Don't Try to Compete on Price
When I started my company 33 years ago (!), I charged what I thought was a fair price for the value my clients derived from my work. I was confident in most everything I delivered and rarely found myself having to explain my prices or negotiate my fees.
I also had a pretty good idea of what my competitors charged and was comfortable that all of us were in sync with our fee structure, and so we won or lost business based on other criteria. Don't get me wrong, prospects asked about pricing at first, but they were more interested in what they were getting for the budget and not so interested in trying to lower the price.
A simpler time? Perhaps.
Back then companies couldn't "shop around" quite as easy as today. The competition was crosstown or cross-country, and so I rarely lost business to a company half-way around the world. But today, my direct competitors can be discovered and evaluated with just a few keystrokes.
If you let yourself get psyched out by companies that charge a fraction of what you charge, you're looking at it the wrong way. Instead, strategically position your value and worth and what you will deliver to your client:
Exceptional work product
Don't undermine your business because someone is buying what they think is the "same" work but for a significantly lower price. Charge what you know is fair and what you are worth and understand that you should never sell on price if you want to succeed.