Conversely,
lower octane = more knock correction = lower boost = more economy.
In terms of pure economy, it all depends upon the price difference
between the grades of fuel. A turbo is not about simply chucking more
fuel into the engine.
The more boost (or compression) you are able to employ, the more
efficiently the fuel will burn, which means extracting more usable
(kinetic) energy out of the same amount of fuel. This is a fundamental
principle of engine design.
The limiting factor is the ability of the fuel to withstand the
initial combustion pressures without detonating spontaneously before
the flame front reaches it. This is what we usually hear as knock,
although there can be other causes for it, too. An engine will be
designed to use a fuel that will not detonate at a given maximum
pressure. This is governed by compression ratio and turbo
overpressure. If lower octane fuel is used there is a danger of knock,
and in order to prevent this, the ignition point is retarded so that
P[max] occures later in the descent of the piston and will
consequently be lower. This will result in relative inefficiency.
An engine that needs to retard its ignition timing to prevent knock is
not using the ideal fuel to exploit its combustion pressure fully, and
cannot be working at optimum efficiency.
Most drivers tend to use the extra energy that a turbo releases as HP
rather than torque (many turboed cars are set up to maximise this),
which may mitigate against achieving greater mpg. One problem with
turbochargers is that they don't start working well until they are
spinning fast, so at lower speeds, running less boost, a turboed car
(which often tend to have lower compression ratios) will be naturally
inefficient.
(Of course, I'm one of