Where a business house holds the means of inflation (5)
I believe the answer is:
cairo
'where a' is the definition.
The answer is a location as well as being a singular noun. This is suggested by the definition.
'business house holds the means of inflation' is the wordplay.
I cannot really see how this works, but
'means' could be 'air' (I have seen 'Means of travelling' mean 'air ' so perhaps 'means' could also mean 'air ') and 'air' is found within the answer.
'business' could be 'co' (short for company) and 'co' is located in the leftover letters.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for cairo that I've seen before include "Capital of Egypt" , "Egyptian capital" , "North African capital" , "Egypt's capital" , "City near the Nile delta" .)