There are many things you can do to an engine to increase its power output, some of which are more effective than others. A common assumption is that, if you make one of these modifications but then don't actually use the extra power, you must get better economy. The logic goes like this:

"Adding device X to my car gives it 10% more power. Therefore, for the same power output as before, I must be using 10% less fuel".

This is understandable, but (99% of the time) entirely false. As a rule, the way a performance add-on makes 10% more power is by simply burning 10% more fuel; the amount of work produced per unit of fuel burnt remains pretty much constant.

That's not to denigrate performance modifications; burning 10% more fuel is an awful lot more complicated than it sounds. On a petrol engine, the limiting factor is how much air can be got into the engine (air is needed to burn the fuel, of course), and since the air volume flow rate is so high (a 2 litre engine at 6000 rpm uses 100 litres of air a second!) it is not a trivial task to increase this. But fundamentally that is how the vast majority of performance modifications work: they allow more air to flow into the engine, which in turn allows more fuel to be burnt and so more power is produced. That is true of induction kits, modified cams, "ported" heads, etc, etc - even exhaust modifications, to some extent. So none can be expected to greatly improve fuel economy.

Another frequent argument is that the intake and exhaust systems of "stock" engines are too restrictive, that is to say it takes a lot of power just to suck the air in and blow the exhaust out. By reducing this loss, not only is power increased, but fuel economy gets better as well. In theory there is a hint of truth in that, but in practice the difference between a "stock" and aftermarket performance exhaust or intake system only really makes itself felt at times of maximum gas flow (full throttle, maximum engine speed - or close to it). Under normal crusing conditions the losses in even the standard system are so low that the effect on economy is vanishingly small.

Also, don't forget that the engine must be heavily restricted in normal driving conditions, otherwise it would be producing maximum power at all times. The whole point of the throttle is to "strangle" the engine and reduce the flow of air and fuel to that required for the desired power output. Making the intake and exhaust less restrictive just means you need to close the throttle more to get the same air flow, and hence power output.

Indeed, some performance modifications may actually make economy worse - for example, modifying the inlet ports to improve gas flow may also reduce turbulence if not carefully done. Having said that, there is a possibility that modifications to increase low-speed torque may benefit economy, by allowing you to drive in a higher gear - this idea is discussed more in my section on "chipping".