◆✓# di.
The utility level of the representative consumer in the foreign country can be obtained analogously. In the next section, we provide numerical examples to show the impact of trade liberalization on cuto↵ productivity level, on patterns of specialization, and on welfare. The result is in contrast to what we obtained in the partial equilibrium analysis.
6 Numerical Examples
We provide two numerical examples. In the first example, we set L = 2⇥ 1010, L⇤ = 1010, ⌧ 2 [1.1, 2], and ✓ = 3. There are three sectors:
1 = 0.5, 2 = 1/3, and 3 = 0.5/3. a1 = (1.1) 1, a2 = 1, and a3 = 1.1.
a⇤1 = a⇤2 = a⇤3 = 1. f is chosen so that ( ✓b✓1) 1f = 1. The increment of ⌧ is 0.01. In all figures illustrating the results, the horizontal axis is the inverse of ⌧ .
Figure (12) shows how patterns of specialization change with the degree of trade liberalization. The results are consistent with intuition. Initially, both countries produce in all sectors. When trade cost is sufficiently low, only the home country produces in the first sector, and only the foreign country produces in the third sector. The second sector is always produced by both countries in the range of ⌧ we consider. Figure (15) shows the relative wage changes nonmonotonically. Initially, it decreases with trade liberalization. It then increases and decreases again.
Figures (16) to (18) show the change of the cuto↵ productivity level ( ˆ'id) for each sector in the home country under general equilibrium. For
the first sector, the cuto↵ productivity level increases with trade liberaliza-tion. For the second sector, there is a range over which it decreases when trade is more liberalized. The third sector experiences decreases, although not apparent, in the cuto↵ productivity level when ⌧ 1 is between 0.68 and 0.705.
However, the results are di↵erent under partial equilibrium. Figure (14) shows the results when w ⌘ 1. Because A2 is smaller than ˆA' it is im-possible for the second sector to experience cuto↵ productivity reduction.
Furthermore, because A < A3 < ˆA' < A when ⌧ 1 is between 0.68 and 0.705, ˆ'id must increase when ⌧ 1 falls within this interval.
Figures (19) to (21) show the change of the cuto↵ productivity level for each sector in the foreign country under general equilibrium. For the first two sectors, the cuto↵ productivity level increases with trade liberalization.
For the third sector, there is a range over which the cuto↵ productivity level decreases. This happens because production in this sector is completely located in the foreign country, and because the relative wage decreases.
The relatively expensive labor of the foreign country reduces demand of the varieties produced in the sector. It decreases labor allocated to the sector, which decreases the measure of entrants and hence the competition level.
Therefore, the cuto↵ productivity level decreases. The result cannot be generated under partial equilibrium.
Although some sectors in both countries experience a decrease in the cuto↵ productivity level, Figure (22) shows that welfare increases under trade liberalization when the wage is endogenized. The loss from decreasing the cuto↵ productivity level is o↵set by the increase in efficiency caused by the reallocation of labor toward comparatively advantaged sectors.
are unchanged. Figure (13) shows how patterns of specialization change with the degree of trade liberalization. Initially, both countries produce in all sectors. When ⌧ 1 is higher than about 0.7, only the home country produces in the first sector. Only the home country produces in the second sector and only the foreign country produces in the third sector when ⌧ 1 is higher than about 0.8. Figure (23) shows the relative wage is monotonically decreasing.
Figures (24) to (29) show the change of the cuto↵ productivity level as a function of ⌧ 1 under general equilibrium. For the home country, the cuto↵ productivity level of all sectors is nondecreasing with the degree of trade liberalization. For the foreign country, the cuto↵ productivity level of the first sector increases with the degree of trade liberalization. The cuto↵ productivity level of the second sector decreases with the degree of trade liberalization when ⌧ 1 is in the interval between 0.76 and 0.79. The cuto↵ productivity level of the third sector decreases with the degree of trade liberalization when ⌧ 1 = 0.8; otherwise it is nondecreasing. It is because when ⌧ 1= 0.8, the sector is produced by only the foreign country.
However, the relative wage slightly decreases when ⌧ 1 increases from 0.8 to 0.8065. Figure (30) shows that welfare increases with the degree of trade liberalization in both countries under general equilibrium.
The results are di↵erent under partial equilibrium. For instance, un-der partial equilibrium, according to Figure (14), ˆ'3d should decrease with the degree of trade liberalization when A > A3 > ˆA'.6 However, once we endogenize the wage, because the wage is decreasing, the amount of labor leaving the third sector is not large enough to decrease the cuto↵ productiv-ity level. Furthermore, under partial equilibrium, trade liberalization never
6Notice that A, A and ˆA' do not change with i.
decreases cuto↵ productivity level of sectors in the small country. However, it is the small country instead of the large one that experiences the decrease in the cuto↵ productivity level when trade is more liberalized under general equilibrium.
7 Conclusion
We established a full-fledged general equilibrium model incorporating firm heterogeneity, endogenous markup, homothetic demand, and patterns of trade that emerge because of Ricardian comparative advantage and the home market e↵ect. Trade liberalization induces reallocation of labor within and across sectors and changes the relative competitiveness of foreign and domestic producers, which contributes to the change in the lowest productiv-ity level required to survive and therefore the average sectoral productivproductiv-ity.
Contrary to one-sector models such as those of Melitz (2003) and Melitz and Ottaviano (2008), trade liberalization may reduce sectoral productivity.
The competitiveness of foreign producers is enhanced by trade liberalization.
However, more labor may be reallocated toward other sectors, which reduces the measure of entrants and the competition level there. When the latter e↵ect dominates the former, we observe a decrease in sectoral productivity.
The problem we considered is similar to those studied by Fan et al.
(2013) and Demidova (2008), but is di↵erent in results. We consider how the change in the wage a↵ects labor reallocation. This minor modification generates results di↵erent from those found in Fan et al. (2013). It is not necessarily true that only the comparative disadvantage sectors of the large country can experience reductions in average sectoral productivity. The sec-tors in the small country may also experience reductions and the reductions
tion is completely located in only one country, no matter what the size of that country, may experience decreases or increases in sectoral productivity, depending on how wage moves. Our result is also in contrast to that of Demidova (2008) who argues that trade liberalization reduces average sec-toral productivity in technologically inferior countries. For instance, in our model, the average sectoral productivity of sectors in which production is located in only one country may decrease with trade liberalization. How-ever, whether production in a particular sector will be concentrated in only one country depends on comparative instead of absolute technological di↵er-ences. Finally, the reason for the exit of low-productivity firms is di↵erent.
In Fan et al. (2013) and Demidova (2008), it is because of the asymmet-ric ability that only high-productivity firms are capable of overcoming the fixed cost to export. In our model, it is because of the markup decreasing with the level of competition. Therefore, we also found that the markup in-creases in sectors whose average sectoral productivity dein-creases with trade liberalization.
The model generates the policy implication that trade liberalization is not always productivity improving by forcing low-productivity firms to exit.
Trade liberalization also does not necessarily reduce markup. Besides, in the numerical examples, we show that the qualitative impact on productivity distribution can be sensitive to the parameters of the model. Although the examples show that some sectors experience decreases in productivity and increases in markup, the welfare is accreted with the degree of trade liberalization.
This model lends itself to testable hypotheses. In particular, it sug-gests that how trade liberalization a↵ects the average sectoral productivity and markup in each sector is a↵ected by how the factors are reallocated
across sectors. Sectors that expand after trade liberalization are more likely to experience markup reduction and productivity improvement by weeding out low-productivity firms. Testing these hypotheses can be a direction for future research.