such initiative as falls

[Iwanna]

The administrative overheads of a business are low to the extent that everyone working in the business can be trusted to behave in a way that best promotes the interests of the firm. If they can each be trusted to take such responsibilities, and to exercise such initiative as falls within their sphere, then administrative overheads will be low. It will be low because it will be necessary to have only one man looking after each job, without having another man to check upon what he is doing, keep him in line, and report on him to someone else.

——This paragraph is about the costs of a business. I am not quite clear what the meaning of the word "fall" is in this context.

[Barb_D]

You can substitute the word "is" with no change in meaning.

Does this fall within your sphere of influence? = Is this within your sphere of influence?
Does this fall under your purview? = Is this within your purview?

[Molly]

It means come under, be classified or included ("Fall into a category")

[Iwanna]

many thanks to Barb and Molly

[Molly]

[Nessie]

Hi,

[MrPedantic]

Hello Nessie,

"As" here is a relative pronoun, and the subject of "falls"; thus

1. to exercise such initiative as falls within their sphere

means approximately

2. to exercise the initiative that falls within their sphere

or

3. to exercise whatever initiative falls within their sphere

Best wishes,

MrP