Catalog of Capital-Theoretic "Paradoxes"

This post lists capital-theory 'paradoxes' or 'perversities'. The label of 'paradox' or 'perverse' merely indicates that they are inconsistent with traditional marginalist theory. I think of the following:

• Reswitching of techniques: Out of a given book of recipes, a technique is cost-minimizing at two ranges of the rate of profits, with some other technique cost-minimizing in-between. A technique is a combination of processes, one for each industry, that characterizes production in the economy as a whole.
• Capital-reversing: A switch point is a rate of profits or wage at which two techniques are cost-minimizing. Around a switch point with capital-reversing, a lower rate of profits is associated with a technique being replaced with one with a lower capital-intensity. Or around such a switch point, a higher wage is associated with a higher labor intensity. You can say that a labor demand curve, for the economy as a whole, slope up.
• Reverse labor substitution: Around a switch point with reverse labor substitution, a higher wage is associated with the adoption of a process in a specified industry with more labor hired per unit gross output in that industry. You can say that a sectorial labor demand function slopes up.
• Process recurrence: In a specified industry, the same process can be in the cost-minimizing techniques at two different rates of profits, with a different process being in the cost-minimizing technique in-between.
• Recurrence of truncation: The cost-minimizing technique, in models of fixed capital, can require that an old machine be discarded before its physical life ends. The recurrence of truncation occurs when the same economic life of a machine is adopted in an industry at two different ranges of the rate of profits, with a different economic life in-between.
• Reswitching of the order of fertility: In models of rent, the order of fertility is the order in which different (types of) land are cultivated, at a given rate of pofits, as output expands. This order can be the same at two ranges of the rate of profits, with a different order in-between.
• Reswitching of the order of rentability: In models of rent, the order of rentability is the order, at a given rate of profits of lands when sorted by rent per acre. This order can be the same at two ranges of the rate of profits, with a different order in-between.
• Association of the lengthing of the economic life of a machine with smaller capital-intensity: The adoption of a longer economic life of a machine can be consistent with a smaller capital-intensity.
• Association of the adoption of a machine requiring a more roundabout process with smaller capital-intensity: The cookbook can have a choice of the use of different types of in an industry. The technique that is more roundabout, that is, with a machine that lasts longer, with a smaller capital-intensity.

The relationships among these different phenomena are tedious to state.. The reswitching of techniques implies that capital-reversing occurs. But capital-reversing can occur without the reswitching of techniques. Reverse labor substitution can occur without either reswitching or capital-reversing. I guess process recurrence cannot occur without reverse labor substitution, but reverse labor substitution can occur without process recurrence. The recurrence of truncation is analogous to process recurrence, but somewhat different. The recurrence of trunctation implies that reverse labor substitution occurs. This recurrence is consistent with an absence of the reswitching of techniques. The reswitching of the order of fertility is consistent with no variations in quantity flows. Which lands are fully farmed and which are only partially farmed need not vary. Thus, the reswitching of the order of fertility does not imply the existence of capital-reversing. I hasten to add that the reswitching of techniques and capital-reversing can arise in models with rent.

The above list is not complete. For example, in models of international trade, a country can specialize as in the theory of comparative advantage, with less output than in autarky. Something like the reswitching of techniques can arise in models of spatial economics. Around a city, two areas at different distances from downtown might be specialized for agriculture, with an area specialized for industry in-between. (I haven't looked into this last case in any detail.)

Many economists may have never seen the economic theory that I draw on. But the above phenomena, which might be called Sraffa effects, follow from the assumptions of mainstream economics. In other words, this post describes some elements of modern economics.