Minimum wage was lowered, it would increase unemployment at the low end of the wage scale. In a paper written for the Cato Institute following the increases in the early 90's, it was shown that workers in the lowest income bracket suffered net job loss. The study looked at teenagers and workers without a high school education and found that those unemployment in those groups increased following the increases in minimum wage. There was a drop in employment amongst all workers during this period, but it was lower than among workers in the most vulnerable groups.
In terms of individual employees, those who remain employed benefit, those who lose their jobs do not. However, many of the minimum wage jobs are subject to high turnover, so the decline in employment is as likely due to attrition as anything else. Individual companies face an immediate decline in productivity as wages rise, but over time will compensate for this by finding ways to operate with fewer employees. This will occur either by squeezing more productivity out of remaining workers, hiring more productive workers, shifting work abroad or increasing automation. The reality is that minimum wage jobs are usually service sector jobs and cannot be shifted abroad nor replaced with automation, so the first two options are the most likely.
Indeed, the likelihood of long-term productivity increase is high because there will be new workers attracted into the labor pool by the higher wages, a theory put forth by Bill Clinton when he raised the minimum wage in the 90s and supported even by right-wing economists. These workers will replace the lowest-productivity minimum wage workers, who will be the ones to suffer the greatest loss of employment. This increase in average worker productivity is ultimately good for the economy. In an efficient economy, the least productive workers will by the ones without jobs. Moreover, in many cases these are teenagers, who will over time become more productive - the loss of one minimum wage job does not preclude them from re-entering the workforce at a future date. Indeed, the average teenager will lose several jobs before achieving a stable position in the workforce, regardless of minimum wage policy. There is little social impact to increasing unemployment levels amongst the least productive workers in society, given that just 1.2% of minimum wage earners are household heads and only 2.8% of low-wage earners are single parents.
If we assume that companies will even out productivity in the long run via the means above, then the largest impact will be on net employment. In many parts of the U.S., companies that employ workers at minimum wage levels are perpetually hiring - they cannot fill positions at these wage levels. The impact of the economy overall is minimal as well, because the lowest-income workers contribute little to the economy.
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