Apart from the preferences of the agents, an efficiency criterion, , is used to assess the reform. For this aim the total production in both regions have to be calculated, lowered by the total costs of migration. Related to one firm from each region, the variable is defined as follows:
In contrast to the above mentioned intuition, figure 5 shows, that central UI may well be preferable for efficiency reasons. For every given benefit rate ,
is positiv. This means, that firms and workers who profit from central UI, could compensate those, who are worse off. The figure also shows, that only firms from the rich region would be better off with regional UI. With the given functional relationships and parameters, the conjecture that the interests of agents from the poor region are contrary to the interests of those from the rich region, cannot be confirmed. While the profit differences for the firms are considerable, the preferences of workers from both regions toward central UI are only weak.
The described results can be explained by the partial effects summarised in figures 1 and 2. Because region 1 (region 2) has an unemployment rate below (above) average, the UI tax rate is lower (higher) in the case of regional UI. If workers are sufficiently risk-averse, this leads to lower (higher) equilibrium wages. Then, employment is higher (lower) in equilibrium, which reinforces the initial effect on the UI tax rate. The effects on the expected utility of workers and also on migration are not quite clear, yet. On the one hand, the relatively lower UI tax rate and higher probability of entering employment have a positive impact on migration from the poor to the rich region, respectively. On the other hand, wages are, in comparison to central UI, higher in the poor region, and lower in the rich region, which has a negative influence on migration. For the specific functions and parameter values we assume the positive effect prevails, so that equilibrium migration is higher in the case of regional UI. The additional costs of migration may explain to some extent, why the efficiency criterion supports central UI. The contrary effects on the expected utilities, together with compensatory migration involve the relatively small preference of workers from both regions towards central UI.