I never considered Hayekian triangles too important to figure out, as long as I got the general gist, but I've recently begun dedicated research on capital theory and have the intention of getting it down "pat" (I know a lot of people here aren't going to like it, and I don't intend to start a debate [and I don't intend to humor a debate just yet], but my intentions are to show how elastic inside money in a competitive market does conform with time-oriented capital theory; hey, you never know, I might find that the two aren't compatible). I even spent some money and bought Böhm-Bawerk's three-volume Capital and Interest (I actually found the nice Libertarian Press hardcover set for a relatively cheap price, and in very good condition)—two reasons: first, to understand the progress in capital theoretics between Menger and modern day; second, I learned from Reisman that some contributions by past thinkers tend to "slip through the cracks", so to speak.
I am currently re-reading Prices and Production (just the lecture series), taking notes and trying to understand Hayek's argument perfectly (I realize that Pure Theory of Capital is probably a better representation of Hayek's argument, but again, I think understanding the historical progression of the theory is just as important—Pure Theory of Capital can come later).
Taking notes on lecture two, though, I have a few questions. Rather than re-state them here and insert the relevant images I will link to my post on my blog: "Two Questions on Prices and Production".
I have a rough idea of the answers, but others's opinions could probably make my interpretation much more accurate. Thanks.
EDIT: No need to answer the first question; I neglected the original means of production.
Regarding question 2:
In both diagrams, interest is represented by the boxes at the top with dotted lines. In the first diagram, the interest rate is such that the top stage of production requires 8 units of savings, the next stage requires an additional 8 units for a total of 16, and so on. In the second diagram, increased savings have driven down the interest rate, so each stage only requires 4.3 units of savings. This permits two more layers of production. When an economy is evenly rotating (in equalibrium) there is no entreprenurial profit but there is interest whenever there is any demand for loanable funds.
We actually figured it out.
In both diagrams, interest is represented by the boxes at the top with dotted lines.
The boxes at the top represent the original means of production, and yes this is what I wasn't considering. Both diagrams model a stationary economy, in any case, with no profit/interest.
I have to admit that I don't own a copy of Prices and Production but I have to disagree with your conclusion that there is no interest in an evenly rotaing economy. I based my interpretation of the P&P diagrams on the almost identical Figure 45 in Man, Economy, State (Chapter 6, Section 4: The Time Market and the Production Structure, page 391 in the 2004 scholar's edition, page 334 in the 1993 edition). The reason that there is interest in an evenly rotating economy is that interest is the compensation that is paid for time. Each stage of of production, even in an evenly rotating economy, must be completed before the subsequent stage can begin and this takes time.
The evenly rotating economy is not stationary. People still must go to work every day operating the same equipment in order to produce exactly the same products (and services). If any stage fails to produce its required amount, the entire economy would begin to deteriorate and would no longer be evenly rotating. The prices of consumer goods must compensate all the levels of production for the time it takes to move the products from any particular stage to the final consumer good. Without interest, the early stages of production would have to wait until the final product was sold to the consumer before receiving the same compensation as the last stage. The original means of production must be in place before production can begin, and this requires savings which requires interest because, if savings didn't receive interest, no one would bother to save.
I have to appologize. In re-reading the section of MES to which I referred, I realized that Rothbard added another column to account for interest. Nonetheless, I stand by my point that there is interest income in an evenly rotating economy.
Jonathan M. F. Catalán:How does society-wide saving of ¼ of income lead to a ratio of 30:90?
In the first case (figure 2), the time preference of society remains unknown; all we know is that the total ratio of consumption to investment is 40:80, or 1:2. On page 238 Hayek assumes that the total savings rate equals 25%, or 1/4th of the total income, which equals 40. If society reduces consumption by 25% in figure 3, and if total consumption was 40 in figure 2, then total consumption in figure 3 must be 30 (40x25%=10, 40-10=30). If total savings/investment was 80 in figure 2, and if total savings/investment rises by 10 in figure 3, then total savings/investment must now equal 90 (120-30=90). Thus the ratio between consumption and investment/savings, in figure 3, equals 30:90 or 1:3.
Jonathan M. F. Catalán: This is actually not necessarily correct, and represents an improvement on Hayek’s capital theory since Prices and Production (I haven’t read Pure Theory of Capital, so I’m not sure what improvements Hayek made himself). George Reisman actually makes this point in Capitalism, arguing that a change in time preference is actually not necessary to lengthen the structure of production (that is, the proportion of money demand for producers’ goods relative to that of consumers’ good does not actually have to increase). This is because each period of production is actually likely to increase the total stock of goods, meaning that even if time preference remains the same the aggregate quantity of capital and consumer goods have actually increased.
In order to lengthen the structure of production, i.e., increase the total number of higher phases relative to the lowest phase of production (consumer goods), the ratio of exchange between consumer goods and producer goods (or consumption and savings respectively) must increase in favor of the latter. It is true that as the economy engages in more capitalistic/roundabout methods of production, that total output will increase, and therefore total savings and consumption, in absolute terms, will increase as well (even if the ratio between consumption and savings remains constant). But this does not constitute a lengthening of the structure of production, represented by the Hayekian triangle. Rather, every phase of production, including the lowest phase (consumer goods) will expand by an equal proportion (the triangle will expand vertically and horizontally in a proportionate manner, but the shape of the triangle remains unaltered, though the area necessarily increases). This is why the trade-off between consumption and investment is only a short-term phenomenon, and why the methods of production, either more or less capital intensive (represented by the Hayekian triangle) depend on the ratio of exchange between consumption and investment (in relative terms).
Jonathan M. F. Catalán: The traditional Austrian explanation of the structure of production through Böhm-Bawerk’s average period of production was always a point of contention with me. It didn’t seem realistic to assume that changes in time preference, in favor of present consumption, could really lead to less capitalistic means of production.
Well, Hayek explains why this is necessarily true in Prices and Production. Keep reading (it’s basically the entire point of the book).
"If we wish to preserve a free society, it is essential that we recognize that the desirability of a particular object is not sufficient justification for the use of coercion."
Esuric,
But this does not constitute a lengthening of the structure of production, represented by the Hayekian triangle. Rather, every phase of production, including the lowest phase (consumer goods) will expand by an equal proportion (the triangle will expand vertically and horizontally in a proportionate manner, but the shape of the triangle remains unaltered, though the area necessarily increases). This is why the trade-off between consumption and investment is only a short-term phenomenon, and why the methods of production, either more or less capital intensive (represented by the Hayekian triangle) depend on the ratio of exchange between consumption and investment (in relative terms).
I still don't understand why this is necessarily true; I don't see why an increase in capital goods, without an increase in time preference, will lead to an equal distribution of these capital goods amongst the existing phases of production. I take Mises's stance where it's argued that how entrepreneurs will use capital-goods depends entirely on their own personal evaluations. Mises used this argument to suggest that increased time preference doesn't necessarily lead to a lengthening of the structure of production, because how the available capital goods are used is entirely up to the person investing them.
All the same, how new capital goods (that is, capital goods over and above the supply necessary to maintain that level of productivity) is entirely up to the entrepreneur responsible for investing them. They can be invested into a new industry, and the goods produced by this new industry can belong to an order entirely dictated by the process of production they may join (which is dynamic, depending on each and every different exchange which may take place within society). Or, they can be invested into the existing industries. But, I don't understand why they should be necessarily equally and proportionally invested along the already existant lines of production.
I think this is why Reisman argues that the capitalistic intensiveness of society doesn't only depend on time preference, apart from whatever ratio is necessary to cause a level of production where the quantity of capital-goods progressively rises. Reisman argues that changes in time preference change the rate at which capital-goods are accumulated.
Well, Hayek could be wrong.
I still don't understand why this is necessarily true
Again, this is the entire point of the book, which you haven't really addressed. But I will give you a very crude and quick explanation:
Prices guide production. As total consumption increases, and therefore total savings falls, there is a higher demand for final goods and services relative to producer/future goods (savings is the demand for future goods). This increases the prices and therefore the profit margins of the lower phases of production relative to the higher phases of production. This, in turn, leads to additional capital accumulation towards the lower phases away from the higher phases of production (arbitrage).
Additionally, a higher rate of consumption relative to savings means a higher rate of interest, and because the higher phases of production are more sensitive to changes in the interest rate (an inverse relationship between interest rates and investment), relative to the lower phases, this also leads to a contraction in the structure of production. Remember, money flows from the bottom up (from the lowest phase to the higher phases) and goods flow from the top down (from the highest phase to the lowest phase); the lowest phase of production is most sensitive to changes in aggregate demand, while the highest phase is most sensitive to changes in the interest rate--this is why the area's of the boxes, and their numerical values, shrink as you move from the lowest phase towards the highest phase--they represent the money stream (it's also why there is no paradox of saving).
You should also remember that Hayek is using static analysis here where there is no technological innovation, where there is monetary and intertemporal equilibrium, and where there is perfect information.
You're going to have to explain why Hayek is wrong, and why prices don't guide production and influence investment decisions.
I never said prices don't influence investment decisions. I said that higher time preference is not necessary to create more capitalistic methods of production. I gave my reasoning in my previous post.
Edit: I deleted my response. I will just continue to read Prices & Production. I can only handle so many debates at once.