This argument is circular - your conclusion (that the West prosperity is dependent on the exploitation of the Third World) is assumed in your premise.
The proposition itself is pretty meaningless unless we define which specific countries are involved. But once we do that, the proposition becomes patently false. Any exploitation must necessary involve an actual transfer of material resources between countries. However, countries that actually produce such resources for Western markets in substantial quantities, such as China, Taiwan or Korea, are hardly exploited by any Western country. Au contraire, these countries became prosperous precisely because they had access to Western markets. China's living standards suffer mainly because of the enormous size of its population not because of any "exploitation." Similar argument can be made for India.
On the other hand, countries with dismally low standards of living, such as most sub-Saharan African countries produce very little what the "West" can sell at a profit, and the whole continent's GDP is a drop in a bucket against that of the US or EU. Thus, there is no causal link between African poverty and Northern prosperity. That is not to say that Northern institutions, especially the IMF, are not responsible for the failure of African development - but misguided advice and malicious influence is a very different proposition than saying that Northern wealth is produced in the Third World, which is pure nonsense.
It is possible to criticize US (and EU) economic development policies without making obviously false claims that North/West prosper because of the Third World exploitation. I find such statement to be a propaganda tool of the Third World dictators who use it to deflect popular discontent and direct it at external targets.
Wojtek