Either of them could be correct depending on the meaning you wish to convey.
based on - using the old rates /the higher prices as a basis for the adjustments.
for the - in order to include the old rates / higher prices.
adjust something for - make adjustments for a particular aspect of something:
My wedding dress is too big. We will have to adjust it for size. - the adjustment is to the size, not the colour, style, etc.
I cannot think of a use of ‘adjust for’ without the noun or pronoun between the two words, other than a rewording of the above:
My wedding dress is too big. It will have to adjusted for size.