ABSTRACT
A producer of a differentiated product has to commit α units of labor as a fixed cost and has constant marginal input β. With the total number of products available to consumers being very large, each producer chooses its constant mark-up price as
p = p* = σβ _____σ – 1. (5.4)
Free entry ensures that profit is zero in the long run; hence the long-run equilibrium output of each variety, –x , is a constant, independent of the level of trade costs:
–x = α __β (σ – 1). (5.5)
In autarky (i.e., the case of prohibitive trade costs), the number of differentiated products in each country is given by
nA = µγL____ασ ,
n*A = µ(1-γ )L_______ασ ,
where superscript A represents the value in autarky equilibrium. Units are chosen so that one country’s autarky number of varieties equals its relative size; i.e., by setting (µL/ασ) = 1, we obtain
nA = γ, n*A = 1 – γ. (5.6)
Turning to the trade equilibrium with positive (but not prohibitive) trade costs, the product market equilibrium requires that supply equals demand for each Home product:
–x = c + c˜.
