347
HOW TRADING FIRMS UPGRADE SKILLS 
AND TECHNOLOGY: THEORETICAL 
MODEL
MOJCA LINDIČ
1
 Received: 13 March 2015
Accepted: 28 October 2015
ABSTRACT: This paper studies the mechanisms of skill upgrading in trading firms by 
developing a theoretical model that relates the individual’s incentives for acquiring higher 
skills to the profit-maximizing behaviour of trading firms. The model shows that only the high 
ability individuals have incentives for acquiring higher skills, as long as they are compensated 
with higher wages after entering employment. Furthermore, high-productive firms have 
incentives for investing in higher technology, to employ high-skilled labour, and to engage in 
international trade. The decisions for technology dress-up and skill upgrading coincide with 
firm’s decisions to start importing and exporting as the latter requires higher technology and 
high-skilled labour. Contributions of the paper are twofold: gaining new insights by combining 
fragments of models on individual’s and firm’s behaviours, and broadening the content of the 
Melitz (2003) model by introducing importers and controlling for skilled and unskilled labour.
Keywords: skill upgrading, technology upgrading, trading firms.
JEL Classification: F12; J24; O30
DOI: 10.15458/85451.5
1. INTRODUCTION
The liberalisation of international trade increases firm’s productivity for two reasons; one 
is due to easier access to a better selection of advanced technologies and another is due to 
a better allocation of production factors. The latter channel was among others emphasized 
in the Melitz (2003) model, while the former was for example stressed in Bustos (2011b). 
The Melitz (2003) model explores the effects of trade on intra-industry reallocations and 
aggregate industry productivity by taking into account heterogeneous firms that differ 
regarding their level of productivity. The model concludes that only the most productive 
firms engage in exporting activities. The Melitz (2003) model represents groundwork in 
the recent trade literature and was used as a basis also in the Bustos (2011b) model, which 
explores the effects of trade liberalisation on skill upgrading in exporting firms, where the 
model also differentiates between high- and low-technology firms.
1
 University of Ljubljana, Faculty of Economics, Young Researcher, Ljubljana, Slovenia, e-mail: mojca.lindic@
ef.uni-lj.si
      ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015  |  347-369

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 348
This paper aims to fill the void in the international trade theory by broadening the theo-
retical models of Melitz (2003) and Bustos (2011b), and correspondingly including im-
ports to the model. By doing this, the model also explains recent empirical findings on the 
importance of importing as one of the drivers of firm’ s productivity gains. Evaluating trade 
liberalisation after China’s entry to the World Trade Organization, Bloom, Draca and Van 
Reenen (2011) find that the increased Chinese import competition increased the innova-
tions and adoption of new technologies, which in turn increased the productivity within 
firms, while between firms it transferred employment toward innovative and technologi-
cally advanced firms. The positive impact of importing on the firm’s productivity was con-
firmed also by Halpern, Koren and Szeidl (2011), studying the Hungarian data, Kasahara 
and Rodrigue (2008), studying the Chilean data, and Amiti and Konings (2007), study-
ing the Indonesian data. The latter study points out that these productivity increases are 
a consequence of importing high-quality intermediates, the enhanced diversification of 
inputs, and higher learning opportunities (Amiti, & Konings, 2007). Taking into account 
importers and exporters, Smeets and Warzynski (2010) confirm that both, exporting and 
importing, increase the firm’s productivity, while firms with the highest level of productiv-
ity are engaged in both trading activities. In relation to these findings, empirical papers 
also certify the positive impact of importing on exporting. Bas and Strauss-Kahn (2014) 
emphasize three channels through which importing affects exporting positively. First is 
the indirect productivity channel of increased productivity after importing, which can 
in turn have a positive effect on overcoming export costs. Second is a direct cost channel 
due to changing the input structure towards more cost-effective importing intermediates. 
Finally, through the quality/technology transfer, imported intermediate inputs can enable 
exporting products to be of such quality and technology levels, as desired in the export 
markets. Positive effects of importing on exporting were for example confirmed also by 
Feng, Li and Swenson (2012), studying the Chinese data.
In addition, since the individual’s decisions for acquiring higher skills later have an impor-
tant impact on the behaviour of profit-maximizing firms, another motivation for writing 
this paper was to combine specific individual’s and firm’s decisions. Since the existing 
trade models are based on broader, firm-level decisions, the impetus of the present paper 
is to explore more in depth also the behaviour of individuals and their decision for skill 
upgrading, as these decisions have in turn the effect on skill upgrading within a firm.
The model in this paper bases its framework on the models of Bustos (2011a, 2011b) and 
Melitz (2003), and on the work of Stark and others (see for example Stark, & Wang, 2001; 
Stark, Helmenstein, & Prskawetz, 1998; Stark, & Chau, 1998; and Stark, Helmenstein, & 
Prskawetz, 1997 for reference), who developed models on human capital formation. The 
model first explores the behaviour of individuals, who decide whether to invest in acquiring 
higher skills or not. In this part, the model differentiates between high ability and low abil-
ity individuals, where the individual’s ability level defines the cost level for acquiring skills. 
Upon the level of these costs, individuals decide whether to invest in obtaining the skills or 
not, where this decision relies also on their future wage level. Results suggest that only high 
ability individuals find it profitable to invest in acquiring additional skills, while they in turn 
demand higher wages after entering employment. These findings are then incorporated in 

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 349
the second part of the model, which focuses on exploring the behaviour of heterogeneous 
firms that decide on when to start investing in higher technology, and when to start engag-
ing in trading activities. In this part of the model, profit-maximizing firms differ upon their 
level of labour productivity, where the proxy for higher labour productivity are higher la-
bour costs, indicating a higher employment level of skilled employees. The latter judgement 
is backed up by the results from the first part of the model. Investing in higher technology 
and starting to import and export brings higher fixed costs, but decreases the level of firm’s 
marginal costs, and/or increases the employment of skilled workers, and/or increases reve-
nues. Findings from the second part suggest that the technologically advanced firms employ 
a higher number of skilled workers and that only the most productive firms find it profitable 
to start trading, investing in higher technology and skill upgrading.
This paper contributes to the literature in two ways. Firstly, since the mentioned empirical 
papers emphasized the importance of differentiating between importing and exporting, 
this model accounts for both. Therefore, the model broadens the content of the papers of 
Bustos (2011a, 2011b) and Melitz (2003), who take into account only exporters. Secondly, 
while other theoretical trade models only analysed decisions from a firm’s point of view, 
this paper’s contribution is to combine behaviour of individuals and firms in one model of 
trade. The model therefore broadens the existing trade models by analysing the behaviour 
of individuals and their decision for skill upgrading. This is later incorporated in the firm-
level decisions, by taking into account the firm’s labour demand and productivity.
The remainder of the paper is organised in the following manner: the next section pre-
sents a brief introduction of the theoretical background, which is further on used as a 
reference point to the theoretical model, included in the third section. The last section 
summarises the main findings and includes a conclusion.
2. LITERATURE REVIEW
Melitz (2003) developed an important theoretical model, which explores the effects of 
trade on intra-industry reallocations and aggregate industry productivity. The model uses 
heterogeneous firms that differ regarding the level of productivity, where firms with high-
er levels of productivity produce the same amount of products at lower marginal costs. 
After observing their level of productivity, firms decide to exit or enter the market, where 
new entrants have a lower level of productivity and a higher probability to exit than firms 
that are already on the market. When exploring the effects of trade, the author only fo-
cuses on exports. After firms start exporting, they are faced with higher costs for two rea-
sons; one reason is higher per-unit trade costs, and the other reason are higher fixed costs. 
The latter can be explained as a consequence of establishing new networks, adapting the 
product to the new market, setting up new distribution channels, etc. After introducing 
the possibility to export to the model, firms again observe their level of productivity. Once 
more, the least productive firms decide to exit the market, the firms with medium-level of 
productivity decide to serve the domestic market, while the most productive firms serve 
the domestic market and export (Melitz, 2003).

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 350
The Melitz (2003) model presents the groundwork for many subsequent theoretical mod-
els on trade. Bustos upgraded the Melitz (2003) model by including technology upgrading 
(Bustos, 2011a) and skill upgrading (Bustos, 2011b) into the model. In the first model, 
Bustos (2011a) takes into account profit maximizing firms which decide whether to start 
exporting and whether to invest in higher technology. By adopting higher technology, 
firms pay higher fixed production costs, while their marginal costs are reduced. After 
proving that using high technology and serving the domestic market is always dominated 
by some other choice, firms form four different groups: the least productive firms exit, 
the low productive firms use low technology and serve the domestic market, the medium 
productive firms still use low technology but also export, while only the most productive 
firms upgrade their technology level and export (Bustos, 2011a).
The gains of different production factors, labour and capital to be precise, were included 
already in the Heckscher-Ohlin model (the H-O model), which predicts that countries 
adjust their production and trading on behalf of their factor endowments. The Stolper-
Samuelson theorem in the H-O model indicates that the real returns of the factor-abun-
dant owners increase, and the real returns of the owners of the other factor decrease as a 
consequence of trade (Krugman, Obstfeld, & Melitz, 2012). Relating to the conclusions 
of the H-O model, the relative demand for skilled workers – a scarce factor in develop-
ing countries – should decrease after trade liberalisation. However, the empirical find-
ings show the opposite (see for example Goldberg, & Pavcnik, 2007). Bustos (2011b) has 
filled the gap in trade literature, by exploring the effects of trade liberalisation on skill 
upgrading in exporting firms. The model accounts for two categories of workers, skilled 
and unskilled. As in the previous model (Bustos, 2011a), firms form four different groups 
before trade liberalisation, whereas after liberalisation, they form six groups in total. The 
least productive firms exit. Among the firms that did not export before trade liberalisa-
tion, a fraction of these firms continue serving the domestic market, use low technology 
and downgrade skills; another fraction of these firms still uses low technology, but they 
start exporting and downgrade skills, while the most productive of these firms start to ex-
port, upgrade their technology and skills. Firms that were already exporting before trade 
liberalisation and used low technology continue to export, switch to high technology and 
upgrade skills. Finally, the most productive firms that were exporting and using high tech-
nology before trade liberalisation continue exporting and using high technology, but they 
downgrade skills. The conclusions of the theoretical model were later tested also with the 
empirical model, which studies the effect of Brazil’s tariff reduction on Argentinian firms. 
The model’s predictions that low-technology firms downgrade skills and that firms in the 
upper-middle range of productivity distribution upgrade skills after trade liberalisation 
are consistent with the empirical findings. On the other hand, the prediction that the 
most productive high-technology firms downgrade skills after trade liberalisation is not 
consistent with the empirical findings (Bustos, 2011b).
Finally, as presented in the introduction, it is important to control for the imports in trade 
models, as imports usually serve as a prerequisite to exporting activities (see for exam-
ple empirical studies of Damijan, & Kostevc, 2015; and Altomonte, & Békés, 2010). To 
be precise, by studying the connections between importing, exporting and innovation in 

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 351
Spanish firms, Damijan and Kostevc (2015) find that importing enables firms to first start 
with process and product innovation, and later also with exporting. In addition, export-
ing stimulates further innovation. Although empirical studies show the importance of 
importing, the latter is infrequently included in the theoretical models of trade. One of 
the models that does account for importing is the theoretical model by Amiti and Davis 
(2011), who base their theoretical model on the Melitz (2003) model and control for im-
ports, by including additional costs of importing in the model.
The theoretical model in this paper combines different aspects of the models, presented in 
the literature review and adds also a thorough analysis of individual’s behaviour and their 
decision for skill upgrading. It is necessary to study these decisions, as they later have an 
important impact on the firm’s productivity level, labour demand and labour costs. For 
this purpose, several papers of Stark and others were taken into account (see for example 
Stark, & Wang, 2001; Stark, Helmenstein, & Prskawetz, 1998; Stark, & Chau, 1998; and 
Stark, Helmenstein, & Prskawetz, 1997 for reference). The primary focus is on the paper 
by Stark and Wang (2001), who developed a model of human capital formation in an en-
vironment with and without migration. I bring the model into use as a benchmark and use 
it for explaining the individual’s choice for skill upgrading.
3. THE MODEL
This section presents a simple theoretical model, the first part of which studies the deci-
sion of individuals to invest in acquiring additional skills. The findings of the first part of 
the model are later incorporated in the second part, which analyses the decision of hetero-
geneous firms to start trading and investing in higher technology.
3.1 Setup of the Model
The model takes into account the country, endowed with heterogeneous workforce and 
heterogeneous firms. Firms differ according to the different productivity levels, which are 
the end result of different technologies used, and in regards to firms being included in 
international trade. Concerning the latter, the model differentiates between importing and 
exporting firms, whereas concerning the former, it differentiates between high-technolo-
gy and low-technology firms.
3.2 Individuals
This part of the theoretical model follows the work of Stark and others (see for example 
Stark, & Wang, 2001; Stark, Helmenstein, & Prskawetz, 1998; Stark, & Chau, 1998; and 
Stark, Helmenstein, & Prskawetz, 1997 for reference). Each individual in the economy 
is endowed with a certain amount of efficiency units (θ), which represents the ability of 
a worker. If the average ability of workers in the economy is θ, and the abilities of high 

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 352
ability and low ability workers are θ
S
 and θ
U
, respectively, the following applies: θ
U
 < θ < 
θ
S
. For brevity, the model denotes all individuals with above-average abilities by θ
S
, and 
individuals with below-average abilities by θ
U
. Derivations of the model therefore assume 
two ability levels.
After individuals evaluate their level of ability, they decide whether to invest in acquiring 
higher skills or not. It is assumed that the costs for acquiring higher skill levels are differ-
ent for individuals with different abilities. To be precise, costs for acquiring human capital 
for high ability individuals (k
S
) are lower than the costs of low ability individuals (k
U
); i.e. 
k
U
 > k
S
 > 1. All individuals have an opportunity to achieve higher levels of education and 
become skilled. However, since the costs for acquiring the highest levels of human capital 
are too high for low ability individuals, they will be able to obtain the human capital only 
up to a certain level and will not be able to achieve above-average skill levels.
Individuals with higher abilities will have incentives for acquiring above-average levels of 
human capital, if their costs for acquiring high skill levels will be later compensated with 
higher gross earnings when they are employed. In order to emphasise the period after 
individuals acquire skills, the model denotes high ability, high skilled individuals with Θ
S
 
and low ability, low skilled individuals with Θ
U
. The gross earnings of high ability, high 
skilled workers (w
S
) should therefore be higher than the gross earnings of low ability, low 
skilled workers (w
U
); i.e. 0 < w
U
 < w
S
. Thus, each individual initially bears the costs of ac-
quiring human capital. However, the costs are later transmitted onto firms in the form of 
higher expected gross earnings of high ability, high skilled individuals.
The function of gross earnings for unskilled workers is the following:
w
U
(Θ
U
) = λ[ln(Θ
U
 + 1)] – k
U
Θ
U
,   (1)
where the first term on the right hand side (λ[ln(Θ
U
 + 1)]) represents personal returns to 
human capital, and the last term represents costs of acquiring human capital. The param-
eter λ is assumed to be positive. Furthermore, for convenience, the following is assumed 
as well: λ > k
U
 > k
S
 > 1.
Similarly, the function of gross earnings of skilled workers can be written as:
w
S
(Θ
S
) = λ [ln(Θ
S
 + 1)] – k
S
Θ
S
.    (2)
The succeeding claim proves that the optimal skill level of workers with low ability and low 
skills is lower than the optimal skill level of workers with high ability and high skills. It is 
important to prove that in order to make further inferences on the wage level of skilled 
workers.
Claim 1: The optimal skill level of individuals with low ability is lower than the optimal 
skill level of individuals with high ability.

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 353
Proof: To get the optimal skill level of high and low ability individuals, first order condi-
tions of gross earnings for each level of skills are derived.
()
1
UU
U
UU
w
k
λ ∂Θ
= −
∂Θ Θ +
()
1
SS
S
SS
w
k
λ ∂Θ
= −
∂Θ Θ +
When checking the maxima, the following optimal skill levels of workers are calculated. 
Optimal skill level of the low ability workers (Θ
U
*
) is:
Θ
U
*
 = λ(k
U
)
-1
 – 1.     (3)
Optimal skill level of the high ability workers (Θ
S
*
) is:
Θ
S
*
 = λ(k
S
)
-1
 – 1.     (4)
When comparing both optimal levels and taking into account that k
S
 < k
U
, it is confirmed 
that Θ
U
*
 < Θ
S
*
. ■
Although the previous claim confirms that the high ability workers will have higher op-
timal skill levels than the low ability workers, it also has to be proven that the high ability 
workers will have incentives to invest in their educational attainment and make the best 
of their potential. As mentioned before, high ability workers will have incentives to invest 
in their educational attainment and become skilled, if their future income would increase 
because of that investment. By inserting optimal skill levels of high ability and low ability 
individuals (expressions (3) and (4)) in the functions of gross earnings (expressions (1) 
and (2)), the following can be derived:
w
U
(Θ
U
*
) < w
S
(Θ
S
*
)
λ[ln(λ / k
U
)] – k
U
 [(λ / k
U
) – 1] < λ[ln(λ / k
S
)] – k
S
 [(λ / k
S
) – 1].
Taking into account the assumption λ > k
U
 > k
S
 > 1, it can be confirmed that the gross 
earnings of workers with low optimal ability (w
U
(Θ
U
*
)) are lower, compared to the gross 
earnings of workers with high optimal ability (w
S
(Θ
S
*
)).
For consistency purposes it was also confirmed that w
U
(Θ
U
*
) > 0. The proof for this claim 
can be found in Appendix A.
As only the high ability individuals have incentives to invest in acquiring higher skills, 
total workforce (L) in the country comprises high ability, high skilled workers (L
S
) and 
low ability, low skilled workers (L
U
). Workforce in the country as a whole is therefore the 
following: L = L
S
 + L
U
.

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 354
3.3 Firms
This part of the model takes into account heterogeneous profit-maximizing firms that 
differ in their level of labour productivity and decide whether to adopt a skill-intensive 
technology, and whether to start exporting and importing. The previous part of the model 
concluded that skilled workers have a higher level of ability and can hence be employed in 
a more productive way. This finding will be accounted for in the current part of the model, 
when taking into account the level of firm’s labour productivity. This part of the theoreti-
cal model follows the work of Melitz and Redding (2014), Amiti and Davis (2011), Bustos 
(2011a and 2011b), and Melitz (2003).
3.3.1 Preferences
Following Melitz and Redding (2014), and Bustos (2011a, 2011b), this part considers two 
symmetric countries that engage in bilateral trade after trade liberalisation. Consumer 
preferences are described by a continuum of horizontally-differentiated varieties and are 
assumed to take the Constant Elasticity of Substitution (CES) form:
1
1
0
()
M
Qq d
σ
σ
σ
σ
ωω
−
−

=


∫
,
where ω defines a particular variety of a product, M is the number of existing varieties, 
and σ is a constant elasticity of substitution. The following applies: 1 / (1 ) σρ = − , where 
ρ is a parameter which determines the constant elasticity of substitution, so that 1 σ >
applies. These preferences define the following demand function for each variety ω: 
1
() () q XP p
σσ
ωω
−−
= . Here, X represents the aggregate spending level of consumers, p(ω) 
the price of each variety, and P the price index, equal to:
1
1
1
0
()
M
Pp d
σ
σ
ωω
−
−

=


∫
.
3.3.2 Firm entry and exit
Following Melitz and Redding (2014), and Bustos (2011b), firms pay a sunk fixed entry 
cost f
X
 to enter an industry. After that, firms draw the level of their productivity φ from a 
cumulative distribution G(φ) and with regard to this level they decide whether to exit the 
market or to produce.

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 355
3.3.3 Technology and factor heterogeneity
Products are produced by using a composite factor of production, L, which is composed 
of skilled labour (L
S
) and unskilled labour (L
U
). From the previous subchapter, it follows 
that skilled workers have a higher level of ability, which is reflected in their higher wage 
level w
U
 < w
S
. Furthermore, following Melitz and Redding (2014), and Bustos (2011b), by 
paying an additional fixed cost, firms can upgrade to a high-technology level h, which is 
also more skill-intensive and reduces the firm’ s marginal costs of production. On the other 
hand, the low-technology level l is less skill-intensive and demands lower fixed costs for 
producing goods.
Total costs for low-technology firms are as follows:
1
l SU
q
TC f w w
ββ
φ
−

= +


,    (5)
where f denotes fixed costs, w
S
 and w
U
 are wages of skilled and unskilled workers, respective-
ly, q is the level of firm’s output, φ is productivity level, and (0,1) β ∈ denotes skill intensity.
On the other hand, firms can invest in higher skill-intensive technology. T otal costs for the 
latter can be defined by:
1
h SU
q
TC f w w
αα
η
γφ
−

= +


,    (6)
where η > 1, γ > 1, (0,1) α ∈ , and α > ß. The model assumes that due to a smaller relative 
share of skilled employees in low-technology firms, who use low-technology equipment, 
the labour productivity in low-technology firms is lower than the labour productivity in 
high-technology firms. On the other hand, as a result of investing in skill-intensive tech-
nology, high-technology firms change their skill structure by employing a higher number 
of high ability, high skilled employees. Accordingly, the model assumes that skill-intensive 
technology is brought into use more productively when employing relatively more skilled 
individuals with high abilities. Relating to the findings from the first part, which studied 
the incentives for individual’s skill upgrading, the model also assumes that firms with 
higher labour productivity have higher labour costs, as a consequence of a higher em-
ployment of skilled workers, who earn higher wages; w
S
 > w
U
. Higher labour costs can 
therefore be considered as a proxy for higher employment of skilled workers. These as-
sumptions are consistent with the findings of empirical studies, which confirm that big-
ger firms use more technology-advanced equipment, pay higher wages and employ more 
productive workers (Idson, & Oi, 1999). Similar characteristics have also been confirmed 
in trading firms, which are larger in size and more productive (Altomonte, & Békés, 2010). 
These conclusions are reflected in the assumption that α > ß (expressions (5) and (6)), 
when defining the total costs of low- and high-technology firms.

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 356
3.3.4 International activities of firms
The model is built as a 2-stage model, where costs of trade decrease significantly only in 
the second stage, as a consequence of trade liberalisation. In the first stage, firms decide 
whether to invest in skill-intensive high-technology, whereas in the second stage, firms 
decide whether to engage in trading activities. Similarly as in Melitz and Redding (2014), 
and Bustos (2011b), firms decide to start exporting after realising their level of productiv-
ity, φ, and taking into account the higher costs of exporting. On the one hand, additional 
fixed costs of exporting, f
E
, arise from establishing new sales channels, advertising, adapt-
ing to new laws and rules, etc., while on the other, firms also have to pay additional iceberg 
variable trade costs τ, meaning that τ number of units have to be shipped abroad in order 
for one unit to arrive, where τ > 1 (Melitz, & Redding, 2014). For very similar reasons as in 
the case of exports, importing also entails higher fixed costs, denoted by f
I
 (Amiti, & Da-
vis, 2011). Additional costs of exporting and importing make an assortment of the most 
productive firms that can afford to endure higher costs.
3.3.5 Firm behaviour
Some additional assumptions concerning costs and the change in productivity levels are made 
below. As introduced earlier, this model is of a two-stage type, where in the first stage, firms 
decide whether to invest in high-technology or not and in the second stage, after trade liber-
alisation, firms decide whether to engage in international activities or not. When firms start 
importing, they have access to cheaper technology and/or access to cheaper intermediates. 
It is therefore anticipated that importing increases the productivity of firms for two different 
reasons. First, importing intermediates allows other factors of production to be used more 
productively. Second, importing more affordable technology equipment in turn increases the 
firm’s productivity. Accordingly, the level of labour productivity in firms increases after im-
porting. The model also assumes the fixed costs of acquiring high-technology are higher than 
the fixed costs of importing; i.e. f
I
 < fη. The reason behind this assumption is that when com-
paring the technology level of importing low-technology firms and high-technology firms, 
which invest in technology within their own R&D departments, it is assumed that the increase 
in the productivity level will not be as big in low-technology firms that start importing, com-
pared to the productivity increase in firms that start investing in high-technology. Although 
low-technology firms still have a more affordable option for increasing their level of produc-
tivity through importing, the benefits are not as high, compared to investing into developing 
custom-made high-technology equipment within firms. Finally, due to exporting, firms sell 
their products to a higher number of customers and therefore reach higher revenues.
The following paragraphs describe a two-stage model, where in each of the steps, firms de-
cide between several options and choose the most profitable one. It is assumed that in the 
first stage (before trade liberalisation) importing and exporting is beyond the reach due to 
high costs, so firms can only choose whether to invest in higher technology or not. In the 
second step, after trade liberalisation, firms have an option to start importing, exporting or 
both. The following diagram summarises the steps of the model.

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 357
Figure 1: The flow-chart of events in the two-stage model
SKILL AND TECHNOLOGY UPGRADING IN TRADING FIRMS 10
Figure 1: The flow-chart of events in the two-stage model 
In the listed steps, firms compare several different profit options, which are described next.
Following Melitz and Redding (2014), and Bustos (2011b), the market structure is of 
monopolistic competition type, where each firm chooses its price in order to maximise its 
profits. The profit maximising price is a constant mark-up over marginal costs. In the first 
stage, low-technology firms charge the price
ϕσ
σ
ββ −
−
=
1
1
US
l
ww
p ,
while high-technology firms charge the price
γ ϕσ
σ
αα −
−
=
1
1
US
h
ww
p .
Firms compare the following two options: 
a) No trade, use low technology: 
ββ
σ
ϕ
ϕπ
−
−=
1
)(
)(
US
l
l
w fw
r
,
where π
l
( φ) are the total profits of firms with low-technology levels, φ is the level of 
labour productivity, and r
l
( φ) are revenues, with
σ
ββ
σ
ϕσ
σ
ϕ
−
−
−
−
=
1
1
1
)
1
() (
US
l
ww
XP r .
b) No trade, use high technology: 
αα
η
σ
ϕ
ϕπ
−
−=
1
)(
)(
US
h
h
ww f
r
,
where π
h
( φ) are the total profits of firms with high-technology levels, and r
h
( φ) are the 
revenues, with
σ
αα
σ
γ ϕσ
σ
ϕ
−
−
−
−
=
1
1
1
)
1
() (
US
h
ww
XP r .
According to Melitz and Redding (2014), firms first assess their level of productivity and 
upon that decide whether to stay and produce or whether to exit the market. If they stay, they 
maximise the level of their profits with regard to the level of their productivity. This generates 
a survival bound productivity φ
*
, returning zero profits: π ( φ
*
) = 0. 
FIRMS 
Exit
Stay on 
the market
Low-technology
Domestic 
only                                                                         
Import Export
Import and 
export
High-technology
Domestic 
only                                                                         
Import Export
Import and 
export
In the listed steps, firms compare several different profit options, which are described 
next. Following Melitz and Redding (2014), and Bustos (2011b), the market structure is of 
monopolistic competition type, where each firm chooses its price in order to maximise its 
profits. The profit maximising price is a constant mark-up over marginal costs. In the first 
stage, low-technology firms charge the price
1
1
SU
l
ww
p
ββ
σ
σφ
−
=
−
,
while high-technology firms charge the price
1
1
SU
h
ww
p
αα
σ
σ γφ
−
=
−
.
Firms compare the following two options:
a) No trade, use low technology:
1
()
()
l
l SU
r
fw w
ββ
φ
πφ
σ
−
= − ,
where π
l
(φ) are the total profits of firms with low-technology levels, φ is the level of labour 
productivity, and r
l
(φ) are revenues, with 
1
11
() ( )
1
SU
l
ww
r XP
ββ
σσ
σ
φ
σφ
−
−−
=
−
.
b) No trade, use high technology:
1
()
()
h
h SU
r
f ww
αα
φ
πφ η
σ
−
= − ,
where π
h
(φ) are the total profits of firms with high-technology levels, and r
h
(φ) are the 
revenues, with 
1
11
() ( )
1
SU
h
ww
r XP
αα
σσ
σ
φ
σ γφ
−
−−
=
−
.

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 358
According to Melitz and Redding (2014), firms first assess their level of productivity and 
upon that decide whether to stay and produce or whether to exit the market. If they stay, 
they maximise the level of their profits with regard to the level of their productivity. This 
generates a survival bound productivity φ
*
, returning zero profits: π (φ
*
) = 0.
When comparing zero-profit bounds of low- and high-technology firms in the first stage 
of the model; i.e.
() ()
() ()
lh
lh l h
rr
fW f W
φφ
πφ πφ η
σσ
=⇔−=− ,
it follows that due to the higher fixed costs of adopting new technology, only the most 
productive firms will be able to afford investing in high-technology. For convenience, 
l
W 
is denoted as total labour costs in low-technology firms (
1
l SU
W ww
ββ −
= ), and 
h
W as total la-
bour costs in high-technology firms (
1
h SU
W ww
αα −
= ). Least productive firms will therefore 
use low-technology. Furthermore, the exit bound productivity, φ
*
, is defined by:
1
**
11
()0
ll
Af W
σ
σσ
πφ φ
−−
=⇔= ,
where 
1
1
1
() A
XP
σ
σ
ρ
−
= .
To get the level of productivity, above which a firm finds it profitable to invest in high-
technology, φ
h
, the subsequent two expressions are compared: () ()
lh hh
πφ πφ = , yielding 
the following:
[ ]
1
1
( )( )
h
h hl l
W
Af W W W
σ
φη
γ
−
=−− .
Now, it must apply that 
*
h
φφ <
, which is true as long as 
1
11
() ( ) ( )
h
l hl l
W
W WW W
σ
σσ
η
γ
−−
<− − . 
The latter expression stands when the wages in high-technology firms (
h
W ) are signifi-
cantly higher than the wages in low-technology firms (
l
W ). This is consistent with the 
findings from the first part of the paper, which concludes that higher wages signal a higher 
employment of skilled workers. I believe this assumption is valid as it confirms previous 
empirical findings that firms, which use more technology-advanced equipment, also pay 
higher wages, and employ more productive workers (see for example Idson, & Oi, 1999). 
Therefore, only the most productive firms use skill-intensive technology and upgrade 
skills. In addition, taking into account the last term in the upper expression ()
h
l
W
W
γ
− , the 
relative increase in wages due to investing in higher technology has to be higher than the 
relative decrease in marginal costs; i.e. 
h
l
W
W
γ > , which additionally emphasises the impor-
tance of higher employment of skilled workers in high-technology firms.

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 359
After trade liberalisation in the second stage, low-technology firms compare the following 
four options:
a) No trade, use low technology:
1
()
()
l
l SU
r
fw w
ββ
φ
πφ
σ
−
= − ,
where π
l
(φ) are the total profits of firms with low-technology levels, φ is the level of labour 
productivity, and r
l
(φ) are the revenues, with 
1
11
() ( )
1
SU
l
ww
r XP
ββ
σσ
σ
φ
σφ
−
−−
=
−
.
b) Start importing, use low technology:
When low-technology firms start importing, their costs and productivity level increase 
and add up to:
1
II
I
l I SU I
l
q
TC f f w w
ββ
γφ
−

=++


, where 
I
ββα << , and 1
I
l
γγ << . 
Introducing the factors 
I
β and 
I
l
γ enables controlling for the decrease in marginal costs 
and the changes of the skill structure in favour of the skilled employees after low-technology 
firms start importing. However, as explained above, the increase in the productivity level is 
not as big as it would be if the firms invested in developing the custom-made technology 
within their own R&D departments. Firms charge the price: 
1
1
II
I SU
l I
l
ww
p
ββ
σ
σ γφ
−
=
−
. Tak-
ing these facts into account, profit is as follows:
1
()
() ( )
II
I
I l
l I SU
r
f fww
ββ
φ
πφ
σ
−
= −+ ,
where ()
I
l
πφ are the total profits of low-technology firms that start importing, and ()
I
l
r φ 
are the revenues, with 
1
11
() ( )
1
II
I SU
l I
l
ww
r XP
ββ
σσ
σ
φ
σ γφ
−
−−
=
−
.
c) Start exporting, use low technology:
When low-technology firms start exporting, their costs add up to: 
1 E
l E SU
q
TC f f w w
ββ
τ
φ
−

=++


.
Consequently, firms charge the price: 
1
1
E SU
l
ww
p
ββ
τ σ
σφ
−
=
−
.
Taking these facts into account, the profit is:
1
()
() ( )
E
E l
l E SU
r
f f ww
ββ
φ
πφ
σ
−
= −+ ,
where ()
E
l
πφ are the total profits of low-technology firms that start exporting, and ()
E
l
r φ 
are the revenues, with 
1
11
() ( )
1
E SU
l
ww
r XP
ββ
σσ
τ σ
φ
σφ
−
−−
=
−
.

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 360
d) Start importing and exporting, use low technology:
When low-technology firms start importing and exporting, their costs add up to: 
1
II
IE
l I E SU I
l
q
TC f f f w w
ββ
τ
γφ
−

=+++


. 
Consequently, firms charge the price: 
1
1
II
IE SU
l I
l
ww
p
ββ
τ σ
σ γφ
−
=
−
. 
Taking these facts into account, the profit is:
1
()
() ( )
II
IE
IE l
l I ESU
r
f f f ww
ββ
φ
πφ
σ
−
= −++ ,
where ()
IE
l
πφ are the total profits of low-technology firms that start importing and ex-
porting, and ()
IE
l
r φ are the revenues, with 
1
11
() ( )
1
II
IE SU
l I
l
ww
r XP
ββ
σσ
τ σ
φ
σ γφ
−
−−
=
−
.
When comparing the zero-profit bounds in this stage of the model, the assumption of 
identical countries is considered (Bustos, 2011a), from which it follows that the price in-
dex (P) and the expenditure level (X) are the same at home and abroad. First, the zero-
profit bounds of low-technology firms that do not engage in international activities are 
compared to the bounds of those which start importing in the second stage of the model:
() ()
() () ( )
I
II ll
l l l Il
rr
fW f f W
φφ
πφ πφ
σσ
= ⇔ −= −+ .
For convenience, I again used the abbreviation for the total labour costs in low-technol-
ogy firms (W
l
) and denoted the total labour costs of importing low-technology firms by
1
II
I
l SU
W ww
ββ −
= . It follows that only the most productive low-technology firms will be able 
to afford paying higher fixed costs of importing, while the least productive low-technology 
firms will continue serving the domestic market. To get the level of productivity, above 
which a low-technology firm finds it profitable to start importing, 
I
l
φ , one compares the 
subsequent two expressions: () ()
I II
ll l l
πφ πφ = , and gets the following:
1
1
() ( )
I
II I l
l l l Il l I
l
W
A f W W fW W
σ
φ
γ
−
 = −+ −

.
The expression 
* I
l
φφ < applies, as long as
1 1
11 1
() ( ) ( )
I
II l
l l l Il l I
l
W
f W f W W fW W
σ
σσ σ
γ
−− −
 < −+ −

. 
This is true when the wages in importing low-technology firms (
I
l
W ) are significantly 
higher than the wages in low-technology firms (
l
W ), which again signals a higher employ-
ment level of skilled workers, as follows from the first part of the model. This assumption 
is also valid, since the empirical data confirms that importing firms are on average larger 
and pay higher wages (see for example Altomonte, & Békés, 2010). In addition, taking into 
account the last term in the upper expression
()
I
l
l I
l
W
W
γ
−
, the relative increase in wages due 

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 361
to importing has to be higher than the relative decrease in marginal costs after the start of 
importing; i.e. 
I
I l
l
l
W
W
γ > . This statement corresponds to the initial assumption that the de-
crease in marginal costs due to imports is lower than it would be, should the firms invest 
in developing custom-made technology within their own R&D departments.
Furthermore, when comparing the zero-profit bounds of low-technology firms that do 
not engage in international activities and of those which start exporting in the second 
stage of the model:
() ()
() () ( )
E
E ll
l l l El
rr
fW f f W
φφ
πφ πφ
σσ
= ⇔ −= −+ ,
it follows that exporting low-technology firms do not invest in upgrading their skill structure 
nor do they invest in acquiring lower marginal costs. Therefore, since the productivity level 
of low-productive firms stays the same after they start exporting, low-technology firms will 
export only if the costs of exporting are lower than the increase in revenues after the start of 
exporting. However, following Melitz and Redding (2014), it is assumed that the fixed costs 
of exporting are too high for low-technology firms and therefore present a selection, so that 
only the most productive firms start exporting. As a result, firms that do not invest in acquir-
ing a higher level of productivity – either through importing or through investing in higher 
technology – cannot start exporting since their productivity level is too low.
In addition, the zero-profit bounds of low-technology firms which do not engage in inter-
national activities and of those that start importing and exporting in the second stage of 
the model, are compared with the following expressions:
() ()
() () ( )
IE
IE I ll
l l l I El
rr
fW f f f W
φφ
πφ π φ
σσ
= ⇔ − = −++ .
In relation to the upper comparison, low-technology firms will find engaging in importing 
and exporting activities profitable only if the increase in revenues and productivity level is 
bigger than the increase in costs of exporting and importing. To get the level of productivity, 
above which a low-technology firm finds it profitable to start importing and exporting,
IE
l
φ , 
the subsequent two expressions are compared: () ()
IE IE IE
ll l l
πφ π φ = , yielding the following:
1
1
( )( ) ) ( )
IE I I I
l ll I E l ll I
l
A f WW f f W WW
σ
τ
φ
γ
−
 = −++ −

.
This allows us to check when the productivity level of low-technology firms that import (
I
l
φ ) is 
lower than the productivity level of low-technology firms that export and import (
IE
l
φ ): 
11
11
1
() ( ) () ( )( )
I I E I II I II
l l ll I l ll ll I E l ll II
ll
f WW f W WW f WW f f W WW
σσ
τ
φφ
γγ
−−
 <⇔ −+ −< −++ −

. 
Since f
E
 > 0 and τ > 1, it follows that 
I IE
ll
φφ < , when the wages in importing low-technology 
firms (
I
l
W ) are significantly higher than the wages in low-technology firms (
l
W ), which was 
already assumed. Therefore, only the most productive low-technology firms that will be 
able to compensate for higher exporting costs will start exporting and importing.

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 362
To sum up, after trade liberalisation in the second stage of the model, only the most produc-
tive low-technology firms choose to upgrade skills and to start exporting and importing, 
less productive low-technology firms only import, and the least productive low-technology 
firms continue serving the domestic market. On the other hand, low-technology firms will 
not decide to engage in exporting activities without increasing their level of productivity by 
importing, as their productivity level would be too low to bear exporting costs.
The model now focuses on evaluating the following four options of high-technology firms 
after trade liberalisation in the second stage:
a)No trade, use high technology:
1
()
()
h
h SU
r
f ww
αα
φ
πφ η
σ
−
= − ,
where π
h
(φ) are the total profits of firms with high-technology levels, and r
h
(φ) are the 
revenues, with 
1
11
() ( )
1
SU
h
ww
r XP
αα
σσ
σ
φ
σ γφ
−
−−
=
−
.
b) Start importing, use high technology:
When high-technology firms start importing, their costs and productivity level in-
crease and add up to: 
1
II
I
h I SU I
h
q
TC f f w w
αα
η
γφ
−

= ++


, where 1
II
ββαα <<<< , 
and 
II
lh
γγγ << . Introducing factors 
I
α and 
I
h
γ enables controlling for the increase 
in productivity level and the changes in skill structure in favour of the skilled employ-
ees after high-technology firms start importing. In addition, firms charge the price: 
1
1
II
I SU
h I
h
ww
p
αα
σ
σ γφ
−
=
−
. Taking these facts into account, the profit is:
1
()
() ( )
II
I
I h
h I SU
r
f fww
αα
φ
πφ η
σ
−
=−+ ,
where ()
I
h
πφ are the total profits of high-technology firms that start importing, and ()
I
h
r φ 
are the revenues, with 
1
11
() ( )
1
II
I SU
h I
h
ww
r XP
αα
σσ
σ
φ
σ γφ
−
−−
=
−
.
c)Start exporting, use high technology:
When high-technology firms start exporting, their costs add up to: 
1 E
h E SU
q
TC f f w w
αα
τ
η
γφ
−

= ++


. 
Consequently, firms charge the price: 
1
1
E SU
h
ww
p
αα
τ σ
σ γφ
−
=
−
. 

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 363
Taking these facts into account, profit is as follows:
1
()
() ( )
E
E h
h E SU
r
f f ww
αα
φ
πφ η
σ
−
=−+ ,
where ()
E
h
πφ are the total profits of high-technology firms that start exporting, and ()
E
h
r φ 
are the revenues, with 
1
11
() ( )
1
E SU
h
ww
r XP
αα
σσ
τ σ
φ
σ γφ
−
−−
=
−
.
d) Start importing and exporting, use high technology:
When high-technology firms start importing and exporting, their costs add up to: 
1
II
IE
h I E SU I
h
q
TC f f f w w
αα
τ
η
γφ
−

= +++


. 
Consequently, firms charge the price: 
1
1
II
IE SU
h I
h
ww
p
αα
τ σ
σ γφ
−
=
−
. 
Taking these facts into account, the profit is:
1
()
() ( )
E
E l
l E SU
r
f f ww
ββ
φ
πφ
σ
−
= −+ ,
where ()
IE
h
πφ are the total profits of high-technology firms that start importing and ex-
porting, and ()
IE
h
r φ are the revenues, with 
1
11
() ( )
1
II
IE SU
h I
h
ww
r XP
αα
σσ
τ σ
φ
σ γφ
−
−−
=
−
.
The following two expressions are considered when comparing the zero-profit bounds of 
high-technology firms that do not engage in international activities and of those which 
start importing in the second stage of the model:
() ()
() () ( )
I
II hh
h h h Ih
rr
fW f fW
φφ
πφ πφ η η
σσ
=⇔−=−+
.
For convenience, the abbreviation for the total labour costs in high-technology firms (W
h
) 
is applied, while total labour costs of importing high-technology firms are denoted by
1
II
I
h SU
W ww
αα −
= . To calculate the level of productivity in importing high-technology firms, 
I
h
φ , the subsequent two expressions are compared: () ()
I II
hh hh
πφ πφ = , yielding the following:
1
1
()
II
II I h hh
h h h Ih I
h
WW
A f W W fW
σ
γγ
φη
γγ
−
−
 = −+

.
In order for this expression to be positive, 0
I
h
φ > , 
I
h
γ and γ must not be too far apart. This 
means that the marginal cost reduction of high-technology firms that do not engage in in-
ternational activities and of those which start importing in the second stage of the model, 
should not differ substantially. This coincides with the assumption from the previous part 
of the paper, stating that importing brings lower marginal cost reduction, compared to the 
marginal cost reduction due to investment into high-technology. In addition, the level of 

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 364
productivity of high-technology domestic firms, 
h
φ , and the level of productivity of high-
technology importing firms, 
I
h
φ , is compared as well. The expression 
I
hh
φφ < applies, as 
long as 
[ ]
1
1
1
1
( )( ) ( ) ( )
II
II h h hh
h l l h h Ih I
h
W WW
fWW W fW W f W
σ
σ
γγ
ηη
γ γγ
−
−
−
 − −< −+

. 
The latter expression is valid when the wages in high-technology firms (
h
W ) are significantly 
higher than the wages in low-technology firms (
l
W ). Also, the wage level in high-technology 
firms should increase substantially as a consequence of importing (
I
h
W ). Again, following 
the conclusions made when studying the skill upgrading at the level of individuals, both 
presumptions signal a higher employment level of skilled workers and were already as-
sumed in the previous part of the paper.
Next, the following two expressions are considered when comparing the zero-profit 
bounds of high-technology firms that do not engage in international activities and of 
those which start exporting in the second stage of the model:
() ()
() () ( )
E
E hh
h h h Eh
rr
fW f f W
φφ
πφ πφ η η
σσ
=⇔−=−+ .
To get the level of productivity, above which a high-technology firm finds it profitable 
to start exporting,
E
h
φ , the subsequent two expressions are compared: () ()
E EE
hh h h
πφ πφ = , 
yielding the following:
[ ]
1
1
1
(1 )
E h
h Eh
W
A fW
σ
τ
φ
γτ
−
= − .
Since it was already assumed that 1 τ > , the productivity level of high-technology ex-
porting firms will be positive; 0
E
h
φ > . In addition, the level of productivity of high-
technology domestic firms, 
h
φ , and the level of productivity of high-technology ex-
porting firms, 
E
h
φ , is compared as well. The expression 
E
hh
φφ < applies, as long as 
[ ] [ ]
11
11
1
( ) ( ) (1 )
hh
h l l Eh
WW
f W W W fW
σσ
τ
η
γ γτ
−−
− −< − . The latter expression con-
firms that only the most productive high-technology firms, which will be able to compen-
sate for higher exporting costs, start exporting.
By confirming that the most productive high-technology firms engage in trading activities 
after trade liberalisation in the second stage due to their initial higher level of productiv-
ity, it is possible to compare the zero-profit bounds of high-technology firms that start 
importing and of those which start exporting in the second stage of the model:
() ()
() () ( ) ( )
IE
IE I hh
h h Ih Eh
rr
ff W ff W
φφ
πφ πφ η η
σσ
=⇔−+ =−+ .
High-technology firms choose between the start of importing and exporting on be-
half of their productivity level; high-technology firms decide to import if their pro-
ductivity level is not yet high enough to start exporting, whereas more productive 

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 365
high-technology firms start exporting in order to increase their revenues. This makes 
it possible to compare the productivity levels of high-technology firms that start im-
porting (
I
h
φ ) and high-technology firms that start exporting (
E
h
φ ) and see that high-
technology firms start importing, when the level of bound productivity is higher; i.e.  
[ ]
1
1
1
1
1
(1 ) ( ) ( )
EI I I I
h h E h h hhI h hh I
h
f W W f WW f W WW
σ
σ
γ
φφ τ η
τγ
−
−
 <⇔ −< −+ −

. 
The latter expression applies if the wage level in high-technology firms (
h
W ) is significant-
ly lower than the wage level in high-technology importing firms (
I
h
W ): 
I
hh
WW < , which 
is again a sign of a higher employment level of skilled workers. Moreover, the decision 
between the start of importing and exporting will depend on external factors; i.e. the cost 
level of importing and exporting. If the costs of importing are significantly higher than 
the costs of exporting, only the most productive high-technology firms will be able to 
afford importing. In contrast, when the opposite holds, only the most productive high-
technology firms will be able to afford exporting.
The next step compares the zero-profit bounds of importing high-technology firms and 
of high-technology firms that start importing and exporting in the second stage of the 
model:
() ()
() () ( ) ( )
I IE
I IE I I hh
h h Ih I Eh
rr
ff W ff f W
φφ
πφ πφ η η
σσ
= ⇔−+ = −++ .
It follows that high-technology firms will find exporting and importing profitable only if the 
increase in revenues will be bigger than the increase in costs of exporting. To get the level of 
productivity, above which a high-technology firm finds the start of importing and exporting 
profitable,
IE
h
φ , the subsequent two expressions are compared: () ()
I IE IE IE
hh h h
πφ πφ = , obtaining 
the following:
1
1
1
(1 )
I
IE I h
h Eh I
h
W
A fW
σ
τ
φ
γτ
−
 = −

.
This shows when the productivity level of high-technology firms that import (
I
h
φ ) is 
lower than the productivity level of high-technology firms that export and import (
IE
h
φ ):
 
11
11
1
( ) ( ) (1 )
I
I IE I I I I I h
h h h h Ih h h Eh h
f W W fW W W fW W
σσ
γ
φφ η τ
γτ
−−
   <⇔ −+ − < −
  
. 
Again, the latter expression applies if the wage level in high-technology firms (
h
W ) is sig-
nificantly lower than the wage level in high-technology importing firms (
I
h
W ); 
I
hh
WW < . 
Findings from the part of the model, studying the skill upgrading at the level of in-
dividuals, again indicate higher wages being a signal of a higher employment level of 
skilled workers. In addition, if the costs of importing are significantly higher, compared 
to the costs of exporting, only the most productive firms will be able to afford the start 
of importing.

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 366
Finally, since the decision of high-technology firms on when to start exporting and im-
porting depends also on external factors; i.e. the cost level of exporting and importing, 
the analysis from the previous paragraph has to be repeated for high-technology firms 
that decide between starting to export, and starting to export and import. Therefore, the 
zero-profit bounds of exporting high-technology firms and of high-technology firms that 
start importing and exporting in the second stage of the model are compared with the 
following expressions:
() ()
() () ( ) ( )
E IE
E IE I hh
h h Eh I Eh
rr
f fW f f fW
φφ
πφπφ η η
σσ
= ⇔−+ = −++ .
From this it follows that high-technology firms find exporting and importing profitable 
only if the increase in the level of productivity is bigger than the increase in costs of im-
porting. To get the level of productivity, above which a high-technology firm finds it prof-
itable to start importing and exporting,
IE
h
φ , the subsequent two expressions are compared: 
() ()
E IE IE IE
hh h h
πφ πφ = , yielding the following:
1
1
( )( ) ( )
IE I I I I
h E h h Ih h hh I
h
A f f W W fW W W
σ
τ
φ η γγ
γγ
−
 = + −+ −

.
One can now check when the productivity level of high-technology firms that export (
E
h
φ ) 
is lower than the level of high-technology firms that export and import (
IE
h
φ ):
 
[ ]
1
1
1
1
1
(1 ) ( )( ) ) ( )
E IE I I I
h h E h h E hhI h hh I
h
f W W f f WW f W WW
σ
σ
γ
φφ τ η τ
τγ
−
−
 <⇔ −< + −+ −

. 
The latter expression applies if the wage level in high-technology firms (
h
W ) is signifi-
cantly lower than the wage level in high-technology importing firms (
I
h
W ), which again 
signals a higher employment level of skilled workers after importing. Concerning external 
factors, if the costs of importing are significantly high, only the most productive high-
technology firms will be able to engage in both, exporting and importing.
To sum up, after trade liberalisation in the second stage of the model, only the least pro-
ductive high-technology firms serve only the domestic market, where the decision on 
whether to start importing, exporting or both depends on the level of wages before and 
after importing, on the firm’s productivity level and on external factors; i.e. the level of 
export and import costs. Interestingly, when high-technology firms decide whether to 
start exporting or not, the final decision is not based on the wage level of high-technology 
non-trading firms and high-technology exporting firms. Making inferences from the first 
part of the paper which studied the skill upgrading at the level of individuals, this would 
be a sign of a higher employment level of skilled employees. Therefore, skill upgrading 
occurs only in firms that import or firms that engage in both; importing and exporting.
4. CONCLUSION
The theoretical models of trade have been evolving through history in a desire of a thor-
ough interpretation of international flows. Recent theoretical trade models account for 

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 367
firm heterogeneity, and also for technology and skill upgrading. Guided by these theories, 
I developed a theoretical model, which explores the individual’s decisions for investing in 
skill upgrading and the firm’s decisions to start technology upgrading and trading.
The model in this paper is divided in two parts. First part explores the behaviour of indi-
viduals and their decisions on whether to invest in acquiring higher skill levels. The findings 
suggest that since the education costs of low ability workers for acquiring higher skills are 
excessive, only high ability workers achieve higher skill levels. In addition, in order to have 
incentives for acquiring higher skills, high ability, high skilled workers demand higher wages 
after entering employment. The latter conclusion is then brought into use in the second part 
of the model, which takes into account the firm’s decisions on whether to invest in higher 
technology and whether to engage in international activities. The model suggests that before 
trade liberalisation, only the most productive firms invest in acquiring higher technology 
levels, where higher labour costs of these firms signal a higher employment level of skilled 
workers. After trade liberalisation, costs of importing and exporting diminish and firms 
have an option to start engaging in international activities. Taking into account low-tech-
nology firms first, the most productive low-technology firms choose to skill upgrade and to 
start exporting and importing, less productive low-technology firms also upgrade skills but 
start only importing, and the least productive low-technology firms continue serving only 
the domestic market. Low-technology firms therefore use importing as means of increasing 
their productivity level before the start of exporting. This finding on learning-by-importing 
was confirmed also in empirical studies (see for example Damijan, & Kostevc, 2015; and 
Altomonte, & Békés, 2010). On the other hand, low-technology firms do not engage ex-
clusively in exporting, as their productivity level is too low to cover exporting costs. With 
regards to high-technology firms, only the least productive high-technology firms do not 
start importing and/or exporting after trade liberalisation, where the decision on whether to 
import, export, or both, depends on the firm’s productivity level, the skill upgrading before 
and after importing, and on external factors; the level of export and import costs. Skill up-
grading in high-technology firms after trade liberalisation takes place only in firms that start 
importing, or that start engaging in both, importing and exporting.
The model highlights several facts, which would be noteworthy of further empirical test-
ing. One could empirically analyse the following findings of the theoretical model: (i) 
firms with better skill structure also start importing; (ii) importing firms have a better skill 
structure than non-importing firms; and (iii) by having an access to cheaper technology 
and/or to cheaper intermediates, imports serve for increasing the technology level before 
the start of exporting.
The key contributions of this model are a differentiation between importers and exporters 
and a thorough analysis of the behaviour of individuals and firms, where the connection 
between the two has been made by linking fragments of models on the individual’s and 
the firm’s behaviour. The possible limitations of the model present additional assump-
tions, which had to be made when developing the model; e.g. the increase in the wage 
level of skilled workers after investing in high technology (
h
l
W
W
γ > ), and after the start 

ECONOMIC AND BUSINESS REVIEW  |  VOL. 17  |  No.  3  |  2015 368
of importing (
I
I l
l
l
W
W
γ > ), compared to the decrease in the marginal costs in these firms. 
Furthermore, the model also assumes that the productivity level increase after importing 
is lower compared to the productivity level increase after investing in high-technology. 
These additional assumptions to some extent limit the value of the model, as it would be 
hard to test them empirically. In addition, although the model considers three dynamic 
phase shifts; i.e. the individual’s decision to acquire skills, the firm’s decision to opt for 
high technology, and the firm’s decision to start importing and/or exporting, it is limited 
in discussing only two firm’s decisions simultaneously (e.g. high-technology vs. low-tech-
nology, no trade vs. importing, etc.). Since nowadays firms face the changing environment 
which demands complex decision-making on a daily basis, this structure of the model 
would be limited to transform in everyday environment. Although losing a more static 
structure of the model would greatly increase its complexity, this limitation would be use-
ful to be taken into account in further studies. Nevertheless, despite the aforementioned 
shortcomings, I believe the model’s conclusions bring contributions to the field of knowl-
edge, since the conclusions are also consistent with previous empirical findings and open 
several possibilities for further empirical analyses.
REFERENCES
Altomonte, C., & Békés, G. (2010). Trade Complexity and Productivity. CeFiG Working Papers, Paper No. 12.
Amiti, M., & Davis, D. R. (2011). Trade, Firms, and Wages: Theory and Evidence. Review of Economic Studies, 
79(1), 1–36.
Amiti, M., & Konings, J. (2007). Trade Liberalization, Intermediate Inputs, and Productivity: Evidence from 
Indonesia. American Economic Review, 97(5), 1611–1638.
Bas, M., & Strauss-Kahn, V . (2014). Does importing more inputs raise exports? Firm-level evidence from France. 
Review of World Economics, 150(2), 241–275.
Bloom, N., Draca, M., & Van Reenen, J. (2011). Trade Induced Technical Change? The Impact of Chinese Imports 
on Innovation, IT and Productivity. NBER Working Papers, Paper No. 16717.
Bustos, P . (2011a). Trade Liberalization, Exports, and Technology Upgrading: Evidence on the Impact of MER-
COSUR on Argentinian Firms. American Economic Review, 101(1), 304–340.
Bustos, P. (2011b). The Impact of Trade Liberalization on Skill Upgrading: Evidence from Argentina. Barcelona 
GSE Working Paper Series, Paper No. 559.
Damijan, J., & Kostevc, Č. (2015). Learning from trade through innovation: Causal link between imports, ex-
ports and innovation in Spanish microdata. Oxford Bulletin of Economics and Statistics, 77(3), 408–436.
Feng, L., Li, Z., & Swenson, D. L. (2012). The Connection between Imported Intermediate Inputs and Exports: 
Evidence from Chinese Firms. NBER Working Papers, Paper No. 18260.
Goldberg, P . K., & Pavcnik, N. (2007). Distributional Effects of Globalization in Developing Countries. Journal 
of Economic Literature, 45(1), 39–82.
Halpern, L., Koren, M., & Szeidl, A. (2011). Imported Inputs and Productivity. CeFiG Working Papers, Paper 
No. 8.
Idson, T. L., & Oi, W . Y. (1999). Workers Are More Productive In Large Firms. The American Economic Review, 
89(2), 104–108.
Kasahara, H., & Rodrigu, J. (2008). Does the Use of Imported Intermediates Increase Productivity? Plant-Level 
Evidence. Journal of development economics, 87(1), 106–118.

M. LINDIČ | HOW TRADING FIRMS UPGRADE SKILLS AND TECHNOLOGY: THEORETICAL MODEL... 369
Krugman, P . R., Obstfeld, M., & Melitz, M. J. (2012). International Economics: Theory & Policy (9th ed.). Boston: 
Pearson.
Melitz, M. J., & Redding, S. J. (2014). Heterogeneous Firms and Trade. In Gopinath, G., Helpman, E., & Rogoff, 
K. (Eds.), Handbook of International Economics (4th ed., pp. 1–54). Elsevier.
Melitz, M. J. (2003). The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity. 
Econometrica, 71(6), 1695–1725.
Smeets, V ., & Warzynski, F . (2010). Learning by Exporting, Importing or Both? Estimating productivity with multi-
product firms, pricing heterogeneity and the role of international trade. Aarhus University, Department of Eco-
nomics Working Papers, Paper No. 10–13.
Stark, O., & Wang, Y. (2001). Inducing Human Capital Formation: Migration as a Substitute for Subsidies. Uni-
versity of Bonn, Center for Development Research, Discussion Papers on Development Policy, Paper No. 11.
Stark, O., & Chau, N. H. (1998). Human Capital Formation, Asymmetric Inofrmation, and the Dynamics of Interna-
tional Migration. Reihe Ökonomie / Economics Series, Paper No. 52.
Stark, O., Helmenstein, C., & Prskawetz, A. (1998). Human Capital Depletion, Human Capital Formation, and 
Migration: A Blessing in a “Curse”? Reihe Ökonomie / Economics Series, Paper No. 55.
Stark, O., Helmenstein, C., & Prskawetz, A. (1997). A Brain Gain with a Brain Drain. Reihe Ökonomie / Eco-
nomics Series, Paper No. 45.
APPENDICES
Appendix A
Claim 2: The gross earnings of rational individuals with the low ability are positive (i.e. 
w
U
(Θ
U
*
) > 0).
Proof: Consider rational workers, who maximize their gross earnings and therefore 
achieve the optimal level of ability:
w
U
(Θ
U
*
) = λ[ln(λ / k
U
)] – k
U
 [(λ / k
U
) – 1].
After simple calculation, one gets the following:
w
U
(Θ
U
*
) = λ[ln(λ) – ln(k
U
) – 1] + k
U
.
Knowing the following inequality holds: λ > k
U
 > k
S
 > 1, it follows that w
U
(Θ
U
*
) > 0. ■