> Wages are a function of the scarcity of labor

This assumes an unconstrained "market" for the exchange of labor and wages, just as the claim that "prices are a function of the scarcity of goods" assumes an unconstrained "market" for the exchanges of goods and money.

But this is not the only model for economic exchanges of labor, goods and money. The Romans, for example, did not use market pricing, but instead were primarily a "cost-plus" economy (you paid the cost plus a known margin).

I know it is extremely hard when most of us have been embedded in a neoliberal, market-centric culture for our entire lives to think this far outside the box, but there really is no law of nature that says that what I pay you to do work for me must depend on how many other people could do the work.