Gravity Equation Interpretation
My understanding is that the gravity equation can be derived from different settings.

You can assume that each country

1/ produces only one product. This is knwon as the "Armington assumption" as in Armington (1969) and allows a simple derivation of the gravity equation as in Anderson and Van Wincoop (2003).

2/ is specialized in different products (or varieties of a product, given that each variety of a good counts as a distinct product). This is the case worked out by Feenstra, where products are differentiated by their country of origin. So, each country produces many distinct products.

Then the question is to know if the number of products is fixed, as in Armington (1969), or endogeneous and varies due to free entry, as in the monopolistic competition models.

References 


ANDERSON, J. E., AND E. VAN WINCOOP (2003): “Gravity with Gravitas: A Solution to the Border Puzzle,” The American Economic Review, 93(1), 170–192.
ARMINGTON, P. S. (1969): “A Theory of Demand for Products Distinguished by Place of Production,” International Monetary Fund Staff Papers, 16, 159–178.