You are correct that "cost" has more than one definition, but, as already discussed, the one we are talking about equates to consequence, not an amount of money. Your milk analogy doesn't fit. Whether or not a so-called consequence is seen as a consequence is in the eye of the beholder.

I'm well aware of the narrowing you imposed. Consequence in these terms still equates to an objective reality, even if the underlying source of it can be described as subjective. The consequences of rising milk prices is an objective reality, even if your purchasing habits are subjective.