The volume of air and
how fast it is traveling provides for good fuel economy.
Imagine yourself blowing through a typical soda straw. You'll be able to have that air traveling at high rate of speed.
Now imagine yourself trying to blow through a 5" pipe. Oh yes, the 5" pipe can flow more air, but the velocity of that flow will be much less than with the straw.
The air intake system of a Corolla, (or any modern car), is not very restrictive at all. Toodling around town or going down the highway, the engine gets all the air it needs. At very high 5,000 rpm + engine speeds, a very slight improvement could be made, but it will hardly be noticeable, if at all and it wouldn't be helping fuel economy.
Keep in mind that vehicle manufacturers have very stringent C.A.F.E., (Corporate Average Fuel Economy), standards they must maintain or pay millions of dollars in fines, so you can bet if they could improve fuel economy with simply bolting on some kind of air induction system, or a computer chip, or a larger diameter exhaust system, they would have done so right from the factory. If it's not broken, don't fix it.
With today's modern computer controlled engine management systems, the amount of airflow into an engine is determined by the vehicles onboard computer.
What those modifications will do is increase high rpm power, again 5,000 + rpm's. But the reduction in torque in the low to mid rpm range will reduce torque and thus fuel economy.
Good modifications for fuel economy will include high performance LRR/Low Rolling Resistance tires, reducing the vehicles weight with carbon fiber parts and light weight wheels, high performance synthetic motor oils and transmission fluids, like AMSOIL synthetics. Slight gains in fuel economy and power can be also be had from NGK Iridium spark plugs. :thumbsup: