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Is there any differences between "come at a cost of" and "come at a cost to"?

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Energy efficiency may come at the cost of consumer confidence

Free drug samples come at a cost to patients.

Insects also readily evolve resistance to chemical insecticides, and increased use of these chemicals would come at a great cost to human health.

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my vote is for at the cost of That's an idiom and we all know that. I'm confused as I found examples using cost to as well! Nice question. +1 –  Maulik V May 12 at 14:25
    
I think "a cost of X" means we spend X, whereas in "a cost to Y", Y is who or what that is affected by the spending. –  Damkerng T. May 12 at 14:34

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up vote 3 down vote accepted

I would think that at a cost of describes what it will cost, e.g. at the cost of a lot of money. Or, in the example, it will cost consumer confidence (that is, there will be less consumer confidence because of energy efficiency).

At a cost to indicates who is paying the price, in the example, the patients pay the price.

So, yes, there is a difference. If I would write your second example as follows:

Free drug samples come at a cost of patients.

This would imply that the free drug samples cost us patients, presumably because they die!

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There is a subtle distinction here that is easily overlooked, and appears to have gotten mixed in with the original question: "at a cost of" is not the same as "at the cost of".

"At a cost of (something)" says that (something) is a measurement of how much it will cost:

Changing the health care system will come at a cost of several million dollars.

However, "at the cost of (something)" usually means that (something) will happen as a result:

Changing the health care system may come at the cost of reduced care for some patients.

On the other hand, "at a cost to (something)" means that (something) will be harmed in the process:

Changing the health care system may come at a cost to patients.

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