For that to be true, you would have to assume that raising the minimum wage does not increase the cost of products&services, and does not raise the price of everything at the same time as well (I.e. a min wage earner earning $5, then getting wages raised to $7, will still be earning an equivalent of $5 when adjusted by the resulting inflation).
You need to demonstrate some things to follow that line of logic. They are:
- The efficiency of $5 workers vs. $8 workers
I'm saying you are using nominal values, when the real value of those is the same. The efficiency of a worker earning $5 in year 1 is the same as the efficiency of a worker earning $8 in year 2 when adjusted for the 60% inflation caused by the rise in that wage. Now, I'll grant you that the inflation jump won't be in the entire economy. As i mentioned previously, high level services and products used by wealthy people will probably not be affected, but things used by those same minimum wage earners, like fast food, bread, milk and other produce, discount store prices, and other businesses like that will be.
- The operating margins of the company
In a perfectly competitive market, margins, and thus profits, are zero. A lot of the companies that have minimum wage workers are in industries with enormous competition. McD's has Burger King, White Castle, Hardee's, Checkers/Rally's, Wendy's, Arbys, Roy Rogers, and even Taco Bell to compete against if you include substitutions. Thus I expect their margins to be tiny, pennies per hamburger (close to $0.13 for a BigMac back in 2001, no idea what now). Small margins = raise prices or reduce costs (employees)
- The law of diminishing returns regarding more workers
This is almost irrelevant, as any company that hopes to compete would keep only the workers it needs. Companies don't hire more employees just to give someone a job. Those that do that are beaten out on price and fail.
- The quality of service or products using cheaper labor
Again, irrelevant, because the quality of the product or service is what you are selling, not what you are giving away for free. The reason Checkers/Hardee's can charge more than McD's for their burgers and still stay in business is because they provide more quality burgers. It is NOT because they pay their employees more, and the employees choose to make better burgers as a "thank you" to the company. So, if the quality of your product sucks, yes, you can hire more competent employees and pay them a higher wage (which wouldn't have anything to do with minimum wage laws), but then you would have to include that increased cost in your product, or go broke. And if the quality of your product sucks compared to your competitor, but you are both paying the same wages, then obviously something else is wrong. And if your product just plain sucks, then no amount of well paid employees will help you anyway.
Let me know where I've missed something