Question

Suppose that unemployment insurance system is structured such that Bmin = 200, Bmax = 500, and B = 100 + 0:5w in between, where w is the previous weekly wage and B is the level of weekly UI bene ts. Graph this bene t formula and calculate the bene ts and replacement rates for workers who earned $100, $500, and $2000 in the last week of working.

Answer 1

The relation between unemployment benefits is given as:

B = 100 +0.5w

This means that when w = 0, B = 100.

However minimum UI B_min = 200 according to unemployment insurance system.

Let us find the wage level at which B = 200

200 = 100 +0.5w => w = 100/0.5 = 200

Hence, for all w < 200, unemployment benefit is contant at B_min level.

Similarly when w = 800, B = 100 + 0.5*800 = 500 which is the maximum unemployment benefit that can be provided.

Hence for all w > 800, unemployment benefit is constant at B_max level.

Plotting this graphically, we get the following graph (Red shape determines actual UI system)

Replacement rate is the percentage ratio of unemployment benefits paid through unemployment insurance system to worker's pre-retirement income (in the last week of working).

Mathematically, it is calculated as:

• Now when, wage in last week of working w = $100,

Unemployment benefits after quitting = $200

Hence replacement rate for worker = (200/100)*100 = 200%

• When wage in last week of working w = $500,

Unemployment benefits after quitting = 100+0.5*500 = $350

Hence replacement rate for worker = (350/500)*100 = 70%

• When wage in last week of working w = $2000,

Unemployment benefits after quitting = $500

Hence replacement rate for worker = (500/2000)*100 = 25%