years’ relevant experience (addition by myself: The recommended private teaching rate always falls into this bracket, and it is £27 for 2009/2010).
3. Credit Level: £28.50 - £31.00 per hourAllows for recognition of further teaching experience; quality and additional qualifications; experience and status as a performer.
4. Advanced Level: at least £32.00 per hourApplies to teachers who do advanced or specialised work or who have additional extra duties or responsibilities. These teachers should be paid at a higher hourly rate commensurate with such work or duties. Extra duties and responsibilities include those required of a Head of Department (e.g. Head of Strings, Administrator or Music Co-ordinator.)
After 5 years of teaching experience (and over 10 years as a professional performer), I certainly don't see myself lower than standard level. I could enter credit level with my experience, but I decided not to because of the area I live in and the people I teach - at some point, you will price yourself out. I will be at the higher end of the bracket though (I always put my prices up in Jan, not in Sep), which feels justified, and I still offer discounts to people who make a commitment (even those won't be in the lowest bracket though).
In which of those brackets you see yourself is very individual, but I don't think that the lowest one should be left, even for teachers who just start out. If I calculate all my expenses, cost of professional development and the amount of additional (non-contact) hours I put in, I still don't earn much more than minimum wage - this is just something people don't see.
So I would always advise new teachers to be confident in what they do and not sell themselves under value. If you already have low prices, bring them up gradually, maybe even show your existing students the current price ranges if you plan to hike them up at once, and don't accept new pupils at low rates anymore.