Intertemporal Macroeconomic Equilibrium: An Austrian Theory and Its Applications

0:00Why another theory? We have the Productivity Theory that was upheld by Boehm-Bawerk, by Knud Wichsel, by Hayek, but it has not had very much success in recent decades, so I will not talk about it anymore. Then we have the Loanable Funds Market Theory. It is widely used in the Austrian School today, for instance in modern classics of the Austrian School, the structure of production by Mark Skousen or by Roger Garrison in his time and money. But can this theory explain macroeconomic equilibrium?

0:46If I refer to Mises, to Hayek and to Rothbard, the answer is probably no. And the reason is that for the purposes of fundamental analysis, there needs not exist a loanable funds market. So even if there is no loanable funds market, there will be an aggregate investment equilibrium value and equilibrium originary interest rate and so on. So there are more fundamental forces at work independently of the monetary loans. And at last we have the Generalized Loanable Funds Market Theory that was developed by Rothbard.

1:34So here is Rothbard's model. We have a supply of present money, a demand for present money, and the determination of the macroeconomic equilibrium of investment and the interest rate. His model encompasses a number of components of what he calls the time market. So we have three components, the loanable funds market, the exchanges between capitalists, and the exchanges between capitalists and owners of originary factors. These exchanges take place at the different stages of the structure of production. And the problem I have with Rothbard's theory is that, for instance, the exchanges between capitalists and workers are considered, in his theory, as if the workers were the borrowers, they borrow present money and they kind of reimburse, repay the capitalists later with an interest.

2:40So, in his theory here, he formalizes the exchange between capitalists and workers as if it was the exchange between borrowers and lenders of money. And I think that this is not correct, at least I am not convinced by this theory. And this is why I have searched for another theory of macroeconomic equilibrium. So, the point of departure is the concept of the structure of production. So I do not start at all with a loanable funds market, in fact I will not use it at all in the presentation. The structure of production, we have an aggregate consumption, nominal value, nominal value of investment, an aggregate investment, which is the sum of the investments at the different in stages, and the concept, very important in this presentation, of capital intensiveness, which is the ratio of annual aggregate investment to annual consumption.

3:47Now the question is, is this structure with a given capital intensiveness, is it in equilibrium? Or is the equilibrium structure shorter with a lower capital intensiveness or is it longer with a higher capital intensiveness? This is the problem from which I start. So now I turn to the presentation of this model. And this model rests upon two determining elements. First there is the productivity of the lengthening of the structure. The lengthening of the structure is synonymous with an increased capital intensiveness or a greater capital accumulation.

4:34So here the idea is that if lengthening the structure brings a great increase in the total product, then people will tend to save more and augment capital intensiveness. Then there is the intensity of time preference, so here it is quite obvious if time preference is strong, if the preference for the present is high then people will tend to consume more now and reduce saving and investment, capital intensiveness will decline and conversely if time preference is low people will tend to consume less now, increase their saving and so on. So the model shows how that these two aspects of choice interact and how their interaction leads or can lead to macroeconomic equilibrium.

5:26Here is the model and from the formal point of view I have borrowed it from Hayek in the Pure Theory of Capital. He has a similar model, formally similar but theoretically different. So horizontally we have the final production, the quantity of final produce that is produced each year and it is during the current year. And on the vertical axis we have all the future years, so the final product that will be produced next year and the year after and the year after and so on and so forth. And since it will be always the same product that will be produced in the future years, it can change in the current year, but in the future years always the same product will be made, the same product.

6:19So we only need one axis for all the future products. We have here the line of 45 degrees and the representation of a structure of production, a reproducible structure. So this point represents a structure of production that produces the quantity Q1 during the current year, Q1 next year and Q1 the year after and Q1 and Q1 and so on and so forth. So this structure is reproduced each year and by hypothesis here the factors are efficiently utilised, Which means that on account of the capital intensiveness, Q1 is the maximum final produce that the structure can offer. This is an efficient structure in a very straightforward meaning of the term.

7:09Now, the first element is the transformation curve. The transformation curve will indicate what happens when people save or desave. For instance, if people decide to save, then they will consume less in the current year. We see the arrow to the left. And next year, the structure will be heightened. It will be at the higher point and remain there, for instance, if people decide not to save, not to save in the following year. So an additional saving will bring the structure to a higher point next year. And then the next year, if nothing changes, the production will be Q2, and so on and so forth, each year.

7:58They can also want an additional consumption, they de-save, in which case the structure in the following year will be lower. There is just one transformation curve for all the structure of production along the axis, it is translated horizontally. Now, the element of time preference, and yes, I will use indifference curves, but I must say immediately that the concept of indifference curve here is purely used for convenience, for pedagogical presentation. It can be entirely discarded from the presentation, but then The presentation will be longer and more difficult to catch.

8:52So here we have three structures of production that offer the same inter-temporal satisfaction, which means that people are indifferent between remaining at the current structure, so producing Q1 this year and next year and next year, or saving the quantity S, This is the structure on the left, but then they must be compensated by a sufficiently greater increase in production, Q2, or they may decide to consume more now on the proviso that their future consumption, Q3, will not be too low. So this is an indifference curve, very straightforward.

9:38And we have also the map of indifference curves that appears here, very standard, in a way. Now we put the two curves together, so it's very simple. We put the transformation curve and we put the indifference curve. And we have a structure where the two curves cross in this way. This structure is an inter-temporal macroeconomic disequilibrium. Why? Because we see here that people can increase their inter-temporal satisfaction, they can get to a higher indifference curve. Once again, I could make the presentation without using at all the concept of indifference curves, but it would be a bit less convenient.

10:26So we see that people can increase. The stream where they save S and reach the future production and consumption Q2 is preferred to remaining at the same structure Q1, Q1, Q1, Q1. They increase their inter-temporal satisfaction and visually it means that we move from one indifference curve to a higher one. So this structure is in disequilibrium. People will choose here in this case to save more, increase, heighten the structure of production, and we will reach, not necessarily, but generally and most likely, an equilibrium. So this is a representation of what I call the inter-temporal macroeconomic equilibrium.

11:13The two curves are tangent, this is the mathematical conveniency and visualization. The two curves are tangent, which means that at this point, people do not wish to save more, they do not wish to consume more, They just wish to remain exactly at the same point. The structure is in a final equilibrium, whereas here the structure was not in equilibrium. Pretty simple. If the curves cross a different way, for example in this case, the equilibrium, they will choose to consume more now and less in the future, and the equilibrium will be at a lower point, a lower structure. So, the results of this model. There is an existence and stability of equilibrium. Existence, not necessarily.

12:07We could have, from a purely mathematical point of view, I would say, here, the case where people choose to save and accumulate capital without limit. And so the point of the structure would rise up and up and up and up and never stop. Well, it could happen from a mathematical point of view, so not very interesting. And the convergence process is an effect of the inter-temporal actions of the agents who save or dis-save.

12:38Now, let's take a look at this equilibrium. The question is, what is the equilibrium value of capital intensiveness, and above all, what is the equilibrium interest rate at this point? In Rothbard's theory we had a very simple and straightforward answer because in his theory at the point where the two curves cross we have simultaneously the aggregate investment and the equilibrium interest rate determined. But now we see that we need to take a step further. So first, capital intensiveness. And here the problem is, I think, quite simple, because there is a point-to-point correspondence between the transformation curve and there is just one transformation curve that moves horizontally between the structures along the axis, the 45 degrees line.

13:39There is a point-to-point correspondence between the transformation curve and the curve that relates the final produce of the structure and the capital intensiveness that we see here. It's not more difficult or more complicated than this, I think. So here it's simple, once we have an equilibrium structure, where the two curves, the transformation and the difference curve are tangent, we can get the value of the capital intensiveness of the structure following this curve. The real problem and difficulty with this model is the interest rate, the determination of the interest rate. In 1990, Pascal Salin, French economist, has written a macroeconomic textbook, but it's in French.

14:31And in the first chapter, he has a model of equilibrium that is really similar, not exactly the same, but really similar to the one that I have elaborated here. But then in the second chapter, when he wanted to determine the interest rate and investment, He switched completely the theory and he introduced borrowers and lenders and borrowers borrow at interest, lenders lend at interest and there is the haggling of the market and the interest rate is determined, etc. This is something that I, in this model, want to completely make disappear, completely make disappear. So, there is another theory that I will elaborate from this model, and this is the Fetter-Mises theory, in fact, the theory developed by Frank Fetter and Ludwig von Mises.

15:29It's based on the degree of time preference, so in this theory of interest, interest is quite simply a price differential, difference in price between present and future goods. And if the degree of time preference prevalent in society increases, people prefer more the present, then the price differential will be greater, and the interest rate will be greater, and conversely. So this is a theory that does not use at all the loanable funds market. We have here an index in this model of the intensity of time preference.

16:18It is the slope of the curve, a higher slope at the point that crosses the 45° line. A higher slope means a higher degree of time preference and a lower slope, a lower degree of time preference. So we have this, we know, we don't know the quantitative relationship of course between the slope of the curves and the level of the interest rate but we know that the indifference curve with a higher degree of time, with a higher slope leads to a higher degree of time preference and a higher interest rate and the one with the lower degree leads to a lower interest rate. We know this. The problem is a bit more complicated when we compare two structures.

17:03And I have to go very fast right now. I'm running out of time. When we compare two different structures like this, there's a problem because the level of wealth is not the same. So I think that the slope of the curve is not a very satisfying index. And it seems to me that the elasticity which takes into account the level of wealth And so the sacrifice that you make by saving depends on the level of wealth. The elasticity is a better index of time preference. So we could have something like this and the interest rate here appears. Of course, the curve of the interest rate can increase or decrease or remain constant, the lower curve here. I have drawn a decreasing because it's the most likely possibility.

17:52So here the model, we have a structure of production in disequilibrium. We reach equilibrium, we have the corresponding equilibrium capital intensiveness, and we have the corresponding equilibrium interest rate. So I must now jump to the conclusion. This model offers a different foundation for the nature of inter-temporal macroeconomic equilibrium, the convergence process, the determination of equilibrium interest rate and investment, The effects of a lowering of time preference and of technical progress can be quite nicely analysed in the framework of this model.