limit the cost to the finance ministry

Question

In France, more than 12 million are covered by a scheme called Chimage Partial which has cost €26bn so far. It offers 70% of salary on up to €6,927 gross per month. Employees on minimum wage (SMIC) receive 100% . As with the German scheme, firms can claim just part of a worker’s salary and many do, limiting the cost to the finance ministry.

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I have trouble in understanding "limit the cost to the finance ministry", it seems different to phrase "limit sth to sth" - to restrict something to a limited set, a certain amount, or a specific number of something.

• eg.. Please limit your comments to five minutes.
• eg.. Can you limit your remarks to the subject at hand?

Should it be "limit the cost FOR the finance ministry"?

article link :　https://www.theguardian.com/world/2020/may/12/furlough-qa-all-you-need-to-know-about-the-coronavirus-job-retention-scheme

Answer 1

You are correct, this is not an example of the phrase "limit X activity to Y extent".

It's not (limit (the cost) to an amount), it's (limit (the cost to the payer))

This phrase is a combination of "limit the cost" (restrict the extent of the cost in some undefined way) and "the cost to the finance ministry" (the amount that the finance ministry must pay for something). Put together, the phrase can be understood as:

[firms can request less money per employee], which limits the cost that the finance ministry must pay

Answer 2

The phrase "limit the cost to X" in this case means the same as "limit the cost for X", that is, the Finance Ministry will have to pay less.

You are correct that "limit the cost to Y" can mean to set a maximum amount for costs, but the sense must be inferred from the context.

A Google search on the phrase "limit the cost to" shows it is much more common than "limit the cost for", and most of the search results are not references to amounts, but to entities whose costs are to be limited, so it's very common, and therefore valid.