This paper introduces a new model describing the aggregate growth of job markets. We divide the job market in each city into two groups: native job market of size and an immigrant job market of size . A reversible migration of jobs exists in both groups. In addition, the interaction between these two groups creates both native and immigrant jobs. A loss of native jobs also takes place due to the interaction. Through studying initial conditions, job-creation rate, and job-loss rate we discover some meaningful results. The size change of native job market is closely related to that of the migration rate, native job-creation rate, and native job-loss rate. We assume that these rates are proportional to the sizes of two groups and find out that for certain initial conditions, immigrants influence native job markets positively. They create more jobs for both job markets. In addition, we can make conclusions about the future trend of the flow of jobs. People will move to places like big cities where there is a higher concentration of job opportunities. 1. Introduction Much research has been done on the aggregation process in the past few decades. This enthusiasm starts from natural scientists, according to [1–3] and references therein. Biologists find it possible to study the behavior of species via aggregation process [2], and physicists use it to look at dynamics of different systems [1, 3]. With the development of knowledge about networks, aggregation process has been applied to solve many networking problems. These problems vary from population migration [4] to social network about individual interactions in [5, 6]. Some people have introduced this method to social sciences as well, such as [7, 8]. Another field where aggregation process is vastly applied is population dynamics [9–11]. Population groups are viewed as aggregates, and the interaction among them can be assimilated to the ones among aggregates with different sizes. Immigration phenomenon is studied through aggregation process as well, such as in [12, 13]. Here immigration leads to two major effects: catalyzed birth and death rates on the original group. The relative dominance of one effect over the other is analyzed through the growth of the aggregates. Some assume an irreversible reaction scheme when dealing with aggregates: in [1]. Here, is an aggregate with size , and is the rate of migration from to . This scheme shows that for each individual monomer, it prefers larger aggregates and always moves from the smaller ones to the bigger aggregates. However, a more general reversible reaction
References
[1]
F. Leyvraz and S. Redner, “Scaling theory for migration-driven aggregate growth,” Physical Review Letters, vol. 88, no. 6, Article ID 068301, 2002.
[2]
M.-X. Song, Z.-Q. Lin, X.-D. Li, and J.-H. Ke, “Aggregation behaviors of a two-species system with lose-lose interactions,” Communications in Theoretical Physics, vol. 53, no. 6, pp. 1190–1200, 2010.
[3]
J. M. Grogan, L. Rotkina, and H. H. Bau, “In situ liquid-cell electron microscopy of colloid aggregation and growth dynamics,” Physical Review E, vol. 83, no. 6, Article ID 061405, 2011.
[4]
J. H. Ke, Z. Q. Lin, Y. Z. Zheng, X. S. Chen, and W. Lu, “Migration-driven aggregate growth on scale-free networks,” Physical Review Letters, vol. 97, no. 2, Article ID 028301, 2006.
[5]
R. Y. Sun, “Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence,” Computers and Mathematics with Applications, vol. 60, no. 8, pp. 2286–2291, 2010.
[6]
D. Dimitrov and C. Puppe, “Non-bossy social classification,” Mathematical Social Sciences, vol. 62, no. 3, pp. 162–165, 2011.
[7]
Z. Q. Lin, J. H. Ke, and G. X. Ye, “Mutually catalyzed birth of population and assets in exchange-driven growth,” Physical Review E, vol. 74, no. 4, Article ID 046113, 2006.
[8]
K. Zhao, J. Stehlé, G. Bianconi, and A. Barrat, “Social network dynamics of face-to-face interactions,” Physical Review E, vol. 83, no. 5, Article ID 056109, 2011.
[9]
K. Lu, Z.-Q. Lin, and Y.-F. Sun, “Kinetic behaviors of a competitive population and fitness system in exchange-driven growth,” Communications in Theoretical Physics, vol. 50, no. 1, pp. 105–110, 2008.
[10]
I. Daitoh, “Productive consumption and population dynamics in an endogenous growth model: demographic trends and human development aid in developing economies,” Journal of Economic Dynamics and Control, vol. 34, no. 4, pp. 696–709, 2010.
[11]
M. R. Gupta and P. B. Dutta, “Skilled-unskilled wage inequality and unemployment: a general equilibrium analysis,” Economic Modelling, vol. 28, no. 4, pp. 1977–1983, 2011.
[12]
R. Hermsen and T. Hwa, “Sources and sinks: a stochastic model of evolution in heterogeneous environments,” Physical Review Letters, vol. 105, no. 24, Article ID 248104, 2010.
[13]
R. E. Baker and M. J. Simpson, “Correcting mean-field approximations for birth-death-movement processes,” Physical Review E, vol. 82, no. 4, Article ID 041905, 2010.
[14]
Q. Chang and J. Yang, “Monte Carlo algorithm for simulating reversible aggregation of multisite particles,” Physical Review E, vol. 83, no. 5, Article ID 056701, 2011.
[15]
Y. Bramoullé and G. Saint-Paul, “Social networks and labor market transitions,” Labour Economics, vol. 17, no. 1, pp. 188–195, 2010.
[16]
G. L. Wang, W. S. Tang, and R. Q. Zhao, “A birandom job search problem with risk tolerance,” Journal of Applied Mathematics, vol. 2012, Article ID 161573, 12 pages, 2012.
[17]
G. Peri, “Rethinking the area approach: immigrants and the labor market in California,” Journal of International Economics, vol. 84, no. 1, pp. 1–14, 2011.
[18]
C. Bayer and F. Juessen, “On the dynamics of interstate migration: migration costs and self-selection,” Review of Economic Dynamics, vol. 15, no. 3, pp. 377–401, 2012.
[19]
R. Y. Sun, “Kinetics of jobs in multi-link cities with migration-driven aggregation process,” Economic Modelling, vol. 30, pp. 36–41, 2013.
