What is Brand Equity?

I was speaking recently with a marketing professor from a top business school. He is a person I respect very much.

During the course of our conversation he said, "Wal-Mart has no brand equity." I almost choked on my wine. I asked him what he meant. He said that brand equity should create a price premium, and Wal-Mart's strategy has been to focus on low prices. In his mind brand equity always creates a price premium.

Yes, strong brands can get people to pay more. But, isn't paying a premium just one example of the kinds of behavior a strong brand can encourage? What if a brand gets no price premium, but encourages more frequent purchases, a greater share of spending dollars, or referrals? Isn't that a strong brand? Wal-Mart gets a disproportionate share of both wallets and shopping visits, and has millions of loyal customers. It has changed consumer shopping behavior, in a significant way.

So, can you have brand equity with no price premium? Or do you agree with the professor? (Any conversation about Wal-Mart can be incendiary, so please try to separate your answer to the brand equity question from any Wal-Mart rants, which you are also welcome to include in your comments.)