Someone here said that they thought that supply and demand sets prices but the cost plus overhead and profit set price establishes a floor below which the supply and demand set price can't go. In reality he or she is close to the truth but a bit backwards. The owner sets a cost plus price and the demand for the product determines the amount of sales for the product at that price. Virtually every business looks at average costs and sales volume. I doubt that any business calculates or cares what the marginal product is, what it costs them.
No, most businesses probably don't go through the economic theory model when they're setting prices. Becuase the model is just that - a model. More realistically, it's a two part step:
1) Can we sell this widget for MORE than it costs to make this widget? If the answer is yes, then you have a business, if not then you don't go into production at all.
2) What's the most we can charge for it and get enough sales to make whatever target we want? {Or if they're sophisticated enough, what's the optimal price that brings in the maximum gross profit?}
Step 1 is the Cost of Production element. Step 2 is where Supply and Demand come in. Most small businesses probably don't think of it in terms of supply and demand, at least not in any formal sense. But the model still holds - the relationship is still valid even if the players in the game don't know the names of the forces they're responding to.
In addition there are a lot of factors that effect the demand for a product besides the price; advertising, convenience, reputation, etc. At least fifty percent of the employees of almost any modern corporation are working to distance the corporation's products from market forces. To enable them to charge a higher than market price. And they succeed for the most part.
Yes, there are many elements that influence demand, including all the aspects of brand that you've mentioned as well as competition and fungibility. To a degree, some of those same factors can affect the perception of supply as well - especially fungibility. If the consumer believes that your product is special and uniquely different from other products like it, then the supply of that product doesn't include the products of your competitors.
These aren't distancing the company's product from market forces; these tactics only work because those market forces are real. They work by influencing market forces - by influencing demand and by influencing the perception of supply among consumers. It doesn't allow them to charge a "higher than market price". It allows them to affect demand, which in turn sets a new and different market price for their product.
Any action that a company can take that makes their product more unique and less of a commodity generally allows the company to influence the perception of supply. It sets them apart from their competitors and makes them less fungible. This in turn usually allows them to command a higher price by lowering supply. It is exactly those same market forces at work.
So a company that increases demand by promoting their brand effectively and decreases the perception of supply by reducing their fungibility influences both prongs of the price equation - they simultaneously increase demand (through brand) and lower supply (through reduced fungibility) thus increasing their price.
The same thing works with respect to wages, by the way. The more unique and less fungible one's skills are, the lower the supply. The better you are at promoting your own skills, the higher the demand. The lower the supply for your skills and the higher the demand for your skills, the more you get paid for them. Thus we have CEOs and celebrities and professional athletes.