Unemployment of Unskilled Labor due to COVID-19 led Restriction on Migration and Trade

To combat COVID-19 the entire world has resorted to global lockdown implying restriction on international labor migration and trade. This paper aims to check the effect of such restrictions on the unemployment of unskilled labor in the source country. In competitive general equilibrium framework with three goods and four factors restriction on migration raises unemployment for given factor intensity. The results remain same even in a slightly different structure of the economy. In case of trade restriction, however, the rise or fall in unemployment depends on both the structure of the economy and the factor intensity assumption. Abstract To combat COVID-19 the entire world has resorted to global lockdown implying restriction on international labor migration and trade. This paper aims to check the effect of such restrictions on the unemployment of unskilled labor in the source country. In competitive general equilibrium framework with three goods and four factors restriction on migration raises unemployment for given factor intensity. The results remain same even in a slightly different structure of the economy. In case of trade restriction, however, the rise or fall in unemployment depends on both the structure of the economy and the factor intensity assumption.


Introduction and Motivating Environment
Global outbreak of COVID-19 has unnerved the entire world in last few months.
By now it is apparent that Corona virus outbreak took the corridor of physical proximity of affected countries and human beings. This corroborates the role of trade, travel and migration for transmitting Corona virus. And again since the spread of Corona virus has been showing no signs of abating,it has taken the whole world into a synchronized lockdown -complete closure of international borders. A variety of policies are also framed and international sanctions are essentially imposed to restrict international movement of goods and services, and labor. It would lead to inevitable production disruptions. Immobility of labor due to various controls would be accompanied by unnecessary economic cost as well. The impacts would be similar to the one we noticed during H1B visa sanctions imposed by the USA government or during BREXIT. Global production or trade in goods and services would be adversely impacted. When national policies like H1B Visa restriction or BREXIT are responsible for the immobility of labor, a substitute process is also made handy. In this context, production cost rises but the supply chain does not get disrupted because production still takes place (may be by domestic labor). Inability to harness the cost advantage that was possible due to availability of cheap foreign labor will also lead to a rise in the price level along with a fall in demand. This certainly has huge economic impact. However, when the root cause of all restrictions are health related and that too contagious just like the one with COVID-19, then the pathways to an alternative production process no longer remains a viable option. When mobility of resources like labor is restrained worldwide, production in a single particular economy does not get affected alone -it affects the global economy at large. Therefore, naturally, possible sufferers of all such policies are worried about the economic upshots in their domestic fronts. In this globalized world, both benefit and ill effects spill over across the globe. And so is the perceived detrimental effects of policies mentioned to combat COVID-19. Thus, finally the issue becomes a political economic one where international relations among different trading countries are persuaded by the policy outcome. This paper primarily attempts to focus on the effects of restriction on international migration policy which arguably has severe employment effects as this may either cause discontinuation of the stay of immigrants or does not allow new migrant. Such policy would primarily restrict the mobilityof skilled workers such as IT professionals, engineers, etc. And we also know that recent economic prosperity of some countries like Indiahas been predominantly propelled by these skilled workers and their free movement among various occupations and countries. Therefore, the concern is quite justified. What do they apprehend? Due to mobility restriction 1 , domestic supply of skilled workers would rise. This is a kind of reverse migration.
Naturally, this would influence prices of other factors and their employment. One possibility is that they get directly employed in the skilled sector either displacing some alreadyemployed skilled youth which moves to other sector and also pushes some unskilled workers towards unemployed pool leading to an increase in unemployment in the economy. Alternatively, skilled workers can make room for some more capital in the skilled sector and hence return to capital goes up and that of unskilled labor falls. We first present a competitive general equilibrium model of trade where there are three sectors and four factors. Our structure closely follows Jones (1965Jones ( , 1971. We slightly deviate from these two celebrated models through introduction of unemployment. And for distinction among different labors, unemployment, and their connectedness we follow Agenor and Montiel (2015), Marjit and Acharrya (2003), Marjit and Kar (2011), Acharyya and Kar (2014), Chaudhuri and Mukhopadhyay (2010), Mandal and Mandal (2015), etc. However, we do away with any domestic migration from informal to formal sector, and hence Harris-Todaro migration possibility is not taken into account. We assume three factors-skilled labor, unskilled labor, capital-as mobile across the sectors, and one factor as specific to the skilled-labor intensive sector.
All the factor are fully employed except unskilled labor. In this backdrop, we find that there is a rise in unemployment of unskilled labors due to therestriction on labor mobility during COVID-19.The resultis found to depend onthe factor intensity assumptions. However, rise or fall in the output of different sectors does not depend on the factor intensity conditions, though the magnitude of change does.
The remaining paper is structured as follows. In the next section, we first propose a competitive trade model and check different prospects. Then we slightly modify the basic model to see how robust is the theoretical predictions of the basic model. We also check how trade control of any sort, which reflects the Corona-driven policy of restriction on international movements of goods, affects the unemployment condition. Finally, we provide some concluding remarks. The relevant mathematical details are, however, relegated to the appendices.

Methodological Background and the Basic Model
We consider a small open economy endowed with skilled labor ( ), unskilled labour( ) and two types of capital ( and ). There are three sectors, , and . Both goods and factor markets are perfectly competitive. is a skilled-labor ( ) intensive sector. Production of requires , and ; isspecific to .Equation (1) gives the equilibrium condition of where per-unit cost is equal to the price: Here, ! is the wage of skilled labors; denotes the rent of ; is the rent of ; " is the price of ; and %& ( = , , , ; = , , ) refer to the input coefficients.
The production of requires , and , with being used intensively. uses unskilled labor and . canbe taken as a public sector whereas is a private sector. The wage of unskilled laboris assumed to differ in both these sectors to capture the fact that employees of the government sector receive more benefit astheir job is relatively secured whencompared to those engaged in the private sector. Thus, the unskilled labors engaged in are paid ' whereas those engaged in get 7 ( ' > 7). 7is the wage fixed through process 2 between the employers and the unskilled employees. is intensive in the use of . The cost-price equations of and aregiven,respectively,as follows: Here ( is the price of and * is the price of .
The relation between ' and 7,is given as where, > 0 and exogenously given as a mark up over the private sector wage.
Therefore, when private sector wage rises, government sector employees also get higher wage.
We consider , and to be fully employed but full employment of is not achieved. The endowment conditions for unskilled labor, skilled labor, and areas follows: (5) denotes the amount of unemployed unskilled labors in the economy. The amount of unskilled labors who are employed is simply given as: This completes the framework of our model. We have nineequations and nine variables namely, ! , ' , , , , , , + and , . ' is obtained from (4). is determined from (3) as 7 is given. With and ' at hand, we get the value of ! from (2). Putting the value of ! and in (1), we get . %& ( = , , , ; = , , )are determined by the Constant Returns to Scale (CRS) assumption. is calculated from (7). Using the value of in (6) we calculate the value of . By substituting the value of and in (8), is determined. Further, substituting the value of and in (5) we get + .Putting the value of + in (9), we get the value of , . Thus, the model is solved.

2.1.Restriction international labor mobility
With a restriction oninternationallabor movement migration of particularly skilled laborsfrom developing or poor countries to rich countries is stopped and/or skilled labors are forced to return from developed to developing economies. As a result, there is an increase in the supply of skilled laborin the source economy. Since there is no change in price of the goods, there will be no change in the factor prices whatsoever and consequently the input coefficients remain unchanged.However, there may be changes in the output of different sectors. From (7), we get the percentage change in as, From equation (10) Consequently, producers have no further incentive to change their output level as, given the situation, they are already producing at their optimal point. Now, using (10), from (6) we have the percentage change in the output of sector as Using the values of @ and @ , from (8) we getthe relative change in : The positive change in , as seen in equation (11), is because sector does not absorb the skilled laborsreturned to the economy. Therefore, the excess skilled labor is employed in . Since also uses ,who are paid more than those engaged in , unskilled labors from will move out to get employed in . As a result, contracts. When contracts, along with it also releases which can be usedin . Thus, there is an expansion of as, unlike , it does not face any input constraints. Therefore, with a restriction on migration, remains unchanged, sector expands and sector contracts.
Note that this result is irrespective of the factor intensity conditions. Now, when expands and contracts, being unskilled-labour intensive releases more unskilled labors than required in . Therefore, there will be a rise in unemployment level of unskilled labors. To check the mathematical effect of international lockdown related restriction on labor mobility on the employment of unskilled labor mathematically, we use equation (5) and with the help of equations (9), (11) and (12) we obtainthe change in employment of unskilled labor as follows: Or, the change in unemployment level of unskilled labor is As presumed, since is intensive and is intensive, from equation (13), there is a fall in the employment of unskilled labor or from (14) a rise in the unemployment level of unskilled labor.Thus, we have the following proposition: Proposition 1: Given the factor intensity assumptions, there is a rise in the unemployment level of unskilled labors because ofinternational lockdown during COVID-19. ∎

A Slightly Different Framework
In this section, we develop a variant of the model considered in the previous section. Here the skilled-labor intensive sector ( ) uses only skilled labor and for production. can be regarded as the government manufacturing sector which uses , and . Asin the previous model, the unskilled labors employed in receive higher wagethan those employed in non-government sectors. To capture this we assume the wage rate in is ' which is higher than 7-the wage rate in sector .Here, we assume to be a type of capital that is specific to . Therefore, sector uses and a specific factor for production. The conditions showing the cost-price equality of , and are given below: We assume full employment of , , and existing , in the economy. A part of unskilled labor is, however, unemployed. The endowment equations of the factors are: $" + $( = 7 (21) Equations (15)-(21) along with equations(4) and (9), represent the basic structure of the model. There are nine equations and nine variables ( ! , ' , , , , , , + and , ). Hence, the model is solvable.
With the given structure of the economy, if there is an increase in the supply of skilled labor due to lockdown, the following changes occur in each of the sectors: The change in employment of unskilled labors is Or, the change in unemployment of unskilled labor is As in the previous model, there is no change in the price of any good so the factor prices and input coefficients remain unchanged.Now, as the skilled-labor intensive sector uses only skilled labor and , the inflow of skilled labor will positively affect the size of sector (equation (22)).Non specificity of any factor in X is doing the trick. As also uses , additional amount of is drawn from and thus there is a fall in (equation (23)). releases capital ( ), skilled labor and unskilled labor. and get employed in but remains unemployed. Though uses for production but the limited supply of and unchanged factor prices restrict from changing the input composition, leaving unaffected because of restriction on international labor mobility (equation (24)). Therefore, there is excess supply of unskilled labor leading to a rise in unemployment (equations (25) and (26))of unskilled workers. However, these results depend on the factor intensity assumption.If was intensive and was skilled-labor intensive then would absorb the excess supply of skilled labor and would contract in order to supply to . As also uses , the employment level of unskilled labor would have risen.Therefore, when we consider a different framework, factor intensity in production plays an important role in determining the effect of an increase in the supply of skilled labors on the employment of unskilled factors. Thus, we have,

Proposition 2:Not the structure of the economy, but the factor intensity of different sectors is fundamental in determining the level of unemployment of unskilled labordue to restriction on international labor mobility during COVID-19. ∎
Together with this, we also propose: Proposition 3: If a particular sector faces any resource constraint, it remains unaffected due tointernational lockdown.
Proof:In the basic model,one specific factor, whose supply islimited, was used by the skilled-labor intensive sector. Even if the skilled labor is used intensively in that sector, unavailability ofthe specific input in the economy restricted it from expanding. In contrast to this, in the extended model when was able to acquire inputs, we saw its expansion with increased supply of skilled labor.On the other hand, in the extended model, sector was unaffected because of the similar reason that led to non-changing in the basic model. In the basic model, suppose countries impose restriction on its imports. If is the importable good, there must be a decline in the demand for from the rest of the world (ROW) and since the country concerned is assumed as small compare to the ROW, the price of would decline. A fall in the price of will cause its output to fall releasing some of the factors employed in it. As is specific to , the rent of , fallsand would be used more intensively in . On the other hand, assuming no change in the requirement of , there will be a fall in per-unit requirement of (though the factor intensity assumption would not be changed). Thus, remains fully employed in but some and are released 3 . and gets employed in . Since is intensive it requires more than released from . This extra demand for is met by a fall in . When falls, is also released which is used in . However, as is unskilled labor intensive more is released than demanded for the expansion of leading to an increase in unemployment of unskilled labors 4 . Now if we consider the extended version of the basic model, restriction in imports by the ROW again leads to a fall in the price of discouraging its production.
There is a reduction in the output of and consequently and are released. These and can get employed in . Also, following Stolper-Samuelson's argument there is a fall in the price of the factor used intensively in i.e., ! , and there is a rise in the price of less intensively used factor i.e., a rise in . In what follows, there will be substitution of 3 Here, except , all the factor prices remain unchanged. As # is fixed, from equation (3) does not change and from equation (4) ' remains constant. Moving to equation (2), since ( is unaltered, ) also remains the same. Thus, only is affected by trade restriction.
factors in production. Again, as also requires , additional is acquired from the unemployed pool of the economy thereby reducing the level of unemployment. 5 Sector remains unaltered as it uses a specific factor, .
Therefore, unlike the case of restriction on international labor migration , when the ROW opts for restriction on trade, the effect on unemployment of unskilled labors depends on the specific structure of the economy.
Thus, we propose that: Proposition 4:Unlike restriction on labor migration,the effect of trade restriction on unskilled unemployment depends on specific structure of the economy.
Proof: See discussion above.

Conclusions
In this paper, we consider two slightly different general equilibrium frameworks to check the effect ofinternational lockdown which has been adopted by all countries across the globe to control the spread of COVID-19. First we analyze the case of restrictionon labor migration on employment of unskilled labor. Though having different structures of the economy, we see that unemployment of unskilled labor rises in both the frameworks. But the factor intensity assumptionis important irrespective of specific economic setup. In the next section, we check the employment effect of another protectionist policy, trade restriction. It is found that in case of restriction on international trade, the effect on unemployment depends on the type of economy; though as in the case migration control, the factor intensity here also plays an important role in arriving at the results.

Determination of wage in sector
The wage is determined by the labor unions by maximizing their utility function subject to the labor demand. We assume the firms to be price takers. Let the utility function of the union be: = ( , * , * ) ; where s the wage rate, * is the employment in Z, * is the relative price of . is quasi-concave and increasing in and * .
The labor demand function is * = 0 = * ( , ), here is the rent of , 0 is the partial derivative of the cost function, ( , ), and Z is the output. The demand for labor is negatively related to wage.
The first order condition implies The wage rate is determined from the above condition. The second order condition of the maximization problem also holds:
With changes in the ! and there are changes in the per unit factor requirements of and . Using the Envelope condition and the elasticity of substitution between and in , " , we get Similarly, assuming A )( = 0, we obtain Using Cramer's rule, from (C.4) and (C.7) we get the following values NOTE: There is no conflict of interest.