"Raise the price of the product" sounds much better, I think.

Well, if the context reflected only one product, selling for a single, undifferentiated price everywhere, then "prices" would not be a good choice of wording. I can visualize a context where a single product might price differently in different markets, in which case "prices" might be used.

You and Randy are right... "prices" is not the best word to use here. Just "price" would work and so would "pricing" or "pricing structure" which suggests multiple prices for multiple products or in different markets for example. Also, only small companies have a single product. Larger companies have multiple products or "product lines". So, a more natural sentence might say "You could easily raise the pricing structure of your product line."