My response is something like this.

" I feel that my standard rate is justified due to my knowledge, the quality of the code I produce, my flexibility and my ability to learn and pick up new skills and technologies quickly. I have other clients who are paying my full daily rate and they very satisfied with the work I produce.

I completely understand if this is non negotiable. And I realise asking for an increase on the rate you offered may mean I may miss this opportunity to work with some exciting new projects, technologies and people which would be a great shame. "

Any feedback on the above would be greatly appreciated.