I found this great article at www.fastcompany.com. The major take aways for businesses that do not want to compete on price are:

1. Develop Powerful Branding – Effective and unique branding puts your product in a competitive space that has little to do with price, and more to do with being cool, trendy (or timeless), and of great quality.
2. Strategic Marketing – This encompasses the four Ps of marketing and much more. In luxury marketing you need to be thinking about the four Es (exclusivity, emotion, engagement, and experience). While Apple won’t admit that they intentionally create product shortages in order to create a buzz, it is certainly part of the reason why customers are willing to pay huge premiums to have their products as soon as they are released.
3. Excellent customer service – Customer service is something you can not afford to lack. From getting customer’s to try your products and services to keeping them loyal, customer service is the lynch pin that sets you appart from competitors.
4. A product that doesn’t disappoint – All of the above won’t mean anything if you don’t have a stellar product. Take a page from companies like Apple and Patagonia who are committed first to making the best product possible.

If a product can’t live up to the expectations set by its marketing, it won’t be successful for the long term