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Workers from region 2 emigrate if the expected utility in region 1 - taking migration costs into account - exceeds expected utility in region 2. In equilibrium, the utility a worker from region 2 expects in the case of emigration is the same as in his home region. Thus, workers from region 2 are indifferent concerning the regions. As a consequence, the extent to which migration occurs, depends positively on wages and the rate of employment in region 1, and it depends negatively on wages and the rate of employment in region 2 (Borjas; 1996, S. 314). Due to the costs of migration, workers from region 1 strictly prefer to stay in their home-region. The following equation poses the condition for a migration equilibrium:
where
is the share of workers in region 1. The first row of equation (8) stands for the expected utility of a worker from region 2 who emigrated to region 1. The second row contains (with a negative sign) the expected utility of a worker from region 2 who stays.
The condition for an equilibrated budget in the case of a central UI reads:
![\begin{displaymath}
F^{UI}= n^1 K \tau w^1 + n^2 K \tau w^2- (s M-n^1 K) \beta w^1- [(1-s) M - n^2 K] \beta w^2 =0.
\end{displaymath}](img75.png) |
(9) |
In equation (9), the revenue of the UI,
, has a positive sign, and the expenditure
has a negative one. If the budget is balanced, both must sum up to zero.
Equations (8) and (9) respectively describe, how migration (symbolised by
) and UI contributions (
) react if variables, which are exogenous from the point of view of the UI or a single worker, vary. They build a submodel, which determines
and
, whereas the outcome of the wage-bargains in both regions is taken as exogenous. This technique allows to consider only that part of the model, which depends on the organisation of UI. Partially differentiating equation (9) yields the following comparatively static results:
In the appendix, it is shown that the signs of the derivatives with respect to wages only follow if the rate of employment in the region with a better endowment with infrastructure (region 1) is higher than the average. This condition will be referred to hereafter as condition a. The contribution rate depends positively on
if
(condition b). The reason is that migration to region 1 increases the number of unemployed who are eligible for benefits according to the wage rate
. If this wage rate is higher than
, the expenditure of the UI increases with a given number of employed in both regions.
Partially differentiating the implicit equation (8) gives
where
denotes the utility of a worker from region 2 after emigration to region 1.
is always positive because otherwise the union would not have an incentive to reach an agreement.
is ambiguous in general. The sign depends on the value of the expression between square brackets in the numerator. Because labour has a higher intramarginal productivity in region 1, it is likely that
and
. By definition,
. The condition for a negative relationship between UI contributions and migration (condition c) is
Model TC consists of the characteristic submodel described above, and the submodels determining wages and employment in both regions. The equilibrium conditions needed to calculate the endogenous variables are equations (1) and (6) respectively for the poor and the rich region, equations (8) and (9). Figure 1 illustrates and summarises the interactions between endogenous variables in the model. Each arrow represents a direct partial effect. The arrows are labeled with the sign of the effects, respectively. If the effect is ambiguous, the arrow is labeled with a sign and the letter of the condition that must hold to yield the respective result.
Figure 1:
Partial effects in model TC
 |
Next: Regional UI, endogenous contribution
Up: Endogenous tax rate
Previous: Endogenous tax rate
Helge Sanner: Regional Unemployment Insurance, Potsdam 2001