Labor Demand Curves Slope Down?

Consider the consequences of capital-reversing. I like to say that one is that explaining wages and employment by well-behaved supply and demand functions for labor is of doubtful logic. Here's what some others have had to say:

"the pattern of activities adopted in the face of long-run factor-price changes can be complicated and counterintuitive. Consequently, the long-run demand for factors can be badly behaved functions of factor prices." -- Michael Mandler (1999) Dilemmas in Economic Theory: Persisting Foundational Problems of Microeconomics, Oxford University Press.

"However, as was argued in Section 3 with regard to 'perversely' shaped, that is, upward sloping, factor-demand functions, this possibility would question the validity of the entire economic analysis in terms of demand and supply." -- H. D. Kurz and N. Salvadori (1995) Theory of Production: A Long Period Analysis, Cambridge University Press

"The essential point of the criticism concerns the factor demand curves. The discovery that factor demand curves may be positively sloped in the relevant range, not negatively..." -- Bertram Schefold (1990) "Joint Production, Intertemporal Preferences, and Long-Period Equilibirum," Political Economy: Studies in the Surplus Approach, V. 6, 1990, pp. 162-163.

"there is not necessarily an inverse monotonic relation between the cost-minimizing quantity of an input and its price... Figures 6.17a-6.17c can be interpreted as demand curves for labour... in Figure 6.17b, ...the sectoral demand curve is upward-sloping... I have shown in Figure 6.17c that the aggregate demand curve is not downward-sloping in the presence of reswitching: indeed, like the sectoral demand curve, it is not even monotonic. Reswitching is sufficient, not necessary, for the aggregate demand curve for labour not to be downward-sloping: to see this, consider Figure 6.18..." -- J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press

It is a theme of this blog that mainstream economists have yet to integrate this challenge into their theories and teaching.