An engine uses the least amount of fuel while engine "braking". It uses even less fuel than when idling.
Remember, while in gear and slowing down, it is the cars momentum that is keeping the engine running NOT the combustion process, which requires fuel, air, and compression.
So, if you're at 70mph in 4th at 4000rpm and you down shift to 2nd and engine rpm jumps to
5500rpm you are NOT using more fuel just because the rpm goes up.
Higher revs can cost more fuel, but you are NOT acclerating at this point, you are using the cars momentum to rev that engine to that speed. It is using little to NO fuel at that point.
There is vacuum being created in the cylinders and the throttle being nearly closed is creating a "braking" effect slowing the car even more.
As far as does rpm cost in more fuel? That's an interesting question because even though it seems to make sense that 2000rpm will use less gas than 4000rpm, you have to also consider what gear you are in, what load is on the engine such as up or down hill, and at what rpm does the engine work it's most efficient?
CVT transmissions work on the idea that engines have a "sweet spot" where they are the most efficient, where throttle opening and engine pumping are providing the best power output being the most efficient with the fuel being used. That is part of the reason whey CVT trans cars get better MPG even though the engines tend to rev to a higher rpm and want to stay there longer.
Lugging the engine in a high gear while at low rpm can actually waste more fuel due to extreme pumping loss as the engine is wasting power just trying to "breathe" or pump air in and out of itself. A combustion engine is, afterall, an air pump.
Larger throttle openings, in cars with throttle valves, allow the engine to breath easier as there is less power being used to draw in that air compared to smaller throttle openings that give a greater restriction to air coming in. One suggestion for better MPG is to start off in 1st normally without big throttle openings and "jack rabbit" starts, but then shift sooner and use BIG throttle pedal pushes giving a larger intake opening the cylinders by which to breathe easier. So, you would start in 1st with normal throttle, once under way you bigger throttle to open the plate more but shift sooner, say at 2500-3000rpm, then quick shift to 2nd and give big throttle again till about 2500-3000rpm, and repeat.
It's hard to change how we drive, so for me it's hard to do that technique for a whole tank of fuel to test it out. However, from my initial tests there may be something to it afterall.
Give it a try.