I'm having trouble with the notion of the higher order capital goods being more interest rate sensitive. For instance, it makes sense that a segment of production which is capital intensive is sensitive to interest rates. If the rate of interest is too high in the perspective of an entrepeneur he will not invest in the needed capital. And it seems intuitive that higher order processes are more capital intensive just from observation of an economy. Burger flippers basically just need a grill and a restaurant, more of the costs are in labor, whereas griddle/frier producers require a complex array of machinery and tools for the fixing thereof. But what is the reason that the segment of production furthest from the final good is necessarily the most interest rate sensitive?
For example, if we're producing HomeDepot miniShacks, the entire process might go like this: logging->cutting->treating->assembling->transporting->selling. How is it necessarily the case that logging is more capital intensive and thus interest rate sensitive than treating wood with chemicals?
The standard explanation is that higher order goods are furthest from the final good and so there is a longer period between the initial investment and the "payoff" - that period in which revenue starts coming in and interest can start to be paid off. But the producer of higher order goods does not have to wait for the demand from the final good producer; due to the forward-looking nature of entrepeneurship, a producer of a good "one level" beneath him will buy that highest order good to satisfy his own business plan. This is ultimately dependent on how much of the final good is bought from what is produced, but the point is that the producer of the highest order good is not deprived of revenue for a greater period of time (or at least not the period of time it takes for one "round" of production to occur). He can sell his good to the next producer down the line. So what in Bohm-Bawerk's laws makes it completely implausible/impossible that the segment of production "beneath" him is less capital intensive? Or am I not conceiving of this issue correctly?
It occurred to me that producers in those segments furthest from the final good will be more subject to both time lag and more layers of entrepeneurial failure/success. Mises might call this the higgling of the market. But it doesn't seem a compelling reason that, granting abstention from consumption and reallocation of said absentions into the loan market, process N's frontier of production will necessarily expand greater than N-1's (N here being a 'stage' of production).
The Anarch is to the Anarchist what the Monarch is to the Monarchist. -Ernst Jünger
Here's my guess:
From first pinciples:
1. People have time preferences, that can change. A time preference means how much more do I love having my food now than later? This makes a difference to an economy, in that people who are impatient and want it now can be convinced to wait by promising them more in the future. How much more? That's what we call the [originary] interest rate. if they are very impatient, you need to promise them more, a higher rate of interest.
2. Thus, the interest rate is determined by time preference.
3. Since people are impatient, any method of production that is quicker will be preferred. So if there is only so much available for production, the quickest feasible method will be adopted. Only if more capital becomes available will longer methods be adopted. Of course, the longer methods will only be adopted if they are more productive. Otherwise, why wait longer to get the same or less than before?
4. When interest rates go down, ultimately it because people are more patient. They don't want it all now. They consume less than before. This frees up resources for more production. But since people are consuming less, there is no point in making more for immediate consumption. Thus the best way to use the newly freed resources is to start using more efficient methods, ones that will get you more ouput per unit input [even though it might take longer]. But since the only unused methods are the more time consuming ones, new investments will of neccesity be invested in the time consuming methods. Bottom line, lower interest rates means investments in production methods that take longer.
5. The amount of time being measured is from scratch to final product. Thus, in your example, logging->cutting->treating->assembling->transporting->selling takes less time than
logging->initial cutting-> fine tuned cutting ->treating->assembling->transporting->selling.
In other words, there might be a method of cutting that requires two steps and wastes less lumber, but the whole process now takes longer, because it takes longer to do those two steps than the single old step.
6. Usually, superior production comes from introducing some new step [that the money was not there for until now]. Where else would it come from, ceteris parebis? The concept of division of labor might be relevant here.
I think these last two ideas, which I labelled 5 and 6, are not essential. What counts is that lower interest rates encourage longer but superior processes, which there was no money for until now.
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It's easy to refute an argument if you first misrepresent it. William Keizer
What I'm not getting in here is how the "longness" of a process and its efficiency are necessarily correlated. I understand that since consumers are saving more and consuming less it will be less profitable to invest in consumer goods industries. And also that non-specific capital is freed up. So now we have cheaper non-specific capital and a lower interest rate. Entrepeneurs will take this and invest in producers goods further away from the final good. But how do we know that the further away from a final good we are, the relatively higher capital costs and interest payments will be in the constitution of a segment of production's costs?
EDIT: Or is it rather that the prospective lengthening of the production process is the only place for the released capital to go?
Ok I think that might be it. Thanks for nudging me. I'll just write out what I'm thinking.
Let 1 be the highest stage of production and 10 the lowest.
Following the reduction in consumer spending, stage 10 will be the worst wounded by the drop off in consumer spending, stage 9 the second worst, and so on. Stage 1 or 0 will have been the least wounded by the drop off in consumer spending and so the most suitable places to allocate the freed capital. This still doesn't sound very Bohm-Bawerkian though, whose explanation is the foundation of Austrian capital theory.
I've always wondered about this, and I need to do more thinking about this, but I think that the reason is that there's no alternative to capital being produced. Remember that we start off with the original factors of land, labor, and time, but what do we get when we combine these things? We get either capital goods or consumers goods. Remember that as soon as you cut down a tree for logs that those logs are capital goods and remain capital goods for the duration of the period of production. Even the improved aspects of land are "capital", such as irrigation and other such improvements.
Therefore whenever the production structure is lengthened it must do so by producing a greater amount (at very least value) of capital than previously existed, otherwise nothing more could actually be produced. Stage X which is added to the production structure because of the decrease in the interest rate would have nothing to show for its existence if it didn't add more capital to the production structure.
Once again the way that Rothbard describes the production structure (I believe you have read MES, Jargon) answers the question. At each stage of production either two or three things are combined to create another. In the first ever productive stages land and labor are combined to create a capital good. From that point onward and everywhere worth mentioning in our economy land, labor, and capital are used either to produce another capital good or a consumers good. Because a lengthening of the production structure necessitates an additional period of production in which capital goods are not produced, additional capital is created instead.
I feel like there's still something I'm missing here, although this is necessarily true within the model we are working with. Therefore I think that this is at least a part of the answer, although there may be more to it. The only exception is when "human capital" is accumulated and individuals spend more time becoming educated or receiving valuable job training. This would not be capital accumulation per se, but it would have many similar affects.
Does this make sense?
Neodoxy: (I believe you have read MES, Jargon)
(I believe you have read MES, Jargon)
I have not. Human Action in its place. Ought I to read MES as well?
At each stage of production either two or three things are combined to create another. In the first ever productive stages land and labor are combined to create a capital good. From that point onward and everywhere worth mentioning in our economy land, labor, and capital are used either to produce another capital good or a consumers good. Because a lengthening of the production structure necessitates an additional period of production in which capital goods are not produced, additional capital is created instead. I feel like there's still something I'm missing here, although this is necessarily true within the model we are working with. Therefore I think that this is at least a part of the answer, although there may be more to it. The only exception is when "human capital" is accumulated and individuals spend more time becoming educated or receiving valuable job training. This would not be capital accumulation per se, but it would have many similar affects.
At each stage of production either two or three things are combined to create another. In the first ever productive stages land and labor are combined to create a capital good. From that point onward and everywhere worth mentioning in our economy land, labor, and capital are used either to produce another capital good or a consumers good. Because a lengthening of the production structure necessitates an additional period of production in which capital goods are not produced, additional capital is created instead.
I believe that the state of affairs your describing could be just as easily a thickening of the capital structure as it is a lengthening. Or even a slight lengthening and thickening. The best explanation I've got, in regards to abstention from consumption and increase in supply of loanable funds is that the former of the two is the most significant in determining the shape of the capital structure (why decreases in societal time preferences will elongate the structure of production). The latter is undoubtedly the most important in determining the scope/quantity of the capital structure. The reason being, in reference to the shape of the capital structure, is that those enterprises furthest from consumer demand, in terms of how much they are effected by a drop in consumer demand, will be the least harmed by a dropping off of consumer demand. The addition of credit will help many entrepeneurs, but especially those who are least harmed by the lag in consumer demand. The pain from the drop-off in consumer demand is felt in decreasing magnitudes as we ascend the structure of production. I've got a few ideas for why that might be, but I'd like to hear what yours are as well.
I think that my best explanation is that more of the costs of higher order processes go towards servicing interest payments as it is necessarily more capital intensive. But does one apodictically use more capital goods in the production of a capital good than one uses in the production of a consumer good?
Jargon,
I'm afraid that I don't think that you're explaining yourself very well.
My point is that within the productive structure model the thing that is passed down within each productive stage is capital. Remember that capital is an exceedingly broad concept. This is something that stunted my understanding of economics for over a year. Trees that grow in the wild are originally land, but after they are cut down for logs and sent to a lumber mill (which we will call the next stage of production) they become capital. Grapes that have been left to ferment are capital, nails are capital, everything that isn't directly land or labor at that time is capital. Therefore the question is: "how would you elongate the production structure without an increase in the quantity of capital available?". I can't think of any besides increases in human capital which then becomes an augmented form of labor rather than capital that is passed on to the next stage. Remember that at each point in time land, labor, and capital are combined to make either a consumers or producers good. The logs from the first stage are then guided by workers, machines made in previous stages of productions, and the omnipresent factor of land (space) to produce boards that eventually go to the chair maker.
Therefore increasing the length of the production structure will almost certainly lead to capital accumulation.
As for why the later stages of production are interest sensitive, I don't think it has anything to do with consumer spending per se, merely what this does to the value of money that is allocated wherever this money is allocated. This is to say that if consumer spending decreased and somehow no change in the purchasing power of the monetary unit or increase in the availability of loanable funds resulted, then the later stages of production would find themselves just as "underfunded" as the later stages. However, with a fall in the interest rate either caused by an increase in loanable funds (consumption to investment) or an increase in the purchasing power of existing funds (consumption to plain saving) stages further away in time are more sensitive due to compounding interest. Remember that annually compounding interest looks like this:
P(1+i)^t
Therefore as t grows larger the higher the amount paid back in interest needs to be. If I borrow at a rate of six percent and then do nothing, add no additional costs and just wait for the project to ferment or whatever for 5 years, then I will have to pay back 133.8% of the principle. If the interest rate were a mere 4 percent then I would only have to pay 121% of the principle. This is obviously a very large percentage change, the lion's share of which is attributable to the time factor. Also notice that the total change, a decrease of 12.8 percent, is slightly higher than a non-compounding value would be (change interest rate [.02]*the number of years [5]. This is 10 percent, giving us a 2.8 percent difference. This is not huge but it of course grows larger at longer periods of time and larger shifts in the rate of interest). Meanwhile a single year stage of production would only be affected by a 2% change. Therefore as the interest rate changes investment in the latest stages of production are the most sensitive since they have the larges "t" value that extenuates the differences in the interest rate.
"I have not, Ought I to read MES as well?"
Most definitely. While the two books complement each other in such a profound way that I have a hard time even explaining it, I find MES to be a better work of economics proper, while Mises does a much better job of explaining the underlying theories.
Neodoxy: Therefore increasing the length of the production structure will almost certainly lead to capital accumulation. As for why the later stages of production are interest sensitive, I don't think it has anything to do with consumer spending per se, merely what this does to the value of money that is allocated wherever this money is allocated. This is to say that if consumer spending decreased and somehow no change in the purchasing power of the monetary unit or increase in the availability of loanable funds resulted, then the later stages of production would find themselves just as "underfunded" as the later stages. However, with a fall in the interest rate either caused by an increase in loanable funds (consumption to investment) or an increase in the purchasing power of existing funds (consumption to plain saving) stages further away in time are more sensitive due to compounding interest. Remember that annually compounding interest looks like this: P(1+i)^t Therefore as t grows larger the higher the amount paid back in interest needs to be. If I borrow at a rate of six percent and then do nothing, add no additional costs and just wait for the project to ferment or whatever for 5 years, then I will have to pay back 133.8% of the principle. If the interest rate were a mere 4 percent then I would only have to pay 121% of the principle. This is obviously a very large percentage change, the lion's share of which is attributable to the time factor. Also notice that the total change, a decrease of 12.8 percent, is slightly higher than a non-compounding value would be (change interest rate [.02]*the number of years [5]. This is 10 percent, giving us a 2.8 percent difference. This is not huge but it of course grows larger at longer periods of time and larger shifts in the rate of interest). Meanwhile a single year stage of production would only be affected by a 2% change. Therefore as the interest rate changes investment in the latest stages of production are the most sensitive since they have the larges "t" value that extenuates the differences in the interest rate.
Let's go back to Cruseau economics for a moment. We have the fable of the fisherman. He can either catch two fish a day and eat both of them, or catch two fish a day and save some of the fish. Building a net to catch more fish will take 2 days, whereas just catching fish takes only one day. So he'll need to have some food for those two days of net-building. So he underconsumes for two days of fishing and saves two fish. He uses these two in the next two days to build his net. His brand new capital, which allows him to catch more fish, was undeniably born from his underconsumption. Put another way, capital accumulation was not compatible with his original consumption preferences. We can say that the production of capital (the net) was further from consumption than simply laboring to catch a fish.
But what is the significance of this story when we transition over to a capitalistic system with a developed division of labor? Yes, we may say that when the logger cuts down a tree in the forest, this production process is very far temporally from the final stage, the consumption good (a dinky shack that is sold at home depot). But let's compare the significance of the logger and the netmaker. The netmaker had to underconsume to increase his capital stock, in order that he would both not starve and would have time enough to make his net. The logger, on the other hand, took on a loan and will have to pay interest, but did not suffer any initial underconsumption. To the logger, it is relatively unimportant that his stage is far from the consumption stage, because all he has to worry about is whether the plank-curer (the man 'below him') will buy his logs. Thus, the quantity of time which is of significance to the logger is not how much time it will take to log, cure, ship, assemble, stock and sell. The significant quantity of time, to his considerations, is how much time it takes to log.
The planning businessman cannot help employing data concerning the unknown future; he deals with future prices and future costs of production. Mises, Human Action, 225
The planning businessman cannot help employing data concerning the unknown future; he deals with future prices and future costs of production.
Mises, Human Action, 225
The plank-curer is not 'peering down the length of the capital structure' telling the logger how long it will take for the logs to turn into cured planks and finally into mini-shacks. He is anticipating future conditions and arranging for them, by purchasing the logs. If he fails he fails, but such is the nature of entrepreneurial activity.
What you are saying above, I believe, is that, because the logger is the furthest from the point of consumption (in a temporal sense) he is most vulnerable to the price of loanable funds, because the amount of time his endeavor will take is of the utmost importance. I am responding that it matters not how far he is from consumption. What matters is how far, temporally, he is from the person who will purchase his product, no matter where he might be situated in the capital structure.
So tell me, why should it be apodictically true that the logger's endeavor is more time-consuming than the plank-curers? In a Robinson Cruseau Scenario we know this to be true, because Robinson will not enjoy the higher rate of consumption which an increased capital stock affords him until the construction thereof is complete. But in a division of labor, the credit comes from outside one's own savings and it doesn't matter (in regards to the cost of the endeavor) how long it takes until the supply of the consumption good is benefitted by the completion of a capital-structure-elongation-phase.
I put forward a reason I came up with as to why processes furthest from production might be the most time consuming, in light of the above. And that was that a reduction in consumer demand hurts their revenue streams the least. But I still don't see a reason why, apodictically, a societal lowering of time preference means that stage 1 of 7 production processes must expand more than stage 2 of 7. So, while I do believe that a societal lowering of time preference does mean that the earlier stages of production will expand, I believe that I believe so far different reasons than those who follow Bohm Bawerk on this issue. I think they do so, due to a combination of the happy coincidence that earlier stages of production are usually capital intensive and heavy construction, and so more time consuming, and that drop off in consumer demand hurts them the least. But I can easily envision scenarios in which a societal lowering of time preference does not lengthen the capital structure so much as it thickens it in certain areas (meaning that it could be envisioned that stage 2 of 7 expands more quickly than stage 1 of 7 thanks to the new societal preferences).
Ya dig?
I think that Jorg Guido Hulsmann is thinking along the same lines I'm thinking on this topic. Could be wrong though. I'll have to reread his essay on the structure of production again.
Tisk tisk Jargon, I think you're forgetting a very simple detail about how the structure of production and costs work.
"What you are saying above, I believe, is that, because the logger is the furthest from the point of consumption (in a temporal sense) he is most vulnerable to the price of loanable funds, because the amount of time his endeavor will take is of the utmost importance. I am responding that it matters not how far he is from consumption. What matters is how far, temporally, he is from the person who will purchase his product, no matter where he might be situated in the capital structure."
I think that you are right about our differences, but I think that you are wrong on causality. The reason why what matters is how far away the logger is from consumption is because his costs "stick" to the product throughout the productive structure. Let's assume that after an increase in investment resulting from a decrease in consumption we have finally reached the new equilibrium position, thusly bypassing all problems of entrepreneurial error in the short run. Now if the logger's total costs are (without interest) $500, then this has to be paid for all down the line, and due to interest it magnifies not only in that stage but throughout each stage. If we assume (for the sake of brevity) three stages of production with equal costs. Thusly for the three stages we have:
Let I=1+i
500I=S1
S1I+350I=S2
S2I+275I)=S3
Or, if we were to expand out this problem we would get
500I^3+350I^2+275I^1=Total amount paid by consumers
The cost from the first stage is passed down to each stage and must be paid for at interest until the consumers pay off the total costs. The plank-curer pays 500 dollars for the logs and then he must pay for that at interest. So to must the chair maker who must pay for the costs of the logger and the plank-curer at interest. Thusly, decreasing I decreases costs dramatically all down the line.
For this reason the logger need not say "hmm... The production structure appears to be lengthening today. I'm gonna go log me some logs cuz I'm a logger who logs", rather the logger might just see the demand for his logs increases because now the plank curer's costs have gone down, while at the same time the logger's supply curve shifts to the right precisely because his prices have gone down.
Do YOU Dig?
Also,
I do agree that a change in the interest rate is just as likely to cause, as you say, a "thickening" in the production structure as it is to lengthen it, although this does in truth count as a "lengthening" of the structure of production since more total time is spent in production than was previously the case.
I've been saying it a lot lately, but seriously guys; Man, Economy, and State.
Neodoxy: The reason why what matters is how far away the logger is from consumption is because his costs "stick" to the product throughout the productive structure. Now if the logger's total costs are (without interest) $500, then this has to be paid for all down the line, and due to interest it magnifies not only in that stage but throughout each stage.
The reason why what matters is how far away the logger is from consumption is because his costs "stick" to the product throughout the productive structure.
Now if the logger's total costs are (without interest) $500, then this has to be paid for all down the line, and due to interest it magnifies not only in that stage but throughout each stage.
How/Why?
If we assume (for the sake of brevity) three stages of production with equal costs.
Ok, but we didn't anyways. We assumed 3 stages with the costs 500, 350, and 275
Thusly for the three stages we have: Let I=1+i 500I=S1 S1I+350I=S2 S2I+275I)=S3 Or, if we were to expand out this problem we would get 500I^3+350I^2+275I^1=Total amount paid by consumers
Thusly for the three stages we have:
Maybe it's the way you set this up, but it makes no sense to me. Exactly who is paying the cost 'S1'? If the manufacturers in S2 have to pay costs which have 'stuck' to the product from the first stage then why are their operating costs not higher than the manufacturers in S1?
The cost from the first stage is passed down to each stage and must be paid for at interest until the consumers pay off the total costs.
How?
The plank-curer pays 500 dollars for the logs and then he must pay for that at interest. So to must the chair maker who must pay for the costs of the logger and the plank-curer at interest. Thusly, decreasing I decreases costs dramatically all down the line. For this reason the logger need not say "hmm... The production structure appears to be lengthening today. I'm gonna go log me some logs cuz I'm a logger who logs", rather the logger might just see the demand for his logs increases because now the plank curer's costs have gone down, while at the same time the logger's supply curve shifts to the right precisely because his prices have gone down. Do YOU Dig?
The plank-curer pays 500 dollars for the logs and then he must pay for that at interest. So to must the chair maker who must pay for the costs of the logger and the plank-curer at interest. Thusly, decreasing I decreases costs dramatically all down the line.
Sad to say that I do not dig. And if all this were true (not saying that it isn't) wouldn't it necessitate that any societal lowering of time preference would induce a thickening of the production structure most prominently in the bottom/later stages? As, apparently, they pay for the interest payments of all those producers above them? Which would then be proving the exact opposite of Bohm Bawerk's structure of capital...
"How/Why?"
Because otherwise losses would result to the producers in the first stage of production and this production structure does not last. If there's just you, me, and bob each of whom are capitalists producing in one year over the course of 3 years, you produce the first capital good and I pay you for that. Then using your capital good I produce the second capital good and Bob pays for that, then Bob produces the consumers good and the consumers pay for it. The consumer spending must be enough to pay off all of our combined costs or else the production structure was unsustainable. I have to pay for your costs or else you would not produce your good, but because my payoff comes from Bob he has to pay for the cost, not only of my product but also of your product. If the costs didn't "stick", then I might (ignoring interest payments for now) pay you 5$ for your capital good, spend $5 producing my capital good on top of that, and then Bob would only pay back for MY capital good with $5 and I would be 10 dollars net in the hole.
Thusly interest payments drastically increase the amount needed all down the line because you take out a loan to cover your costs, then I take out a loan to cover your costs, my costs, and your interest costs. Then Bob has to take out a loan to pay off my costs, your costs, his costs, my interest payment, and your second round of interest payments.
"Ok, but we didn't anyways. We assumed 3 stages with the costs 500, 350, and 275"
That was my fault. I sometimes fumble over myself when making examples. I thought I erased that bit.
"Maybe it's the way you set this up, but it makes no sense to me. Exactly who is paying the cost 'S1'? If the manufacturers in S2 have to pay costs which have 'stuck' to the product from the first stage then why are their operating costs not higher than the manufacturers in S1?"
All of the "SX's" was supposed to signal the number of the stage of production. Thusly whatever capitalist is forwarding the funds in stage 1 is paying for stage 1. The "operating costs" are higher in stage 2 than stage 1 if you include the price of capital. If you're talking about variable costs at any particular point in time they are wholly unaffected by this. That is the whole problem, all costs of production ultimately come from the consumer, and all investment opportunities have to at very least match the interest rate. Therefore the period of time between when the consumers good hits the market and when the production which ultimately leads to that good first begins matters since the longer any good takes to produce the greater the opportunity cost will be. I don't understand where, in your current conception of the production structure, the money to pay off the original stages comes from.
Remember, in the market economy the interest rate is the opportunity cost of time. The longer the production period, the higher the opportunity cost in the form of interest, whether this be implicit or explicit through preexisting funds invested into the company or loans taken out from banks.
Are we getting any deeper now?
Neodoxy: Because otherwise losses would result to the producers in the first stage of production and this production structure does not last. If there's just you, me, and bob each of whom are capitalists producing in one year over the course of 3 years, you produce the first capital good and I pay you for that. Then using your capital good I produce the second capital good and Bob pays for that, then Bob produces the consumers good and the consumers pay for it. The consumer spending must be enough to pay off all of our combined costs or else the production structure was unsustainable. I have to pay for your costs or else you would not produce your good, but because my payoff comes from Bob he has to pay for the cost, not only of my product but also of your product. If the costs didn't "stick", then I might (ignoring interest payments for now) pay you 5$ for your capital good, spend $5 producing my capital good on top of that, and then Bob would only pay back for MY capital good with $5 and I would be 10 dollars net in the hole. Thusly interest payments drastically increase the amount needed all down the line because you take out a loan to cover your costs, then I take out a loan to cover your costs, my costs, and your interest costs. Then Bob has to take out a loan to pay off my costs, your costs, his costs, my interest payment, and your second round of interest payments.
Ok I see that the the consumer demand for the capital structure of a given consumer good must be equal or greater than the production costs for the capital goods within that structure.
Therefore the period of time between when the consumers good hits the market and when the production which ultimately leads to that good first begins matters since the longer any good takes to produce the greater the opportunity cost will be.
To whom does it matter? The capitalist of the earliest stage? And if it is only the next capitalist, not the seller of the final good, in the Str.-of-Prod. who buys his good, why does it matter how long the whole Str.of.Prod takes to complete?
"To whom does it matter? The capitalist of the earliest stage? And if it is only the next capitalist, not the seller of the final good, in the Str.-of-Prod. who buys his good, why does it matter how long the whole Str.of.Prod takes to complete?"
I explained this earlier:
"For this reason the logger need not say "hmm... The production structure appears to be lengthening today. I'm gonna go log me some logs cuz I'm a logger who logs", rather the logger might just see the demand for his logs increases because now the plank curer's costs have gone down, while at the same time the logger's supply curve shifts to the right precisely because his prices have gone down."
The fact is that if you agree with me on the point above then this MUST be the case. It ultimately doesn't matter who finally figures it out, but someone has to or else the productive structure will run at a loss. Because costs, including interest, are ultimately passed on to the next stages of production (in equilibrium) it must matter because that is simply how much cost accumulates.
However, upon further reflection I believe that it is most likely to begin with the original stages of production. If we think of a single producer whose costs fall as a result of the decrease in the interest rate, then he will almost certainly be able to maximize profits by increasing output (MC falls at every quantity and therefore hit MR at a greater quantity). Then the second order capitalist will be able to do the same because his costs are lower, and so on down the line.
Edit
Further on this last point, not only does the MC of the first stage of production decrease, therefore increasing profit-maximizing output, but the same happens for the next stage of production. Because his costs have decreased his demand for inputs increases. Therefore not only does the supply of first order capital goods shift rightward, but the demand does as well, dramatically increasing the quantity of first order goods produced.
If the we take a disequilibrium condition where length of production is "too long" and interest ultimately pushes the costs of production as a whole over consumer expenditures on the total product. If this occurs then the final stage of production will run a loss. In light of this they realize that the costs of inputs exceed output and will therefore they will decrease their demand and refuse to buy the entirety of the second to last stage's capital. This moves down the line until the original stage of production must cut the amount it's supplying as demand has shifted to the left.
Remember that this is the "final" possible way that this could occur. This is the fail-safe in the capitalist system if the entrepreneurs in the final stage don't realize that this will be the case and cut their demand, and the producers before that realize that the final stage producers will do this, and therefore cut their demand, on and on to the original stage of production.
Neodoxy: "To whom does it matter? The capitalist of the earliest stage? And if it is only the next capitalist, not the seller of the final good, in the Str.-of-Prod. who buys his good, why does it matter how long the whole Str.of.Prod takes to complete?" I explained this earlier: "For this reason the logger need not say "hmm... The production structure appears to be lengthening today. I'm gonna go log me some logs cuz I'm a logger who logs", rather the logger might just see the demand for his logs increases because now the plank curer's costs have gone down, while at the same time the logger's supply curve shifts to the right precisely because his prices have gone down." The fact is that if you agree with me on the point above then this MUST be the case. It ultimately doesn't matter who finally figures it out, but someone has to or else the productive structure will run at a loss. Because costs, including interest, are ultimately passed on to the next stages of production (in equilibrium) it must matter because that is simply how much cost accumulates.
Well, yeah. But I find this to be kind of a non-answer. Of course an increase in the supply of loanable funds will lower the costs for producers, but I can't help but feel like your answer skirts the issue, which is, why the person who buys from the logger should have express stronger demand than the person who buys from the plank-curer, by nature of his being an 'earlier' stage capitalist.
Anyways I think that I've come up with an explanation which is satisfying enough, that early stage capitalists will not have to suffer a cut-back that late stage capitalists must suffer in the face of reduced consumer demand. So according to this idea, it will tend to be the earliest stage capitalist who is most encouraged by lowering of societal time preference, but there may easily and often be other factors which guide the SoP to thicken at the top rather than lengthen (for instance if the cost of new expensive durable producers goods was much higher in a stage of production 'one level' beneath the earliest stage of production than in that earliest stage, then a thickening would occur).