Numerical Illustration of Welfare Losses
When Mobility is Restricted

                        US                                              Mexico

             VMP=w           PQ                      VMP=w            PQ

      1          $25,000      $25,000        1             $21,000         $21,000

      2          $23,000      $48,000        2             $19,000         $40,000

      3          $21,000      $69,000        3             $17,000         $57,000

      4          $19,000      $88,000        4             $15,000         $72,000

      5          $17,000    $105,000        5             $13,000         $85,000

      6          $15,000    $120,000        6             $11,000         $96,000

      7          $13,000    $133,000        7              $9,000        $105,000

      8          $11,000    $144,000        8              $7,000        $112,000

      9            $9,000    $153,000        9              $5,000        $117,000

    10            $7,000    $160,000      10              $3,000        $120,000

Case 1. There are no mobility costs. Equilibrium is reached when the wage is $15,000 in each market--when there are no obstacles to mobility (such as border checks by the Border Patrol). If the Border Patrol actively discourages mobility by illegal aliens, then fewer workers will cross over from Mexico to the US. If four workers are discouraged, then L = 2 in the US and L = 8 in Mexico. This gives the US a value of output of $48,000 and Mexico a value of output of $112,000 (compared to $120,000 and $72,000 respectively when mobility was not discouraged). This in a net loss of $32,000 between the two countries (a loss of $72,000 for the US and a gain of $40,000 for Mexico).
 

Case 2. To be done as an exercise. Assume there are mobility costs such that the equilibrium wage differential is $4,000 between the US and Mexico. Work out an example like that illustrated in case 1.