Yes. Costs are determined by the sale price, not the other way around. For example, if the sale price of a product increases, the demand for its components raises, which raises their cost.

If a would-be producer cannot source materials that would cost him less than the sale price, he just won't build the product.

[1] has more details on the subject.

[1] https://mises.org/library/whats-cost-got-do-it-0