| The new jobs create an increase in employment of 1 million.
But, according to the definition of unemployment, it creates an additional
1.5 million people looking for work and therefore classified as part of
the labor force. So the effect of the new jobs is to increase employment
by 1 million and increase the labor force by 1.5 million. |
| So does unemployment rise or fall? Let x be the
size of the labor force without the new progarm, and let y be the
number of people who would have jobs without the new program. Then, without
the program, the unemployment rate is |
| u = 1 -
y/x. |
| Now, with the program, the number of people with jobs
goes up to y+1, while the size of the labor force goes up to x+1.5.
That is, the unemployment rate with the program is |
| v = 1 -
(y+1)/(x+1.5). |
| The change in the unemployment rate caused by the new
program is therefore |
| v -
u = 1-(y+1)/(x+1.5)
- (1-y/x). |
| You can easily work out that this expression is positive
if y > 2x/3, and negative otherwise. Note that if y >
2x/3, then u = 1-y/x
< 1/3 That is, if the original unemployment rate is less than 33.3 percent,
the program increases unemployment. |