Heterodox
Table 1: Lower Rate of Profits around a Switch Point Tradional Marginalist Story'Perverse' Marginalist Story Traditional Austrian StoryGreater net output per workerSmaller net output per worker More roundabout techniqueMore roundabout technique Switch pt. in region 2, 1st in region 52nd switch point in region 3, 2nd in region 6 'Perverse' Austrian StoryGreater net output per workerSmaller net output per worker Less roundabout techniqueLess roundabout technique 1st in region 3, 1st and 3rd in region 6, switch point in region 72nd switch point in region 5 My examination of triple-switching in the corn-tractor model allows for drawing some conclusions about Austrian capital theory. The corn-tractor model, like the Samuelson-Garegnani model, is useful for investigating certain aspects of
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| Tradional Marginalist Story | 'Perverse' Marginalist Story | |
| Traditional Austrian Story | Greater net output per worker | Smaller net output per worker |
| More roundabout technique | More roundabout technique | |
| Switch pt. in region 2, 1st in region 5 | 2nd switch point in region 3, 2nd in region 6 | |
| 'Perverse' Austrian Story | Greater net output per worker | Smaller net output per worker |
| Less roundabout technique | Less roundabout technique | |
| 1st in region 3, 1st and 3rd in region 6, switch point in region 7 | 2nd switch point in region 5 |
My examination of triple-switching in the corn-tractor model allows for drawing some conclusions about Austrian capital theory.
The corn-tractor model, like the Samuelson-Garegnani model, is useful for investigating certain aspects of capital-theory. In obsolete theory from economists of the Austrian school, capital-intensity is associated with roundaboutness (Hennings 1987). A more roundabout technique is identified here with the use of a tractor with a longer lifetime. Only cases in which each type of tractor lasts for the same time in both industries are considered in this article. Thus, the degree of roundaboutness is unambiguous here. In the Austrian theory, a more roundabout technique, in a comparison of stationary states, is supposed to result in a greater net output per worker.
In a stationary state, tractors of each age are operated in parallel, both in the tractor industry and in the corn industry. At the end of each year, the oldest tractors are discarded and the appropriate number of new tractors are added to the stock. The sum of the prices of production of the stock of tractors is the value of capital. Following Steedman, I take a non-physical measure of capital-intensity to be the ratio of the value of capital to the value of net output. The capital-output ratio is a dimensionless number, while the units for the ratio of the value of capital to employment depends on the choice of the numeraire. In a stationary state, net output consists solely of corn, which is consumed. Net output per worker is an unambiguous physical quantity here.
For completeness, I repeat my summary (Table 2) of the analysis of the choice of technique in various regions.
| Region | Cost-Minimizing Technique | Notes |
| 1 | Type II | No switch point. Type II tractors are dominant with sufficiently low coefficients of production in producing Type II tractors. |
| 2 | Type II, Type I | Around the switch point, a lower rate of profits is associated with a more roundabout technique, a greater capital-output ratio, and more consumption per person-year. |
| 3 | Type I, Type II, Type I | Around the first switch point, a lower rate of profits is associated with a less roundabout technique, a higher capital-output ratio, and more consumption per person-year. Around the second switch point, a lower rate of profits is associated with a more roundabout technique, a lower capital-output ratio, and less consumption per person-year. |
| 4 | Type I | No switch point. Type I tractors are dominant with sufficiently high coefficients of production in producing Type II tractors. |
| 5 | Type II, Type I, Type II | Around the first switch point, a lower rate of profits is associated with a more roundabout technique, a greater capital-output ratio, and more consumption per person-year. Around the second switch point, a lower rate of profits is associated with a less roundabout technique, a lower capital-output ratio, and less consumption per person-year. |
| 6 | Type I, Type II, Type I, Type II | Around the first and third switch point, a lower rate of profits is associated with a less roundabout technique, a greater capital-output ratio, and more consumption per person-year. Around the second switch point, a lower rate of profits is associated with a more roundabout technique, a smaller capital-output ratio, and less consumption per person-year. |
| 7 | Type I, Type II | Around the switch point, a lower rate of profits is associated with a less roundabout technique, a greater capital-output ratio, and less consumption per person-year. |
Marginalist economists typically thought of prices as scarcity indices. A higher price of an input into production supposedly signals to mangers of firms to adopt processes in which now cheaper resources are substituted for that input.
"Assume that somewhere ... a new opportunity for the use of some raw material, say, tin, has arisen, or that one of the sources of supply of tin has been eliminated. It does not matter for our purpose ... which of these two causes has made, tin more scarce. ... If only some of [the users of tin] know directly of the new demand, and switch resources over to it, and if the people who are aware of the new gap thus created in turn fill it from still other sources, the effect will rapidly spread throughout the whole economic system and influence not only all the uses of tin but also those of its substitutes and the substitutes of these substitutes, ... without the great majority of those instrumental in bringing about these substitutions knowing anything at all about the original cause of these changes... The mere fact that there is one price for any commodity ... brings about the solution which (it is just conceptually possible) might have been arrived at by one single mind possessing all the information which is in fact dispersed among all the people involved in the process.” (Hayek 1948: 85-86)
This concept of the role of prices is undermined by the Cambridge capital controversy
Bliss (1975), in arguing for general equilibrium theory as an apposite response rejects this role of prices, at least when comparing equilibria:
"Even people who have made no study of economic theory are familiar with the idea that when something is more plentiful its price will be lower, and introductory courses on economic theory reinforce this common presumption with various examples. However, there is no support from the theory of general equilibrium for the proposition that an input to production will be cheaper in an economy where more of it is available. All that the theory declares is that the price of the use of an input which is more plentiful cannot be higher if all other inputs, all other outputs and all other input prices are in constant proportions to each other."
Suppose the rate of profits were an index for the scarcity of capital. A lower rate of profits would indicate that capital was more plentiful, in some sense, as compared to labor. Following the ideas of economists of the Austrian school, managers of firms would be encouraged to adopt more roundabout processes at a lower rate of profits around a switch point (Table 1). According to traditional marginalist reasoning, they would adopt a technique, at a lower rate of profits, with a higher capital-output ratio and more consumption per worker. The switch point in region 2 and the first switch point in region 5 are the only switch points that conform to these outdated ideas.
Other switch points illustrate that these ideas cannot be sustained in general. Consider the first switch point in region 3, the first and third switch points in region 6, and the switch point in region 7. Around these switch points, a lower rate of profits is associated with a higher capital-output ratio and more consumption per worker. Traditional marginalist reasoning is still validated. But, contrary to the expectations of economists of the Austrian school, a less roundabout technique is adopted. As shown in region 7, the disconnection between roundaboutness and capital-intensity does not even require reswitching for its demonstration.
The second switch points in regions 3 and 6, on the other hand, conform to Austrian but not to marginalist reasoning. Around these switch points a lower rate of profits is associated with a more roundabout technique, a lower capital-output ratio, and less consumption per person-year. More roundabout techniques need not be associated with greater capital-intensity or greater net output per worker.
Yeager (1979), in trying to justify Austrian theory with a concept of waiting, expresses puzzlement:
"One paradox not cleared up to my full satisfaction concerns consumption… Since this consumption paradox is a direct arithmetical implication of paradoxes already cleared up, and in particular of capital reversal or perversity, one might contend that no paradox remains. Yet this remark is not wholly satisfying."
The second switch point in region 5 contradicts both Austrian and marginalist reasoning. Around this switch point, a lower rate of profits is associated with a less roundabout technique. And it is associated with a lower capital-output ratio and less consumption per person-year. Perturbing parameters for a single example of triple-switching illustrates a variety of the so-called paradoxes discovered during the Cambridge capital controversy.