The minimum wage doesn't address underemployment.
Underemployment is a far larger driver of poverty. A minimum wage does nothing to address underemployment.
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For many families, it is not low wages that contribute to conditions of poverty, but underemployment.
Only 7% of families living in conditions of poverty in the US have a family member that works full time. This means that policies affecting a minimum wage have limited impact on 93% of the families living below the national poverty line.
Implementing or increasing a legal minimum wage spurs job creation through increased demand. This might bring more adults into the workforce and allow for more families living in poverty to secure full-time work. Therefore, the assertion that policies governing a minimum wage would do little to lift families out of unemployment is incorrect.
Underemployment is a larger driver of poverty than low wages.
[P1] Underemployment and unemployment are more responsible than low wages in developed economies. [P2] A minimum wage will have no effect on underemployment and unemployment. [P3] Therefore, a minimum wage is not effective at reducing poverty.
Rejecting the premises
[Rejecting P2] Policies affecting a minimum wage create jobs, reducing unemployment and underemployment.