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Insidb said:
If you increase minimum wage, you increase overhead. If you increase overhead, you increase costs.

If you increase minimum wage, you increase consumer capitalization. If you increase customer capitalization, you increase revenue.

Unless one business is paying every single worker, they benefit from the increased capitalization of all customers.

The inflation fallacy is based on the false premise that only costs will increase to businesses (by ignoring increased capitalization of customers).

A few things:

1. You are only thinking of the dichotomy of large businesses, with high profit margins versus. consumers. Small businesses which can't afford massive increases in the cost of labor will go out of business outright. This is especially true if they are in a perfectly competitive market, and are consequently price-takers.

2. I have never seen the argument that it will increase capitalization among the poor. In fact, the opposite argument (it will increase aggregate demand) is given. for why we should have higher minimum wage laws But if this were always true, why not indefinitely increase the minimum wage? Most people are not going to invest their new wages into capital. They are going to go buy video games, televisions, and new cell phones with a sizable minority who are currently not meeting their basic needs using that money on those needs. Think about the people who make minimum wage. They aren't future business owners who will accumulate capital, with the exception of the sizable portion of students making minimum wage. But they have supplementary income from other sources (financial aid or parents.) 

3. There is very little evidence that aggregate demand will increase. While it is clear that average wages will increase, it is also clear that a percentage of the populaton will become unemployeable. That percentage will likely counter-balance any gains in the group who get higher wages. The last empirical statistic I had read was something like a 10% increase in minimum wages leads to a 1% increase in unemployment on average in cities and states that have instituted such policies. These tend to be places with high average wages already (like San Fransisco and LA.) Imagine the effects in places like the mid-west or south where the cost of living is much less, and overall the population is less productive, but they can use cheaper labor to theier advantage. More than anything else, it seems to me as if it will centralize capital to large cities, and only increase demand in large cities.