Most people will. Most people will spend an extra $500 for a brand they believe in. They will spend an extra $5000 for the perception of better quality and longer lasting product.
So why do so many companies put all of their eggs in the price basket? Price doesn't build loyalty (don't tell Walmart, it will ruin the surprise). Price doesn't inspire advocacy. To paraphrase Seth Godin - price doesn't create a Tribe.
I love Nike. I mean really love them. My first pair of running shoes twenty years ago...Nike. If you look in my closet now, multiple pairs of...Nike. I identify with Nike. I am not the tall athletic woman running through the tv spot, but when I wear Nike I feel like her.
Every other pair of shoes in the store could be half the price, it won't matter, I will still buy Nike. I am a part of their tribe.
Isn't that how you want your customers to feel about your company, your product, your service. Don't you want to be chosen...no matter what?
Then change the conversation. Make it about your customer. About who they are. About what they need. Stop talking price. Start forming relationships.