levels, and conditions that determine the number of firms that enter into existence each
period. These equations will, amongst other things, determine the productivity of the
average firm φii and the price level. However, unlike in the perfectly symmetric setup
of Melitz (2003), Felbermayr, Prat, and Schmerer (2008) or Eckel and Egger (2009), we
need to know labor market outcomes to pin down these variables. However, conceptually,
the section is close to Melitz (2003), and will therefore be deliberately brief.
There is an infinite number of potential firms which can enter the market after paying a
fixed and sunk entry cost fe , measured in terms of the final consumption good. Only after
entering, they are able to draw their productivity φ from a known distribution with p.d.f.
g[φ∖ and c.d.f. G[^]. The productivity stays the same as long as the firm exists. Only
firms which draw a φ favorable enough to make non-negative profits will start production
and engage into sales in one or several markets.
Entry into markets. A firm with productivity φ located in country i will engage
in market j if the expected discounted operating profits exceed costs. Hence, the firm
recruits workers with the aim to produce output for market j if and only if
πij и = ∑ ( ι+δ )t πij и- ɪ Lij и- Pifij
1- δ P c
= —F∏ij И - -ichLij И - Pifij ≥ 0. (19)
r + mi [ i ∖
The first term in expression (19) is the discounted flow of operating profits that a firm
in country i with productivity φ obtains from sales in country j. Note that this term
accounts for the fact that the firm may be hit by an (exogenous) exit shock during their
first period of existence in which no profits are forthcoming yet as recruitment of workers
takes one period. The second term describes the costs of recruiting, which arise before
production can start.
The flow of profits from sales to market j is given by
which are revenues in country j of a firm based in country i with productivity φ, Rij [^∖,
minus total costs of employing the necessary amount of workers Lij to achieve those
revenues including the costs to replace the workers who quit (at exogenous rate χ) and
the fixed costs (in units of the final good) to maintain the presence in market j. Note that
we assume that the domestic final output good is used for foreign market fixed costs.14
πij [^] Rij
m - (ws+Pi ci mχii) Lij m
- Pi fij ,
(20)
We may characterize the productivity level which makes a firm indifferent between
operating in a market or not by solving Πij∙ [^*j∙] = 0. This gives the zero cutoff-profit
14 One could alternatively posit that the foreign final output good is used for foreign fixed costs. Another
option would be to assume free trade in the final output good so that Pi = 1 in all countries. This choice
has no major qualitative implications for our findings.
13