How do you create new areas of sustainable competitive advantage to ensure greater retention and probability of your franchise outlets other than your lower price?

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This is a very sophisticated question, and will depend upon the industry in question, regulation in that industry, competition, market opportunities, target demographic, business geographics and a variety of other factors.

However, your main question seems to be, "Can a Business Compete on Grounds Other Than Price?" and the obvious answer is absolutely, and commonly these more "premium" or "non-discount" businesses do just as well or better than their "discount" or "bulk sales" competitor counterparts.

Businesses that aren't "Priced Focused" tend to focus on an alternative - often superior - product benefit.

An example of a business that has utilized both strategies in recent years is Subway (sandwich) which spent years establishing a "Healthy" brand status over competitors with "Jared." Here they focused on a product benefit - "We are more delicious and more healthy than competitor fast food" "Eat Subway - You Will Not Get Fat like the Other Guys Food" (Not saying this is true, or not. Simply pointing out their message).

More recently, and likely targeting the "Value Menus" and "99cent Menus" of competitor brands (Wendy's McDonald's etc.) they introduced and marketed "$5 Foot Longs" and their "FebruANY - any sub from their value menu $5.)

Cold Stone Creamery famously markets quality ingredients, and fresh preparation vs. Dairy Queen's lower prices and discount menu.

Ultimately the job of the marketer is to identify the product benefits of his product, business or service and convey them to the target market in a manner that affects them, and effectuates a transaction. This is a trained and practiced skill - no different than Tennis, Mixed Martial Arts, using Photoshop, drawing comics or architecture.

If marketing is not your expertise, hire a consultant that understands your issues, and has "Walked the Road Before." Don't make the mistake of thinking that because you did some marketing, or purchased some advertising that you're a professional Marketer. Imagine a guy that once did "Some" fighting going in an MMA Octagon vs a Pro - It's not pretty, and one of the many reasons why so many new businesses fail.