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In the late seventies, Commodore sold the PET in Europe at a considerably higher price than in America; they could get away with this because there was less competition there. Some of the American dealers took advantage of this by surreptitiously shipping PETs across the Atlantic, much to Commodore's annoyance.

Technically, how did this work? The PET power supply was built into the case; it had a single power cable that expected ~115 volt (?) 60 Hz, not 220-240 volt 50 Hz. Even if you took out the power supply and replaced it with one suitable for Europe (was it an off-the-shelf item?), the 2001's monitor was a picture tube from a black-and-white TV set, which would presumably have been expecting 60 Hz power. How could an American PET work in Europe?

In the late seventies, Commodore sold the PET in Europe at a considerably higher price than in America; they could get away with this because there was less competition there.

Let's say market structure was different.

Some of the American dealers took advantage of this by surreptitiously shipping PETs across the Atlantic,

Jup, and as well as many customers tried to buy direct. Here payment was the biggest hurdle, but there was a way to pay via the post office - but that's a different story. Well, and haggle with customs - but that's another :))

Technically, how did this work? The PET power supply was built into the case; it had a single power cable that expected ~115 volt (?) 60 Hz, not 220-240 volt 50 Hz.

First and most simple solution was using a transformer (like this). Not cheap, but still saving money - and usually cheaper than a new PS - at least when only converting a few units.

Even if you took out the power supply and replaced it with one suitable for Europe (was it an off-the-shelf item?),

Such 1:2 transformers are stock items, so no need to worry about the PS. The lower frequency doesn't matter as the result is way within tolerances.

the 2001's monitor was a picture tube from a black-and-white TV set, which would presumably have been expecting 60 Hz power.

Why? It derives its timing from the video signal the PET supplies, which in turn is taken from the oscilators, not in any way taken from or synchronized by mains. The video signal is still the same with 50 Hz power, thus no adjustment needed.