The transition of labour in the presence of adaptation cost and labour market segmentation

In this paper, we explore the process of transition of labourers from the traditional to the modern sector. The firms in the modern sector can initially differentiate between migrant workers and native workers. However, as the number of workers from the traditional sector increases, the firm cannot segment the labour market. The migrants bear an adaptation cost. The process of transition of labour (migration) is studied through the replicator map. We study the nature of migration in the long run. When adaptation cost monotonically decreases in the share of labourers from the traditional sector engaged in the modern sector, we get an unstable interior equilibrium and two stable equilibria at the boundary. We show convergence to the stable fixed points. When the adaptation cost is non‐monotonic, we get four equilibrium points of which two are stable and two unstable. We get a stable interior equilibrium point implying that only a fraction of labourers is going to shift to the modern sector in the long run. We also show convergence to the stable fixed points under certain conditions on the derivative of the difference equation.