If you were settled in the new area and established with a reputation there I think you would have a better chance of arguing for the higher amount and likely get it. Since you are also dealing with the new to the area - regardless of if you have provided care before everything is new including routines since your house layout is different etc so it will feel to a certain extent yourself that you are just starting out - efficiency will come quickly just not at first - moved many times and started over since hubby is military.

I would sort of be inclined to set my price at the going rate for this year to get the first clients in and then raise it with each new replacement. That is basically what I have done as I moved. Then I was being judged on all those extra things I was bringing because I was equal in other areas such as cost.