purse strings

Financial resources or control of them, as in His mother doesn't want to let go of the purse strings because he may make some foolish investments. This expression is often extended to hold or tighten or loosen the purse strings, as in As long as Dad holds the purse strings, we have to consider his wishes, or The company is tightening the purse strings and will not be hiring many new people this year. The purse strings in this idiom are the means of opening and closing a drawstring purse. [Early 1400s]

The noun has one meaning:

Meaning #1: a drawstring used to close the mouth of a purse