Immigration model with costs

The model illustrated in Figure 7.1 is the case of costless migration, when workers are free to move across borders without incurring migration costs or facing immigration restrictions. Of course, that is not the case in the real world. Migration costs can be significant. Explicit costs include travel costs and visa fees associated with a move, while implicit costs include psychic costs or cultural adjustments that people experience when they move away from their family and friends. Immigrants may incur costs associated with learning a new language and searching for a new job. The model in Figure 7.1 can be extended to include migration costs.

Assume that migration costs are constant and denoted by the parameter C > o. If workers in the origin migrate to the destination, they must incur these migration costs. When migration costs are added to the model, the net gain to migration is smaller. Figure 7.2 graphs the basic immigration model with migration costs C. Equilibrium occurs when the net gain to migration (after migration costs) equals the return to staying in the origin. In equilibrium, workers migrate until Wp*-C = Wq*, which occurs at L** in the graph. Fewer workers find it optimal to migrate compared to the case with no migration costs—only L** - Li workers migrate (instead of L* - Li workers, as in Figure 7.1). Wages adjust, but not as much as in the free migration case (when C = o). Notice that in the destination, wages still fall when migration occurs (from WQ to W'D'‘), but not as much as in the free migration case (W*). Thus, the wage effects of immigration on natives are smaller when migration costs exist. A desire to protect natives' wages can motivate governments to restrict migrant flows. In fact, governments could charge sufficiently high migration fees to prevent legal immigration altogether.

The immigration surplus is smaller when there are migration costs. The gains to immigrants are smaller as well. With migration costs, there is a deadweight loss, or loss of economic efficiency, compared with free migration. The deadweight loss due to migration costs is the shaded area in Figure 7.2. Part of the deadweight loss is gains that would have accrued to other factors of production in the destination, and part of

Adding migration costs to the basic immigration model

Figure 7.2 Adding migration costs to the basic immigration model

Each immigrant incurs a fixed cost equal to C. In equilibrium, workers migrate until Wq* -C = Wq1', which occurs at L**. The shaded area is the loss in social welfare due to migration costs compared with costless migration.

it is gains that would have accrued to immigrants. Theoretically, the world would be better off if there were no migration costs or immigration restrictions—the welfare gains would be bigger.

In Figure 7.2, migration costs increase as immigration policy becomes more restrictive, leading to larger deadweight losses. However, immigration policy may also have a direct impact on the supply of labor. Countries often will increase border enforcement as a way of restricting immigration. Increased border enforcement will reduce the number of unauthorized immigrants in a destination, leading to a reduction in labor supply. Ironically, an enforcement-induced decrease in labor supply raises wages for the remaining workers in the destination (including natives). Figure 7.3 illustrates this in a supply and demand framework.

Upward-sloping labor supply when immigrants and natives are perfect substitutes

So far, the model has assumed that labor supply in both the destination and the origin is perfectly inelastic, which means that workers will work at any wage. Assume instead that labor supply has some elasticity—some workers are no longer willing to work if wages fall. If labor supply has some elasticity, the labor supply curve slopes up instead of being vertical. An upward-sloping labor supply curve is more realistic.2

The effect of increased enforcement on wages

Figure 7.3 The effect of increased enforcement on wages

An increase in border enforcement decreases the supply of unauthorized workers. This results in a higher wage.

Figure 7.4 graphs the labor market in the destination country when immigrants and natives are perfect substitutes. Notice that the labor supply curve is upward sloping. Immigration causes the labor supply curve to shift to the right, from S to S'. Wages fall from WDto WD’. Total employment increases from iD to L0'. However, with an upward- sloped labor supply curve, employment of natives falls from L0 to LN because only Ln natives are willing to work at the new, lower wage WD’. The number of immigrant workers is L0' -LN.

Effects of immigration in the destination with upward-sloping labor supply

Figure 7.4 Effects of immigration in the destination with upward-sloping labor supply

Immigration causes the supply of labor to shift to the right. The wage falls from W to WD’. The number of natives employed falls from L0 to LN. The number of immigrants employed is L0-LN-

The key difference between an upward-sloping labor supply curve and the perfectly inelastic case is whether workers are willing to work at any wage. As immigration increases the supply of labor, there is downward pressure on wages. If labor supply is not perfectly inelastic, not all natives are willing to work at the new, lower wage. Some natives decide not to work at the lower wage, and employment of natives falls. Note that this has nothing to do with unemployment (recall the model used here assumes zero unemployment). Rather, it implies that even in a model of full employment, some native workers simply decide to exit the labor market altogether because the wage is too low to entice them to work. The assumption is that immigrants and native workers are perfect substitutes in production. Thus, some immigrants replace native workers in the destination. This effect is often described as the lump of labor fallacy. If labor demand is perfectly inelastic and there is a fixed number of jobs in an economy, an increase in immigration leads to the displacement of native-born workers. Returning to our model, in the case of perfectly inelastic supply, all native- born workers are willing to work at the lower wage, so immigration does not lead to a change in the number of natives employed and hence immigrants do not replace natives or “take their jobs.”

The elasticity of labor supply has welfare implications. With a perfectly inelastic (vertical) labor supply curve, the immigration surplus is area C + F + G in Figure 7.5. If labor supply has some elasticity, the immigration surplus is just area C. Other factors of production in the destination earn A+B + C + D + E+ F + C after immigration if labor supply is perfectly inelastic, and just A + В + C if labor supply has some elasticity. If labor supply is perfectly inelastic, immigrants earn J + K+ M; they earn E + F + I + J + L + M if labor supply has some elasticity. If labor supply has some elasticity, some natives (LD - LN) exit the labor force and the wage falls to WE in response to immigration. If labor supply is perfectly inelastic, LD natives remain employed, but at wage W( after immigration. If labor supply is perfectly inelastic, the earnings loss to native-born workers is В + D + E. If labor supply has some elasticity, the earnings loss to native-born workers is В + E + I + L. Overall, there is less of an immigration surplus with elastic labor supply because some native-born workers exit the labor force due to lower wages.

 
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