Unemployment in an Interdependent World

2 Model Setup

Our world consists of N potentially asymmetric countries, indexed by subscript i, with
i = 1, ..., N. Countries have work forces denoted by L_i and labor is the only factor of
production. Firms differ with respect to their productivity level φ as in Melitz (2003).
The labor market features search and matching frictions as in Mortensen and Pissarides
(1994). Our framework generalizes Felbermayr, Prat, and Schmerer (2008) to asymmetries
regarding country size, geographical location, and labor market institutions.

2.1 Demand for intermediate inputs

Similar to Egger and Kreickemeier (2009) and Felbermayr, Prat, and Schmerer (2008),
in each country firms produce a final output good Q under perfect competition. That
good is assembled from a continuum of intermediate inputs, indexed by ω, and supplied
by domestic and foreign firms who operate under conditions of monopolistic competition.
The final output good can be consumed or used by input producers. The aggregate
production function in country i is

σ

{(Mli)^ν-1 [   q[ω]^σ-1 dω{    ,

ω∈Ω_i

where q [ω] denotes the quantity of intermediate input ω, and σ > 1 is the elasticity of
substitution between any two varieties. The set of available intermediate inputs in country
i, Ω_i, has measure MM_i. The parameter ν ∈ (0,1) governs the extent of external economies
of scale:⁸ If ν = 0 the number of available varieties is irrelevant for total output. If
ν = 1 we obtain the case discussed by Krugman (1980) or Melitz (2003). The price index
corresponding to (1) is given by:

Pi=( MM- L,     ^{σ dω})¹ⁱ ■                  ⁽²⁾

where p[ω] is the price of a variety ω. We choose the price index of country one as the
num´eraire, i.e., P₁ = 1.

Similar to Melitz (2003), intermediate input firms are uniquely described by different
productivity levels φ and place of origin, so that we can substitute the firm index ω with
φ and index prices and quantities with country subscripts denoting place of origin and
destination. Due to flow fixed costs, not all firms find it optimal to serve all markets.
Serving foreign customers in country j from country i entails iceberg trade costs τij ≥ 1
(with τ _ii = 1 and τ _ij = τ j_i ) for all i and j. Hence, an intermediate goods producer in

⁸See, e.g., Blanchard and Giavazzi (2003) or Egger and Kreickemeier (2008b), where ν = 0; and
Felbermayr, Prat, and Schmerer (2008) where v ∈ [0, 1].

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