I stand firm. 

I work hard to establish a fair price for my services. If someone does not want to pay then I let them go elsewhere. If you lower your price there is no end to it. People who want low prices always want even lower prices. They will never become a good customer. They will never be a loyal customer and in the end both parties lose. 

If price is the most important factor, then I will not do business with them. Obviously I don't want their business.

I pride myself on doing a good job, and providing high quality services. If that is not important to you and price is more important, we are not a good fit. My customer profile is not someone looking to beat me up on price. I view that as a waste of time.

In the long run, those people get what they pay for. 

If you cut your price, do you provide the same service as someone paying full price? Is your attitude the same? Is your service the same? Is the quality the same? . . . I doubt it. You get what you pay for.