966bde6d52.jpg width=19.2850010871887 height=22.8 /> is the elasticity of labour mobility, and is assumed to be constant5. Labour is completely immobile if, and mobility is perfect if. The previous equation is rewritten as
A fixed minimum wage is paid to unskilled workers employed by the tradable sectors, and that wage is higher than the wage earned in the un-tradable sector. That is
The inter-sector wage differential explains why some unskilled workers are unemployed. This outcome would not come about if all jobless workers could migrate again into the un-tradable sector and economy activity.
When the wage gap between the tradable and untradable sectors is higher, more unskilled workers will stay in the tradable sector. In fact, more unskilled workers migrate than there are vacancies and this explains why some unskilled workers could be unemployed. The unemployment level acts to discourage further labour movements. As long as the wage gap is increased, the unemployment equilibrium rate will be greater.
3. Comparative Static Analysis
The starting point of this section offers concise details about the procedure to make a fairly tractable analysis of the comparative static of the model. The order of this Comparative static enquiry is presented according to the course that LDCs face up when custom barriers are removed. The first issue is to analyse the effects that trade liberalisation produce in the economy, if tariff and external restrictions are minimised. Institutional restrictions imposed on the labour market are studied afterwards, and they are handled through an increase in the minimum wage fixed by the government. Finally, a positive shock on the export sector is introduced, since this effect should be expected as consequence of new competitive conditions.
Seven first-order conditions with respect to skilled and unskilled labour demands, and the skilled wages are derived from Equations (1) and (2). Comparative-static analysis is derived from the previous conditions (see Appendixes 1 and 2). Three cases are studied when there are changes in the parameters related to the trade policy, minimum wage, and export productivity.
3.1. Reduced Model
The seven first-order conditions (see Appendix 1), the two labour balances—Equations (4) and (5)—and the mobility restrictions for unskilled labour—Equation (6)— set up the ten equilibrium conditions of the model. They allow us to derive the following results: Three factor production prices, five levels of demand for workers and the unemployment levels of unskilled and skilled workers.
Skilled labour wages are derived from Equations (35) and (38), and they are
such that wages for skilled worker are positively related to both the minimum wage rate and training-hiring costs per worker. In the case of the export sector—Equation (7)—the skilled worker wage is negatively related to the protected parameter for imports, , and positively related to the productivity level,.
Equations (7) and (8) are replaced in the first order conditions. Then, those conditions are differentiated with respect to labour demands, trade policy parameters, the minimum wage, and technology changes (see Appendix 2), and a equation system is obtained and written in matrix form as
where H is the coefficient matrix; dL is a vector of labour variations and writen in transpose form is. A is a vector of parameters that premultiply the vector dD. The last vector in transpose form is defined as.
3.2. Trade Policy Liberalisation
Two trade policy effects on the labour market are considered. The first occurs when the trade policy is fixed by foreign countries and has a negative impact on domestic exports,. The second occurs when trade policy is fixed by a LDC in order to restrict its own imports,. Both policies are oriented toward reducing international trade flows.
In recent decades, restrictions on trade flows have been substantially reduced in most countries, and the dispersion of protection across products and sectors has been minimised. These processes of reform have hit the import sector as the former protection barriers had allowed many inefficient firms to continue to produce and to undertake few productivity upgrades.
Nowadays countries design their trade policies to liberalise the international markets. The more important trade policies are currently related to bilateral, regional, and multilateral trade agreements that restrict the capacity of countries to change their trade policies. As a matter of fact, they have made a commitment to be involved in the process of globalization and to move their economies toward an integrated world.
International trade restrictions induced by foreign countries,.
If foreign countries remove trade restrictions, domestic firms might raise their own export prices in the international market. The effects are given only in the export sector. Less restriction induced by foreign countries conducts to increase the skilled demand in the export sector and reduce the unemployment rate. These results are presented in Equations (10). This foreign trade policy oriented to be less restrictive also impacts positively the unskilled workers both in the formal and informal sectors, as they are shown in Equation (11). This positive effect is reduced for skilled workers employed in the export sector by the turnover costs, (b − 1).
The parameter is defined as (see Appendix 2)
and it is a decreasing function of the elasticity labour mobility.
Reducing external trade restrictions on exports allows domestic firms to become more competitive in external markets. Policy liberalisation in favour of exports produces two meaningful results. First, the export sector increases its demands for skilled and unskilled workers (labour demand in the import sector is not affected); and second, as long as the export sector gets larger, wages paid for skilled workers go up (Equations 7 and 8), and there is a general reduction of the unemployment rate in the economy as a whole.
Equation (13) is obtained with the results in Equation (11) and shows a reduction of unemployment in the unskilled labour market when the external restrictions are removed.
Cutting the domestic tariff,.
As the economy is opened to external competition, many firms are restructured and stay in the market, but others have to close. When the domestic government cuts its tariffs, the impacts on the skilled labour force are evident in this model. Skilled worker employment in the export sector increases as this sector expands, as shown in Equation (14). By contrast, the import sector is depleted, and therefore demand for skilled workers in this sector falls (15). Moreover export skilled labour demand is soften by the turnover cost, , and the domestic tariff,; Equation (14). Clearly the less import costs affect negatively the skilled labour demand in the import sector, although this effect is reduced by the imperfect labour mobility, given by; Equation (15).
Two opposite forces affect the unemployment rate of skilled workers, as in Equation (16). These results are derived from Equations (14) and (15). On the one hand, there is a positive correlation between the trade policy liberalisation and the skilled labour demand in the export sector; thus, the unemployment rate tends to fall in this sector. On the other hand, there is an unfavourable effect on the import sector, and the unemployment rate in this sector tends to increase. The net effect depends on which sector is bigger. If the tradable import sector is bigger, the overall unemployment rate goes up; see Equation (16).
However, both effects are reduced by the traininghiring costs, as given by for the export sector, and for the import sector. It is well known that job creation takes time, while job destruction can take place immediately. Therefore, there will be a higher overall unemployment rate if the import sector, where the price falls, is the dominant sector.
The impacts on unskilled workers are as follows. Since there is an imported component in production in the export sector, cutting tariffs leads to reduced demand for unskilled labour in this sector. This makes sense when firms in this sector can import intermediate goods at lower prices and substitute locally produced items for imported components. The friction labour mobility (b) does not have a sharp tend to minimise the effect, but this is reduced if proportion of skilled workers is high; see Equation (17).
Lower demand for unskilled labour in the export sector allows the tradable import sector and the untradable sector to increase their demands for these workers; see first terms on the right hand side in Equations (18) and (19). However, lower protective barriers affect these sectors negatively at the same time (second terms). The net effect on demand for unskilled labour with respect to the sectors will depend on which is dominant in the economy. If the tradable-import sector dominates, then a reduction of custom barriers negatively affects the demand for unskilled labour. In turn, a large migration of unskilled workers from the tradable sector to the un-tradable sector could explain lower productivity in the economy overall.
Since there are mobility restrictions on unskilled labour between the tradable and un-tradable sectors, given by the expression in Equation (19), any effects from removing tariffs in the economy are dampened by the market frictions. This also applies to tradable import sector frictions through the term 6.
Equation (20) is derived from Equations (17)-(19). The main implication from Equation (20) is that trade liberalisation increases the unemployment rate among unskilled workers, as long as the import sector is the largest in the economy. If acceptable economic opportunities are lacking in the un-tradable sector, where the market entry costs for firms are relatively low, some workers are forced to be unemployed. As long as the export sector is expanding, this negative effect can be reduced. It is worth saying that in this case mobility restrictions in Equation (20) for export sector are negligible (b), but that restrictions do be significant for import sector,.
An additional implication is the inter-sector wage differential arising from imperfect labour mobility. Once a new allocation of the labour force is established, which constitutes a new stable equilibrium, it features different wage rates among workers in different sectors. International trade liberalisation leads to an increase in the wage gap between the skilled workers in the export and import sectors; see Equations (7) and (8). As long as the share of the export sector goes up, the unskilled labour wage gap between the minimum wage and the wage paid in the un-tradable sector increases. This last outcome is attributable to the decreasing marginal productivity in the un-tradable sector.
The main theoretical results presented in this section can be summarized by noting that a process of international market liberalisation in an LDC produces the following effects on the unemployment rate and unskilled workers employed in the un-tradable sector:
1) The removal of international trade barriers (e.g., through free trade agreements) has two positive effects on the export sector that act to reduce unemployment among both skilled and unskilled workers. Conversely, it has a negative effect on the demand for both skilled and unskilled labour in the import sector. Additionally, these two opposite effects are reduced by the turnover cost, in the case of skilled workers, and by labour mobility restrictions, in the case of unskilled workers.
2) International trade policy liberalisation has a mixed effect on the un-tradable sector and on unemployment among unskilled workers. More competition in the import sector leads to reduced demand for labour in the un-tradable sector and, therefore, increased unemployment in the unskilled labour market. This effect is, however, offset by the labour adjustment in the export sector to some extent.
4. Changing the Minimum Wage Policy and Augmenting Export Sector Productivity
This section begins with a discussion of the effects that a change in the minimum wage has on the unemployment level for different types of workers. The model is then examined in terms of a boom in productivity attributable to free trade, especially for workers employed in the export sector7.
4.1. Changing the Minimum Wage Rate Policy
A critical issue related to free trade agreements is the effect that a minimum wage policy has on the labour market. Since a higher minimum wage raises pay for skilled workers—see Equations (7) and (8)—there is an unambiguously negative effect on demand for skilled labour. Higher wages drive up production cost, which erodes a country’s comparative advantage and destroys jobs, as it is shown in Equations (21) and (22). Hence unemployment exists because the entire labour market is subject to an exogenously specific floor, or minimum, which exceeds the level required for full employment. However, the negative effect regarding skilled workers may be reduced by the turnover cost, and.
The results for the export and import sectors are
Equation (23) points out a positive relation between minimum wage and the unemployment of skilled workers. There is a positively relation to the skilled workers employed and negatively to the turnover-cost, and. Thus the unemployment rate for skilled workers goes up when the minimum wage rises, as it is shown in the next equation
The effect on demand for unskilled workers is equally negative. Three important features should be highlighted. First, lower demand for unskilled workers in the export and import sectors does not have a clear relation with respect to the turnover-cost in the skilled labour market, and. Second, a negative effect for unskilled workers in the import and un-tradable sectors increases as the elasticity of labour mobility increases. Third, these results are increasing as the sharing of skilled labour demands in the economy is lower, that are related to and. These results are shown in Equations (24)-(26).
Consequently, a minimum wage exacerbates the unemployment rate for unskilled workers, as shown in Equation (27). This result is bigger as the elasticity of unskilled labour mobility increases.
4.2. Augmenting Export Sector Productivity
Negative effects produced by increasing foreign competition in the import sector could be overcome if international trade could boost export sector productivity, especially for skilled workers. This positive result is reached simply by finding more efficient ways to use the existing skilled workers and other resources not considered in this model. As further stated analytically, output level is associated with efficiency rather than an accumulation factor.
Opening the economy to international trade exposes producers to greater competition, forcing them to cut cost and increase their efficiency while obtaining greater access to more and better inputs. International trade helps to reallocate resources in favour of more productive uses, as in the export sector. In the extreme case, Equation (1), where higher productivity is located only in the export sector, the demand for skilled workers in this sector goes up—see Equation (28)—while the demand for this type of worker in the import sector does not change, since this sector in this model does not have any relation to the spill-over positive effects, in terms of productivity8. In this sense the skilled labour unemployment rate in the overall economy falls, as shown in Equation (29).
At the same time, higher productivity would probably benefit both formal and informal firms. In addition, it could provide incentives for formalization of some informal firms9, as shown by positive relations among unskilled workers in the export sector and increasing productivity. Mathematically there is a positive relation between unskilled workers and productivity; Equation 30.
The result in Equation (31) shows a rise in the untradable sector, explained by better economic conditions and a decrease in unemployment for unskilled workers Equation (32). In general, firms that operate in the untradable sector could try to reduce their labour costs by replacing permanent workers with part-time labour in order to adjust the higher demand for unskilled workers by the export sector.
The model in this paper analytically links the main labour market issues that empirical research has observed for LDCs. These distinctive features are: The imperfect labour mobility for both skilled and unskilled workers; the labour market distortions in relation to institutional restrictions, such as minimum wage fixed by the government; and the existence of an informal sector.
The results obtained are consistent with stories about how an LDC’s exposure to international trade creates opportunities for some firms, especially in the export sector, while simultaneously contributing to the downfall of other firms in the import sector. In essence, protection of trade shelters inefficient firms. There is evidence that exposing an economy to trade forces causes the less productive firms to exit the market.
International trade works as a catalyst to boost productivity in the economy, especially in the export sector. Empirical analysis of permanent trade liberalisation, like that reported by Dutt et al. , shows an immediate rise in unemployment, but that result tends to be reversed in the long term. However, a policy increasing the minimum wage minimises such favourable outcomes. With an increase in the minimum wage, capacity to compete in international markets falls, and therefore the overall unemployment rate rises as the labour demand in the untradable sector falls.
First-Order Necessary Conditions:
Substituting (35) into (33), and (38) into (36), the first-order conditions can be rewritten as
The first-order conditions, Equations (40)-(43), are differentiated. After that, Equations (4)-(6) and (44) are used, as the first-order conditions again. Thus, the following differentiated equation system is obtained:
taking into account that, and from Equation (6), we have
and the parameter is defined as
The previous four equations are written in matrix form as
The inverse matrix of, denoted by, is
1The consequences of economic liberalisation policies on the skilledunskilled wage inequality in LDC are analysed theoretically by Marjit  and Chaudhuro and Yabuuchi .
2By assumption prices of exports and imports are equal to 1.
3Marjit  considers that households working in informal activities and other people without jobs are unemployed unskilled people.
4An opposite view is that the informal economy is a desirable sector that workers could choose in preference to a formal sector. This internal dualism combines two opposite characterisations. Fields  offers a summary of reasons why workers might prefer working in the informal sector. Among other reasons they could earn more, or at least hope to earn more; also, they value self-employment and the relative independence.
5Casas  derives this type of labour supply from a CES utility function.
6Those parameters are the skilled labour frictions but they indirectly affect the unskilled labour market through the production functions.
7Currently, there are positive spill-over effects on the rest of the economy.
8Davidson and Matusz  find a strong negative correlation between net exports and job destruction using data for both the Canadian and US economies.
9Golberg and Pavnik  find weak evidence for a relation between trade liberalisation and informal employment in Colombia and Brazil. Their model implies that trade liberalisation leads to an increase in informal employment.