I initially sold my app for $39.95. Trying this trick about 4 years ago, I doubled the price to $79.95. Sales went down. Way down. I backed it off to a 50% increase - $59.95 and sales came back up. The volume was lower than at $39.95, but the revenues were higher.
I also sell site licenses for the product at $995, and I bumped that up 50% to $1495. The sales cycle is typically longer, so I let that price stand for a few months. There were no sales. Dropping it back down to $995, sales resumed as they were before.
Bottom line: There is no magic formula. You need to test the price elasticity to maximize your revenues.
I am guessing that at $9.99, prospective customers assume that prior customer purchases don't reflect much due diligence -- that people would buy it for $10 "just to see", and just throw it away if bad. Prospectives might then assume that $20 is enough to get priors to research it, or to think twice before recommending it, and that sales at that price thus do reflect quality.
But prospectives don't know anything about priors purchases, right? Maybe prospectives are assuming that the stuff is selling at that price. After all, the seller knows the market best, right? And there is some truth to that assumption: If it hadn't sold at $20, it wouldn't have been around for long.
If that theory makes sense, it may be that your customers felt that $40 was high enough to suggest the consumer validation they needed. Validation was only one component of their decision, "value" was another, and at 80 they didn't feel the value was there. The theory suggests that if you had cut price below 40, your total sales would have fallen.
I imagine that buyers often treat prices like poker bets, and try to extract information about the underlying hand from the value assigned by the holder.
That's different from what the OP is talking about. You raised prices and volume went down. He raised prices and volume went UP.
At a glance the simple explanation, having some experience in marketing myself, is that $19.99 is a magic price point- 9/10 times you will not see any price point on an infomercial that isn't $19.99 or $19.95. And it's because it's a magic price point. Hard to explain but it works.
If he had gone from $19.99 to 39.99 or from 4.99 to 9.99 it would not ave had this effect- his volumes would have gone down. But if you want to sell something at $14.99, 9.99 or 24.99, don't do it- just sell it at 19.99.
I also sell site licenses for the product at $995, and I bumped that up 50% to $1495. The sales cycle is typically longer, so I let that price stand for a few months. There were no sales. Dropping it back down to $995, sales resumed as they were before.
Bottom line: There is no magic formula. You need to test the price elasticity to maximize your revenues.