Not quite Juz, This is a question thats bugged me ever since fitting fat 16's on my 205 gti so i just worked it out... First Imagine the tyre compresses under weight by a percentge of its wall height and the rims are correct for the width...
For wider rims + tyres (same wall size = same rim diameter) you need lower pressure to get the same effective stiffness (tyre 'squish) hence comfort. This is because the pressure is acting over a larger area - wider rim thus more force.
But for lower profile tyres you want higher pressure to get the same %compression under the cars weight. Possibly more to stop rims getting dented on potholes.
Both are linear relationships (well the wall depth isn't but can be sensibly linearised for small changes) hence for matched tyre+rim sizes (and equal rolling radius) a good approximation would be:
P= tyre pressure
RW= Rim width (inside rim eg. 8 inch) can be subbed for tyre width if you dont have streched/fat look but not ideal
TW= Tyre width (on tyre side eg. 225)
TD= tyre depth (on tyre side eg. 50)
1= original manufacturers spec
2= your new shiny wheels
P2 = P1*(RW1/RW2) -to account for wider rims
P2 = P1*(TW1*TD1)/(TW2*TD2) -to account for smaller tyre wall
Combine these and you get: P2 = P1*(RW1/RW2)*(TW1*TD1)/(TW2*TD2)
Simplified:
P2 = (P1*RW1*TW1*TD1)/(RW2*TD2*TW2)
This works for mixed units as they are fractions and the reason the tyre depth is found from width multiplied by depth is that the depth rating on tyres is actually a percentage of width. A worked example:
S14:
P1 = 32psi, RW = 6.5 inch, TW = 205, TD = 55.
New wheels:
RW = 7.5 inch, TW = 225, TD = 40
P2 = (32*6.5*205*55)/(7.5*40*225) = 37 psi
Only a quick formula i worked out but serves as a pointer. Realistically compressed volume ratios need to be matched but the results wont be far wrong . That means my UK 300zx rims should be run about 28 psi and i always used to run my 205 GTI's tyres too hard - no wonder it was sooo bumpy!!!