Heckscher-Ohlin theory was based on the assumption of constant returns to scale. It does not explain the existence of international trade in the presence of increasing returns to scale.
However, it can be shown that even when two economies are identical in every respect (technology, tastes, factor endowment, etc.), increasing returns to scale provide a scope for gainful trade between them.
The typical PPC of an economy (and used by us earlier) represents:
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(i) Either constant returns to scale in which case it is a downward sloping straight line; or
(ii) Diminishing returns to scale in which case it is concave to the origin (that is, bulging out).
In contrast, with increasing returns to scale, PPC is convex to the origin (inward bending). It represents a situation where a proportionate increase in all inputs results in more than proportionate increase in output.
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For each additional unit of one commodity, we have to forego a smaller than before quantity of output of the other commodity. Once a country starts on the path of large scale production and specialisation, it is able to add to its comparative cost-advantage.
If, however, one country completely specialises in the production of commodity X (by producing OB of it) and the other specialises in the production of commodity Y (by producing OA of it), both can trade and reach a higher indifference curve. This post-trade position is represented by point D on indifference I2 which is higher than I.
Important:
It should be noted that for trade to take place, there is no need for the relative prices of goods X and Y to change. The terms of trade between goods X and Y would be the same as the ratio of their autarky (pre-trade) prices.
The only condition to be satisfied is that each country should choose to specialise in only one commodity and both countries should specialise in different goods.
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Moreover, the after-trade position is not affected irrespective of which country specialises in which commodity. It means to say that we get the same terms of trade, same volume of trade and same composition of consumption by each country.
When we consider the case of trading countries producing a large number of commodities, we find that prevalence of increasing returns to scale increases the possibility of one or a few large firms competing the remaining ones out of the market.
Again, it is a matter of historical incidence as to which firm(s) takes the lead of taking advantage of economies of scale.
If, with increasing returns to scale, we relax one or more assumptions of the preceding analysis, additional possibilities crop up. But we cannot say with certainty as to exactly what will happen.
For example, it is possible (but only possible) that unequal tastes may provide domestic firms an opportunity to reap economies of scale by specialising in certain products and then dominating the international markets as well.
In contrast, however, cases are also known where, even with a nearly non-existent domestic market, some firms have acquired cost advantage in the production of a commodity demanded by other countries.