Am I wrong to assume this? If the min wage was raised from say $7 to $15, would that really hurt peoples purchasing power who were previsouly making between maybe $12-$18 dollers an hour?
sure, because so many people who are productive in the under 15$ bracket would become unemployed, this would have two negative effects
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fewer people producing and sharing in the division of labour, so costs of goods rises, eroding purchasing power of money
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the unemployed need welfare from those still employed, increasing the welfare burden on those still earning higher nominal wages.
It would hurt everyone. Obviously, many of the people who were being paid under $15 per hour would be out of work. It would not be financially feasible to continue the production processes that they were involved in with the higher costs. Other production processes would continue to be financially feasible but the profit margin would be reduced, as the labor costs would increase from, for example, $12 per hour to $18 per hour. People who had been making $15 per hour would take the jobs that were still financially feasible from those who had been making less. This would continue, to a diminishing extent, throughout the payscale. The costs of the goods and services that previously used $7 per hour labor would go up, and the quantity produced would go down.
Meanwhile, many people who had been employing others to do certain jobs would find it financially feasible to do these jobs themselves or leave them undone. The $15 per hour wage earner would no longer be able to afford to pay someone $15 per hour for things like daycare for their kids, yard work, or changing their oil. They would also spend less for goods and other services that included these additional labor costs. In some cases, they would work less in order to do this work themselves. In others, they would reduce the services that they were receiving. Furthermore, the reductions in profits for employers would result in less investment in the machinery and equipment that would make it possible for people to do their work more efficiently. Even people making $100 per hour would have to cut back on their expenses for things like their daily cup of coffee, housekeeping, and other expenses. This would make them less productive. So, increases in the minimum wage hurt everyone.