Does it make sense to "ignore low ball offers"?

I respond to every offer I receive. If I find the offer really low, I will just say "No, thanks for your interest." If they are really interested, they will make a better offer. Negotiation can start from there. I have made more than one sale that way. If also helps to weed out people not interested in negotiating. 

On the other hand, I had one item for sale. To make the example easy, I am going to say the asking price was $1000. This item routinely sells for $1200 and more. The potential buyer and I haggled back and forth a bit and settled on a price of $850 with shipping split. I made arrangement for this person to pay and waited for some time and got nothing. I contacted the person and was asked if I would take $600 for the item. I told him we already had an agreed upon price. Crickets for a couple of more weeks and then he asks if I would sell for $500. I responded with, "For you, I will sell for $950 and you cover the shipping." Never heard from him again. The item ended up selling for very close to my original asking price, so it ended up working out fine for me at least.

Problem is many sellers inflate their price somewhat expecting that they will receive low offers and their prices will give them room to negotiate a fair price, so what exactly is a low ball offer. Earlier in this post a few mentioned 30%, certainly a low offer, but consider if a seller inflates his price by 15% expecting a buyer to ask for a 15% discount, as they routinely do, a  minus 30% offer could in fact lead to a successful conclusion at a fair price. I'm far less concerned with the amount of the offer than the manner in which it is conveyed. 

I expect to negotiate with the seller, If there is no counteroffer then  forgetaboutit I move on. Having said this I as a potential buyer laugh at the high prices of audio gear, the price performance ratio is off the charts.

A fool and his money are soon parted applies to this hobby.

It all depends on how aggressively I've priced the gear for sale.  I rarely use that statement, as it does convey a bit of arrogance.  Better to say "firm and fair" or "a little flexibility with the price" if that is the case.  As a buyer, I am very wary of companies that routinely discount their products by 40-50% based on MSRP, yet somehow make it sound like it's a limited time offer.  Seems to be more associated with cables and various tweaking accessories.  

Price negotiations are just business.  It's never personal.    This is a free country and the buyer is free to make a low ball offer as I am free to not take it.  

When I'm selling something, I have in my mind a bottom price I'm willing to sell it for.  I'm going to ask more than that of course and give myself some room to give back a bit.  Buyers always want to think they're getting a good deal and coming down on your price gives them that illusion.

Negotiating a purchase price is the same logic in reverse.  I have in mind a top price I'm willing to pay for something and start out with a lower offer.  I never low ball people, but there are times when my initial offer does get accepted.