Is it valid to assume that the international price of consumer durables is constant?
The assumption almost never holds. Not for televisions, nor pretty much any other consumer durable (nor wheat, but that's not a consumer durable anyway).

It's a simplifying assumption that's used to make a particular problem easier to solve.

But in reality, the market changes continuously; furthermore there are often oligopolistic forces at play.

The least that should be done, when making the assumption, is to include a discussion about the possible implications on ones results, when the assumption does not hold. One could also do a sensitivity test with and without the assumption; and/or cite other studies that have gone deeper into the implications of using the assumption.

Classical economics has a long, disreputable history of making big claims on the basis of invalid assumptions. It's down to us to change these bad habits.