The elasticity of labor supply is defined as the amount that the labor supply increases in response to an increase in wages. We can look at the problem of how migration would affect this through a hypothetical example.
If you imagine an isolated island with 1,000 potential workers, there might be a labor supply of 900 people working or looking for work. Of the remaining 100, some might be retired, some in school, some full-time parents, and some on social assistance. If wages rose enough, though, some of the students might decide to take part time jobs, pensioners might return to the work force, and so on. The upper limit to this elasticity on an isolated island would be the total number of people on the island not in work who had the requisite job skills.
Even islands are not completely isolated, though. If wages rose on our hypothetical island, people from neighboring islands would migrate to take advantage of higher wages. These immigrants might consist of people inside or outside the labor force in their native lands. Thus, freedom of migration dramatically expands to potential supply of labor to a global population.
An even more dramatic effect comes from skill matches. Imagine that Basket Island has a need for more basket weavers and raises wages for basket weavers to the point that all skilled basket weavers on Basket Island are employed. On neighboring Pottery Island, all people with pot-making skills are employed. Thus we would have two islands with no labor supply elasticity. There might, though, be unemployed skilled potters on Basket Island and unemployed skilled basket weavers on Pottery Island; removing obstacles to migration would create significant elasticity in the regional labor supply.
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