Venancio Salcines
University of La Coruña

Ana López-Pérez
University of La Coruña

Abstract In this work we analyse the relation which exists between a landowner and the immigrant workers contracted illegally by this person. For this reason, a theoretical model is developed based on the interconnection between the illegal and legal labour market. The big landowner analysed exercises a monopolistic power in the contracting of illegal manual labour. The application of a tariff in two parts permits this big landowner to obtain a greater surplus from the worker. Resumen En este trabajo analizamos la relación existe entre los terratenientes y los trabajadores inmigrantes que contratan ilegalmente. Por este motivo, se ha desarrollado un modelo teórico basado en la interconexión entre el mercado laboral legal e ilegal. Los grandes terratenientes aquí analizados ejercen un poder monopolístico en la contratación de mano de obra ilegal. La aplicación de una remuneración del tipo Tarifa en dos Partes le permite a este gran terrateniente extraer un mayor excedente del trabajador ilegal.

1. Introduction    A tariff in two parts is a technique for fixing the prices which permits reducing the consumer surplus. This technique is applicable to the monopolistic markets. Its application is reduced and it has been generally limited to the leisure industry and to companies renting durable goods. This problem has been studied previously (Oi, 1971; Phillips et al., 1983; Braverman, et al., 1983). From this business field the application to the loan market in the rural areas of India, Kaushik Basu (1987) has stood out. The structure of the model presented in this project is linked to the literature indicated previously. In this case an application to the agricultural labour market is carried out, and in particular to the interconnection between a labour market composed of illegal immigrants and big landowners contracting illegal labour. In this market, which remains hidden from state regulation, the big landowner obtains the maximum surplus from the illegal worker.    The objective of this project is to develop a theoretical framework which helps in the study of the relation which is established between the illegal workforce and the contracting big landowner of the aforementioned labour, as well as understanding the price strategies used by the big landowners who act as monopolistic agents. The behaviour of the illegal immigrants is studied from a point in time t, which coincides with their arrival, until a period t+1, in which their situation is legalised. The means of arriving in these nations does not effect the theoretical development of the model, and therefore, it is not taken into account in this project.    In the section "approach and microeconomic formulation of model", the optimisation of the agent´s conduct is shown, and for this reason we begin with a utility function of the illegal day labourer, based on that set up by Oi (1971) and modified afterwards by Basu (1987). The labour life of the immigrant worker is divided into two periods of time, t and t+1 and the different alternatives which can occur in each period of time are established. In this work wages are variables which are defined as a percentage of the level of production of the agricultural exploitation. The aim of this work is not the process through which immigrant workers afterwards, sell their product in a market in perfect competition, obtaining in compensation a wage. It is considered that the objective of each one of the agents to obtain the maximum benefit, for this reason, starting from the worker´s utility function, its maximisation is resolved, obtaining the function of labour demand. Likewise, the big landowner looks for the optimisation of his behaviour, through the maximisation of his function of benefits.    Afterwards, section three deals with a variation in the initial proposals, because, in the model explained in the previous section no restriction with respect to the variables considered in it is established. In this sense it is important to analyse and check the effects which would take place both for the big landowner and the worker if these were under the existence of a minimum wage in the country of origin A. Additionally the repercussions which would come from it if we do away with such restrictions are also included.    Finally, section four presents the main conclusions of the article. 2. Approach and microeconomic formulation of the model.    The model refers to the situation in which illegal immigrants who accede for the first time to the labour market of the host country find themselves. It is based on the existence of two labour markets, legal and illegal, and the interaction of two types of agents: the big landowner and the immigrant worker. The following suppositions are raised:    - Two countries are distinguished, the country of origin A and the host country of the immigrant .    - Illegal immigrants who arrive in the host country are assumed to be a group of people who, after not getting a residence permit decide to work in an illegal way and to postpone a new application to a posterior period.    - The existence of a big landowner who acts as a bidder, is considered to be monopolist in a concrete geographic area.   - The documentation required to get this permit can only be presented in the public administration by the employer, this supposition being not far from reality, because some administrations, like the Spanish one provide for it in its laws. While this collective wait for these bureaucratic proceedings to be carried out, they work illegally.    - Agricultural production is sold in a market of open competition.    - The preferences of the workers are homogeneous.    - The rate of unemployment of country A the one existent in country .    A distinction between two periods of time in the immigrant workers´ working life is established, so, in what is called period t, the immigrant worker is only going to gain access to employment qualified as illegal, because in this stage he does not fulfil the necessary requirements to achieve a legal situation. We understand by necessary requirements the dispositions established by the law (work and residence permit) which every member of the immigrant collective must fulfil to become integrated within the legal framework and regularise their situation. The big landowner acts as a monopolist agent, because he knows the circumstances of illegality in which the immigrant finds himself and his inconveniences in finding a job. For this reason some big landowners will offer the illegal worker jth a wage, wi,t(j), inferior to the one in the market, ws,t(j); being wi,t(j)>0.    The illegal immigrant worker accepts that wi,t(j)<ws,t(j) with expectations that in a near future, called period t+1, he can take part in the legal labour market with a wage ws,t+1(j), being ws,t+1(j)= ws,t(j). The wages earned by the worker jth for the two periods are defined as a percentage of its agricultural production in t, q1(j), and in t+1, q2(j): where, x>0, y>0 and x The wages of the legal day labourer for period t, are: ws,t(j)=y.q1(j) therefore, if q1= q2, then: ws,t(j)=y.q1(j)= ws,t+1(j)=y.q2(j) (2.1)    The function of utility which represents the level of an immigrant worker´s welfare, can be expressed in the following way: U(j)= u (wi,t(j) , ws,t+1(j)), where, u1,u2>o and wi,t(j)> (j) (2.2)    The emotional cost which entails for the immigrant worker to have to leave his native country is defined through coefficient K, where 0<K(j)<1 (2.3)    The average wage obtained by the worker in his native country with probability one is denoted by The following expression shows the cost of opportunity of the immigrant worker. [ (j)*(1+K(j))]= b(j) (2.4)    The expression (2.4) takes the economic cost of opportunity into account, which is represented by the wages the illegal worker does not receive (j), and the emotional cost for being far from his family environment K(j).    In period t the utility of the worker comes from the wages wi,t(j) and in period t+1 it comes from the wages ws,t+1(j).    The function of utility is supposed to be concave and distinguishable and besides it is assumed that all immigrant workers have the same preferences, which means taking into account the supposition of homogeneity of the workers. This supposition, which could seem restrictive is not so restrictive when we deal with this interconnection because most illegal immigrants have as their only aim the regularisation. This makes us suppose, without excessive cost for this model, that the preferences are homogeneous.    In the first period the employer is the one who establishes the economic conditions and the illegal immigrant the one who accepts them, consequently we have on the one hand applicants for jobs and on the other bidders and both interact in a monopolist structure, with interconnection of two labour markets, the illegal and the legal. This situation favours the increase of the employer´s benefits to the detriment of the worker´s surplus.    In moment t we find an only bidder and a group of applicants, each of them tries to achieve their goal of the most possible benefit, which, in the case of immigrant workers would mean receiving his maximum welfare, and for this reason the following maximisation problem is resolved. We suppose that (j) is constant: Max U(j)= u (wi,t(j), ws,t+1(j)), (2.5)    Derived from the resolution to this approach, we obtain the function of labour demand in the illegal market as a function dependent on wages wi,t(j) and the wages ws,t+1(j): Dl(j)=f( wi,t(j), ws,t+1(j)), (2.6) where,    This indicates that there is a positive relation on the one hand between the wi,t(j) and labour demand and on the other hand between the ws,t+1(j) and labour demand, it means the higher the wages wi,t(j) and ws,t+1(j), the higher labour demand.    The next step consists of determining the situation of the big landowner, for this reason has aim will be the obtaining of the maximum benefit for which he should equal his marginal income with his marginal cost, in this way he would act as a traditional monopolist fixing a set price. However, it is important to highlight that the employer is conscious that the interconnection between the legal and illegal markets implies the achievement of a higher benefit through the application of a tariff in two parts.    The period of time t is characterised by the existence of two alternatives for the immigrant worker, or working in the illegal market getting some wages wi,t(j) or working in the legal market getting wages ws,t(j). The function of benefit for the employer would have the following formulation: (wi,t(j) , ws,t+1(j)) = n*[q2(j)-ws,t+1(j)+(ws,t(j) -wi,t(j)] (2.8) where, n represents the total number of immigrant workers. The term [q2(j)-ws,t+1(j)], would act as a fixed amount of a tariff in two parts, the so called "entry fee" in the model of Disneyland studied previously by Oi (1971). The extra income which the employer gets for employing illegal workers, is denoted by Iiw, being defined as: Iiw(j) = (ws,t(j) -wi,t(j)) (2.9) Resulting in (2.8) in the following way: (wi,t(j) , ws,t+1(j)) = n*[q2(j)-ws,t+1(j)+ Iiw(j)] (2.10) If (2.1) is fulfilled, then (2.8) could be rewritten as: (wi,t(j), ws,t+1(j)) = n*[q2(j)-y.q2(j)+(y.q1(j) -x.q1(j))] (2.11) being, therefore: Iiw(j) = (y.q1(j)-x.q1(j)) (2.12) In (2.12) we can observe clearly how the big landowner´s incentive when contracting illegal immigrants is: y.q1(j)-x.q1(j). An increase of x would imply disincentive for the big landowner.    If the immigrant came into the country with a work permit, he would behave according to the following function of utility. This would be similar to the one that the illegal immigrant would have in t+1: U0 (j) u(0,ws,t+1(j)) (2.13)    We call the function (2.13) reservation utility curve. Given the existence of U0, the latest aim of the big landowner is to offer wages which, besides allowing him to maximise his benefits,l, gives the worker a level of utility, U(j), superior to the level of reservation utility, U0(j). This problem of restricted optimisation can be expressed as:    Hence, therefore, the following values of illegal wages are obtained, wi,t(j), and from the wages of the market ws,t+1(j), which maximise the benefit of the employer. This result and the application of a tariff in two parts, as we have already mentioned, offers a benefit l superior to the one which would be obtained if he acted as a traditional big landowner equalling the marginal income and the marginal cost. 3. Overexploitation reduction measures.    The main measure of reduction of the appropriation of the consumer´s surplus is the fixing of minimum wage. The application of this government control would reduce the number of big landowners disposed to contract foreign labour without a work permit. However, in this model we will try to observe the effects of the application of a minimum wages, wm(j), in the immigrants original country.    The minimum wage wm(j) is defined as: wm(j)>0; wm(j)>[wi,t(j)+ (1+K(j))] and wm(j)ws,t+1(j) (3.1)    This decision has an effect on the employer´s benefit. The problem of maximisation, could offer different results:    Supposing that the minimum wage of the worker, wm(j), and the wage of equilibrium, , are equal in t and in t+1, we would have it that the possible solutions are three. One of them will be selected as the wage which maximises the employer´s benefit. The three possible solutions are:    a) The wage of equilibrium are superior to the minimum wage: (>wm(j)). In this case there will be an incentive for the illegal worker to abandon country A to emigrate to country . The immigrants incentive, , for t and t+1 can be defined as: i,t= [(-wm(j)]; i,t+1= [(-wm(j)] (3.3) being i,t>0 and i,t+1>0; Iiw(j)0.    b) On the other hand, both wages could coincide, that is to say, = wm(j). In this case on being i,t= 0 and i,t+1=0, there is no incentive to emigrate to country and Iiw(j) would tend to a value zero.    c) Lastly, could be inferior to wm(j). This would be the most attractive solution for the employer, but the worker would observe how his i,t<0 and his i,t+1<0; being Iiw(j)> 0.    If country A does not apply a minimum wage wm(j) superior to wi,t(j), its workforce would be encouraged to move to country although he does not have a work permit, becoming a illegal workforce. The big landowner can introduce wages, ws,t(j), for all his workers, so, wi,t(j) = ws,t(j). The wages ws,t(j) are the same as the remuneration which the worker would get in the legal labour market in function of his qualifications, being, ws,t(j) wi,t(j) . In this situation the employers benefit would not come from the illegal labour market, because the big landowner would not appropriate the workers surplus, being his Iiw(j)=0. In this way, the expression (3.2) could be defined as: (wi,t(j), ws,t+1(j)) = n*[q2(j)-ws,t+1(j)] (3.4)    Another option which the big landowner has is to establish a monetary amount for the immigrant superior to the one offered in the legal labour market. The situation, in comparison to the previous one supposes inferior benefits for the big landowner, in fact, he will not choose this alternative, because of the three it is the one which has less benefit. Expressed mathematically, we would have that wi,t(j)>ws,t(j), which substituted in the function of the benefit: (wi,t(j), ws,t+1(j)) < n*[q2(j)-ws,t+1(j)] (3.5)    Thirdly, the employer can decide to establish some wages for the immigrants below the one earned in the legal market, that is, wi,t(j). This option means the obtaining of profits which come from both the illegal labour market and the legal labour market. The employer´s benefit in this case would be expressed mathematically in the following way: (wi,t(j), ws,t+1(j)) > n*[q2(j)-ws,t+1(j)] (3.6) From all the aforementioned alternatives, the most interesting for the employer is the last one because, it is this the one which gives a higher profit. 4. Conclusions    The migratory flows cause the movement of a great amount of labour population. In many cases, as in the immigration from Latin America to Europe, it implies travelling long distances. But, there are other migratory flows which comprise neighbouring or very near countries, as is the case of Mexico- The U.S.A., Morocco with Spain and France, or Albany- Italy just to cite some cases. Throughout the present article we have recourse to the literature about the interconnection of markets with the aim of giving a theoretical framework which explains the relationship between the monopolist big landowner and the immigrant worker. In our model we focus on two countries A and which we consider to be neighbouring and where the population has perfect information about the labour market of A and of . The labour market which we study is the agrarian, one, because, as a general rule, it has become one of the main receptor sectors of the immigrant population.    It is shown that those employers who ignore the legal dispositions of contracting labour and contracting immigrant workers try to appropriate the consumer´s surplus, a concept which in this case we transform into the day labourer´s surplus . The day labourer maximises a function of utility very similar to the one set out by Oi (1971) and later by Basu (1987). The employer maximises a function of traditional benefit, but with the difference that he introduces an extra surplus or income which comes from contracting an illegal labour. The model is enshrined in a classical analysis of price discrimination through the application of a tariff in two parts in a way similar to Oi (1971), Phillips´, Battalis´ and Raymond´s (1983), Braverman´s, Guash and Salop (1983).    The worker consents to transferring his consumer´s surplus to the employer in exchange for increasing his stay in country , because this facilitates his obtaining a residence permit. The work is approached in two stages, in the first one the day labourer is illegal and for this reason he is paid very reduced wages, which however, is superior to the one he would get in country A plus a tax which we define as emotional cost and which represents the cost of being far from his family and friends. This overexploitation is reflected in some wages which fulfil the condition of being superior to the cost of opportunity of the worker, when this is illegal. This concept "cost of opportunity" allows us to go more deeply into the causes which provoke the migratory flow, letting us affirm that if the rates of unemployment are similar, an increase in the minimum wage in country A would reduce the migratory flow to country . This conclusion indicates that the government policies which tend to eliminate the existence of a minimum wage could strengthen the existence of migratory flows on reducing the cost of opportunity suffered by the illegal worker when he leaves his country. 5. References Bardhan, P. (1980), "Interlocking factor markets and agrarian development: A review of issues", Oxford Economic Papers, 32. Bardhan, P. and Rudra, A. (1978), "Interlinkage of land, labour and credit relations: An analysis of village survey data in East India", Economic and Political Weekly, 69. Basu, K. (1983), "The emergence of isolation and interlinkage in rural markets", Oxford Economic Papers, 35. Basu, K. (1984), The less developed economy: A critique of contemporary theory, Basil Blackwell and Oxford University Press. Basu, K. (1984), "Implicit interest rates, usury and isolation in Backward Agriculture", Cambridge Journal of Economics, 8. Basu, K. (1986), "The market for land: An analysis of interim transactions", Journal of Development Economics, 20. Basu, K. (1987 a), "Monopoly, quality uncertainty and ´status´ goods", International Journal of Industrial Organization, 5. Basu, K. (1987 b), "Disneyland Monopoly, interlinkage and usurious interest rates", Journal of Public Economics, 34. Basu, K. (1987 c), "Modeling finitely-repeated games with uncertain termination", Economics Letters, 23. Basu, K. (1988), "Notes on nonlinear pricing and monopoly with a comment on Backward credit markets", Journal of Quantitative Economics, 4. Basu, K. (1993), Lectures in industrial Organization Theory, Basil Blackwell Publishers, Cambridge and Oxford. Basu, K. (1994), Some agrarian questions, Oxford University Press. Braverman, A. and Stiglitz, J. (1982), "Sharecropping and interlinking of factor markets", American Economic Review, 72. Braverman, A. et al. (1983), "Defects in Disneyland: Quality control as a two-part tariff", Review of Economic Studies, 72. Braverman, A. y Guash, L. (1984), "Capital requirements, screening and interlinked sharecropping and credit contracts", Journal of Development Economics, 14. Gangopadhyay, S. and K. Sengupta (1986), "Interlinkages in rural markets", Oxford Economic Papers, 38. Gaytán-Fregoso, H. and Lahiri, S. (2000), "Foreign aid and illegal immigration", Journal of Development Economics, 63. Guesnerie, R. and Seade, J. (1982), "Nonlinear pricing in a finite economy", Journal of Public Economics, 17. Mitra, P. (1983), "A theory of interlinked rural transactions", Journal of Public Economics, 20. NG, T. and Weisser, W. (1974), "Optimal pricing with a budget constraint: The case of a two-part tariff", Review of Economic Studies, 41. Nicholson, W. (1997), Teoría Microeconómica. Principios básicos y aplicaciones, Editorial Mcgraw-Hill, Madrid. Oi, W. (1971), "A Disneyland dilemma: Two-part tariffs for a Mickey Mouse Monopoly", Quarterly Journal of Economics, 85. Philips, L. (1983), The economics of price discrimination, Cambridge University Press. Phillips, O. et al. (1983), "Two-part tariffs and monopoly profits", Bell Journal of Economics, 2. Roy, J. and Serfes, K. (2001), "Intertemporal discounting and tenurial contracts", Journal of Development Economics, 64. Schmalensee, R. (1981), "Monopolistic two-part pricing arrangements", Bell Journal of Economics, 12. Sengupta, K. (1997), "Limited liability, moral hazard and share tenancy", Journal of Development Economics, 52. About the Author Autores: Venancio Salcines & Ana López-Pérez Dirección: University of La Coruña Correo electrónico: jvsc@udc.es

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Editor: Fernando González-Laxe. (Universidade da Coruña)
Director: Venancio Salcines. (Universidade da Coruña)
Subdirector: Andrés Blancas. Instituto de Investigaciones Económicas (UNAM)
Editor Asociado para America Latina: Luis Miguel Galindo. Facultad de Ecomomía (UNAM)