Is it valid to assume that the international price of consumer durables is constant? While studying tariffs in International Trade, we often come across a Demand Supply diagram along with a world supply curve that is perfectly elastic. Here we assume that the international or the world price of that good is constant and based on this assumption we carry on with our analysis. 

Considering commodities or goods such as wheat, it is safe to assume that the world price will remain the same as it is produced in huge quantities all over the world and no one country/producer can cause a shift in the supply curve. 

However, consumer durable such as LCD or Plasma televisions are not produced in such abundance and are often produced by certain countries, say for instance Japan or China.

This reasoning has led me to question the assumption made while drawing the world supply curve in the tariff diagram. I would like to know whether this reasoning is valid or not and if not, then why?
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.