The bleeding heart concerns of the Left for job losses from economic policy changes such as from trade liberalisation disappears as soon as they discuss the losers from a living wage increase.
Instead of may the heavens may fall but a manufacturing job must not be lost from trade liberalisation, a brutal utilitarian calculus overtakes Noah Smith and the living wage movement about the small number of job losses that result from modest increases in the minimum wage.
Most are those who support the minimum wage shift gears their applied welfare economics in all other social context to emphasise how the losers should be given priority and greater weight when adding up the social gains and social losses of economic change.
The social cost of the minimum wage is not discussed in this way: how many jobs are lost and that these job losses are much more important than any gains to society.
All that is done is the number of jobs lost is compared with some other social metrics such as how much the wages go up for those that still have a job and that is enough to conclude that there is a socially beneficial change from a minimum wage increase.
Any low paid workers affected by the minimum wage increase are just reduced to numbers and added and subtracted with great ease and few moral compunctions about interpersonal comparisons of utility.
A minimum wage increase is not free if one worker loses their job. The Paretian Criterion states that welfare is said to increase or decrease if at least one person is made better off or worse off with no change in the positions of others.
As Rawls pointed out, a general problem that throws utilitarianism into question is some people’s interests, or even lives, can be sacrificed if doing so will maximize total satisfaction. As Rawls says:
[ utilitarianism] adopt[s] for society as a whole the principle of choice for one man… there is a sense in which classical utilitarianism fails to take seriously the distinction between persons.
Minimum wage advocates fail to take seriously that low paid workers who lose their jobs because of minimum wage increases are real living people who suffer when their interests are traded off for the greater good of their fellow low paid workers, some of whom come from much wealthier households.
As Rawls pointed out, a general problem that throws utilitarianism into question is some people’s interests, or even lives, can be sacrificed if doing so will maximize total satisfaction. As Rawls says:
[ utilitarianism] adopt[s] for society as a whole the principle of choice for one man… there is a sense in which classical utilitarianism fails to take seriously the distinction between persons.
Minimum wage advocates fail to take seriously that low paid workers who lose their jobs because of minimum wage increases are real living people who suffer when their interests are traded off for the greater good of their fellow low paid workers, some of whom come from much wealthier households. Obviously the teenagers and adults thrown onto the scrapheap of society by an increased minimum wage don’t count in the brutal utilitarian calculus Noah Smith and the living wage movement employs.
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Utopia, you are standing in it! 
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