Instead of looking at it from the past, you also need to look at it from the costs. It's not just the marginal theory of productivity, but just basic cash in minus cash out. A $5 an hour increase in wages is a $10K per year per employee increase in costs, not counting the extras so it's about $12K per employee. Five employees and a business is looking at an extra $60K in costs. So the question is what percentage of businesses can find way to absorb that costs. They need to do a combination of raise prices, take the profit hits, or find a way to reduce those costs.
I have said repeatedly that I believe that the marginal productivity theory is bullsh*t. But it is the theory that proponents of the free market advance to show that the market can self-regulate without government interference. That too is bullsh*t.
Yes, this is why the increases have to be implemented slowly over time to allow the market to adapt. And yes, prices aren't set by supply and demand. Prices are set by the owner to an average cost of production plus a profit resulting in a price that he thinks that he can get the sales volume needed to pay back his investment and his work.
Someone here said that they thought that supply and demand sets prices but the cost plus overhead and profit set price establishes a floor below which the supply and demand set price can't go. In reality he or she is close to the truth but a bit backwards. The owner sets a cost plus price and the demand for the product determines the amount of sales for the product at that price. Virtually every business looks at average costs and sales volume. I doubt that any business calculates or cares what the marginal product is, what it costs them.
In addition there are a lot of factors that effect the demand for a product besides the price; advertising, convenience, reputation, etc. At least fifty percent of the employees of almost any modern corporation are working to distance the corporation's products from market forces. To enable them to charge a higher than market price. And they succeed for the most part.
So yes, prices will go up.