Comment by retsibsi

Your max price should be the price such that you're indifferent between buying the item at that price and not buying it at all.

At a shop, usually you're paying less than the maximum you'd be willing to pay, because the shop's prices are fixed and it would be a big coincidence if the price they set happened to match your max price exactly.[1] So even if we model you as homo economicus, it's normal that you're almost always fine with paying $X + $0.01.

In the case where $X really is your max price (i.e. it's right at your threshold of indifference), the idea of rejecting $X + $0.01 seems less silly. You were already very close to deciding $X was too much, so you're probably feeling ambivalent about making the purchase, and the trivial nudge of an extra cent being added to the price might as well be what pushes you over the edge.

[1] There are exceptions, e.g. when you have a negligible preference between brands A and B, so you're defaulting to brand A because the prices are exactly the same, but you would buy B if it were marginally cheaper. But that doesn't affect the main point here.