if sales are down with no effective competition at the high end why would Intel drop prices
Because it's a luxury purchase, not an essential.
An essential purchase (food, medicine, rent, etc.) is driven largely by competition. If there is only one seller, then they can charge high prices. If there are competing sellers, prices fall. All because demand is fixed.
Luxury goods are subject to the supply-demand curve. You don't HAVE to have a Bentley or a five-bedroom house... Or an i7-6700K. Even without competition you're aiming for the point on the curve where buyers x price is the maximum value. You could sell an i7-6700K for £2,000 and some people would buy it, but they would be few. You could sell it for £100 and huge numbers would buy it but you'd make nothing (or a loss). Intel's job is to try and find the point in the middle that gets their executives the most cocaine money.
That's why Intel would drop prices if too few people are buying, and competition is not a requirement for this principle to be in effect.