Uncertain Productivity Growth
2 THEORETICAL FRAMEWORK
is finally sold in the destination country results as
XEt =
XDEt
τ
(9)
Transport costs are avoided if the investor decides to serve the foreign market through a new
affiliate. The wage rate w is determined in the homogeneous good industry Y , where the for-
eign country exhibits a lower wage rate than the investor’s home country due to a less efficient
production technology. The resulting fixed and variable cost structure with
-E < 1 and
IF
wF
1
WE τ θ
<1
(10)
is the proximity-concentration trade-off assumption, which is fundamental in recent trade models
dealing with international market entry strategies and represents the first crucial pillar in the
underlying model (Brainard, 1997, Helpman et al., 2004, and Yeaple, 2008).
2.3 The Evolution of Productivity
The major objective within the established theoretical framework is the analysis of firm-embedded
productivity, introduced as iït, and its impact on the optimal market entry mode under different
scenarios. Therefore, a more accurate coverage of possible productivity developments is necessary.
From a theoretical point of view productivity can evolve in three different manners over time.
1. iï stays constant over time (no productivity growth).
2. iï constantly increases over time (deterministic productivity growth).
3. iï exhibits a volatile productivity increase over time (stochastic productivity growth).
Analytically, these productivity evolutions can be easily modeled by using the following Geometric
Brownian motion denoted in differential notation as
diït = aiït dt + σtftdzt,
(11)
where the parameters α and σ are assumed to be time invariant and represent the growth rate
and extent of volatility, respectively. dzt is the increment of a standard Brownian motion zt with
dzt = etVdt and et ~ N(0,1)
(12)