One of Aguilar's major objections is that the Austrians are inconsistent in what their figures (and more generally, concepts) are supposed to mean. After some (valid) criticisms of Skousen's exposition, Aguilar moves on to Hayek:
What did Hayek, the originator of the structure of production, intend it to represent: a yearly flow of goods or a distribution of wealth? These are, after all, very different things. Hayek (1967, p. 40, italics added) writes:
The area of the triangle shows the totality of the successive stages through which the several units of the original means of production pass before they become ripe for consumption. It also shows the total amount of intermediate products which must exist at any moment of time in order to secure a continuous output of consumers' goods.
Also? In the first sentence, the word "pass" implies a flow of goods passing by during a certain amount of time. The second sentence refers to the total amount of goods that exist at a moment in time. It is highly irregular for a graph to mean one thing and also something else. (Aguilar p. 3)
As we shall soon see, I agree with Aguilar that canonical Austrian capital theory doesn't distinguish between "fixed" and "circulating" capital; I demonstrate the problems with reference to Rothbard below. This flaw is related to the quotation above.
Having said this, it seems that Aguilar clearly oversteps in the excerpt above. At the most basic level, there is nothing at all irregular about a graph meaning one thing "and also something else." For example, a physicist could graph the vertical displacement of an object against time, and say that the graph meant height and also the potential energy stored in the object.
We are thus forced to ask whether in this particular case the graph does indeed represent the two (conceptually distinct) items that Hayek believes. I believe the answer is obviously yes. The Hayekian triangle neatly captures the Austrian insight that (most) consumption goods are descended from 2nd order goods, which in turn are descended from 3rd order goods, and so forth. To maintain a perpetual yearly flow of x bottles of 20-year-old wine requires a structure of production comprised of x bottles of 19-year-old wine, x bottles of 18-year-old wine, and so forth. If we were to graph such a trivial capital structure (which would be a straight line, if we simplistically ignore what happens at the highest stage where the original bottles of wine are first corked), then the resulting picture would show us (a) how many bottles of wine would be ready for consumption each year and (b) the distribution of wine bottles among various stages at any snapshot in time.
Now Aguilar surely knows this; he understands what Hayek and others think they mean by these passages. However’if I follow Aguilar's point’Aguilar would respond that this is pure confusion. The trained mathematician would realize that the units are different. How can one talk of the flow of bottles per year, at the same time as the stock of bottles at a given moment?
It is true that one needs to be careful about units, but even so the same graph can illustrate both meanings (after adjusting for the units). By the very same token, height is measured in meters while potential energy is measured in joules; the same graph can still "mean" both things at the same time, though. No one would accuse my hypothetical physicist of such a basic confusion. If anything, he is correct to stress the close interrelationship between the two (distinct) concepts. Now the purist could object after the lecture, and point out that the two are only related one-to-one if we assume that the object's mass, and the gravitational constant of the earth, are constant irrespective of height. But so what? Holding those things constant, the graph means both height and potential energy, measured in the appropriate units.
I thus see no logical flaw in the Hayekian treatment. Now this leads to a different question: Is the Hayekian triangle a good model of the capital structure? My answer is a qualified yes. I think the Austrian approach captures crucial features that mainstream models (not only of economic growth but especially of the business cycle) neglect, but it has led the Austrians to unrealistically ignore the distinction between so-called fixed versus circulating capital. To quotation from my study guide to Man, Economy, and State:
On pages 523-524, Rothbard writes that in "any equilibrium situation, net saving is zero by definition (since net saving means a change in the level of gross saving over the previous period of time)." These definitions are not entirely compatible with the mainstream approach. For example, standard growth models can certainly have an economy in long-run equilibrium with net investment every period. In this case, net investment would simply mean investment above the amount necessary to cover depreciation, i.e. net investment refers to a growth in the capital stock. Probably the reason for these differing definitions is that Austrians tend to view capital goods as "working capital" or "goods in process," whereas neoclassicals view capital goods almost exclusively as fixed capital: To maintain his output of bread, every period the baker needs to buy more flour, but not a new oven.
Beyond unorthodox nomenclature, this Austrian proclivity to view all current consumer goods as the heirs of nth order inputs of raw materials and labor may lead to serious mistakes in analysis. However, this possibility lies outside the scope of the present reply.
The final tantalizing suggestion in this section is Aguilar's proposed Distribution of Wealth over the capital structure, DWCS. Unfortunately, I cannot comment on whether this would indeed constitute an improvement, because I don't fully understand its construction. Perhaps there is a fuller description elsewhere in Aguilar's work, but from the Critique I can't determine whether the DWCS’which doesn't suffer from the drawbacks that Aguilar rightly notes in Garrison's approach’retains the essence of what is right with the Hayekian triangle.