Ziii + Zjji = (1 - μ)Ei.
(5)
3.2 Production and labor market
The production function for Z is a CES technology being identical in both
countries. It uses skilled labor (S) and unskilled labor (L), at a technical rate
of substitution of 1/(1 - ρ):
Ziii + Ziij = [aSρ + (1 - a)Lρ ] p , (6)
where a is a weighting parameter. Since all firms within a country face the
same homothetic technology and identical factor prices, the Z-sector input co-
efficients are identical across firms. Let wSi and wLi denote the factor rewards
for skilled and unskilled labor in country i. Skipping the arguments, these input
coefficients are determined as
1 1 1 -1
aLZi = μ 1-a ) p-1 [μ wsi ) p-1+μ wa ) p- 1] «
Γ n 1 1 -∣ - p
aszi = ( wSi ´ ~1 μ wi )p- 1+μ wL÷- )p- 1 . (8)
a a 1 -a
Perfect competition in the production of the homogeneous Z ensures zero profits
so that unit costs satisfy
aLZiwLi + aSZiwSi ≥ 1 ⊥ Ziii ≥ 0, Ziij ≥ 0 ∀ i,j ∈ {1, 2}, (9)
where ⊥ indicates that at least one of the adjacent conditions has to hold
with equality. Zero trade costs lead to an equalization of marginal costs across
countries.
The production of manufactures X uses both factors in fixed proportions
(see Markusen, 2002), where aLX and aSX are the corresponding input coeffi-
cients for production. The set-up of firms in the X-sector requires skilled labor
in order to produce firm-specific assets and blueprints as well as unskilled labor
to set up plant-specific assets (production facilities). In line with the literature,
we assume that fixed input requirements are highest for horizontal MNEs, lower
for vertical MNEs, and lowest for NEs. Specifically, national firms need 2 units
of skilled labor, while (horizontal and vertical) MNEs employ 2 + θ units. This
accounts for the higher firm-specific fixed costs of running a multinational net-