Under your set of stated circumstances, MP decreases, and fuel flow remains roughly the same. HP can be somewhat recovered in the climb with mixture leaning toward best power, however this also decreases due to lower air density as altitude increases.
This can be varified in an airplane, such as a Bonanza S-35, with the constant flow type of TCM fuel injection.
An airplane engine with a pressure carburetor, it would also be as above.
Float type carburetor...not sure, haven't flown those for a very long time, so will leave comments on these to others who have more experience in same.
Hope that this has been helpful.