That is the question that occurred to me after reading Tyler Cowen.
If the employers don't want you at the high wage, and don't want you at the low wage, what might your perceived MP be, temporarily or not?
MP means marginal product. It comes from a production function, where output is a function of labor input. Instead, think of Garett Jones workers, who build organizational capital.
Imagine you are the chairman of an economics department. When you hire, do you think in terms of a production function? Probably not. You think about whether you need senior faculty or junior faculty. You think about whether you want to build a capability in behavioral economics or add to your capability in labor market econometrics. How much does salary enter into your thinking?
If a less-than-ideal candidate will take the job for 90 percent of the salary of the ideal candidate, don't you still choose the ideal candidate? Probably if the differential gets as high as 50 percent, you consider the less-than-ideal candidate. But that is a pretty lumpy labor demand schedule.
Individual organizations do not possess production functions, in which output is a continuous function of labor input. Their labor demand is not a continuous function of the wage rate.
Perhaps you can argue that in the economy as a whole, all these individual lumpinesses wash out, and you get a nice smooth aggregate production function. But I would not necessarily count on that.
When I talk about complex, roundabout production and PSST (patterns of sustainable specialization and trade), I am trying to suggest ways of describing an economy without using the concept of a production function. Or, if you insist on a production function, I think you need to allow for large discontinuities in order to explain unemployment.