Under Capitalism a good has an use value (how useful it is?) and an exchange value (how much charge for it?).

Do you have any examples where the use value is in conflict with the exchange value? That is, something useful but not profitable?

@alxcndr Modern news/reporting would be one thing, where the actual journalism is just a loss-leader and the income results from running ads alongside it
@alxcndr housework and looking after children. Yes, we pay cleaners and nannies, but spouses and parents do this work essentially for free.

@joshsharp I feel this is not a working example though, since you can still be profitable if you sell this as a service.

Here the usefulness and the profitability are not exactly antagonistic.

@alxcndr I guess certain medical equipment. Treating patients has an obvious inherent value, but private medical companies under capitalism are reluctant to treat conditions that aren't profitable.