Because if market is efficient the wage should equal marginal product of labor, which is basically what defines productivity.
Also, it says “seemingly”, i.e. if you don’t take a closer look. In fact it completely reflects predictions of classical economics. It’s just that the model is more complex because it has heterogeneous sectors.
Because access to capital gives employer some fraction of employee productivity as a reward. The exact fraction depends where exactly they land in the zone of possible agreement. In transactions (even efficient ones) there is usually hysteresis.
Coase would have said transaction costs. An efficient market doesn't imply no transaction costs. And if you take things out of economic theory it's pretty obvious why you'll hire people for some things and not for others.
It's weird they'd say "classical economics" - the Baumol article links indeed to classical economics/classical political economy but the linked article doesn't bear out the claim. The actual situation is that the original field known as "classical political economy" made the claim that wages are indeed a matter of the cost of reproducing laborers whereas a "modern economics" or "neoclassical economics" as a field/label is where the claim that real wages are tied to labor productivity changes appeared. The particular wages-productivity theory seems to have been articulated around the 1930s [2].
In the absence of a prevailing theory (in this case, supply-and-demand), people tend to go with their biases (in this case, the notion that every input that goes towards producing a product is comparably in value to the finished product). Here the example is the increase in the value of labor because some other more productive use can be found for the labor. Other times its the apparent discrepancy between a low-income worker contributing to the production of a high-value item.
Agreed. Classical economics would say that as the labor supply is restricted workers would switch careers or be initially trained in careers that give them the most reward for their work. This means that candidates for the "retail manager" case would either be of lower quality or harder to find so increases in wages would be seen to offset that.
That sounds like a pretty big assumption. Why should labor prices be other than what is demanded?