Why are increasing returns to scale and fixed costs important in models of international trade and imperfect competition?

What will be an ideal response?

There are many answers. Three of these are
(a) Increasing returns to scale and high fixed costs may be inconsistent with perfect competition. In such a case, the initial autarkic state may be a suboptimal equilibrium. For example, relative prices may not equal marginal rates of transformation. It follows from this that a change in output compositions associated with trade may result in a national welfare for one or both trading countries that is inferior to that associated with the initial autarkic conditions. Hence no "gains from trade."
(b) In a case of increasing scale economies at the firm or plant level, the determination of which product will be exported by which country is ex-ante indeterminate. Therefore, deriving clear implications concerning the effects of trade on income distributions such as may be derived from the Samuelson-Stolper Theorem is no longer generally possible.
(c) Market structures containing positive scale economies and imperfect competition may allow for "two-way trade," or intra-industry trade. As in b. above, the various theorems derivable from the Heckscher-Ohlin model concerning directions of trade and income distributions are no longer generally applicable.