A friend an I, he an economics graduate, were recently discussing the phenomenon of hyperbolic discounting. At first it seemed so bizarre to me this idea, but something in the back of my mind made me feel as though it was actually perfectly consistent with praxeological reasoning and in fact that hyperbolic discounting is, as is time preference, inherent to the axiom of action.
After a while of thinking about it and having searched a few times for “hyperbolic discounting austrian” etc. on the internet I found no explanations of this phenomenon - the only thing i found was a blog on here of Don Lloyd saying that it was the reader’s “homework” to find out the connection between action(in his terms, the subjective theory of value, which I don’t currently see as a necessary qualification) and hyperbolic discounting.
As far as my reading has gone at least on Mises’ and Rothbard’s analyses of time preference, in almost all cases any practical references to time preference have referred only to a pair fo points in time, such as the example of Mises’ when he refers to time preference of an acting man(/woman) preferring 104 dollars in a year rather than 100 dollars now, with the implication being that he/she would prefer 100 dollars now rather then 103 dollars in a year. This example is perfectly understood and a very clear exegesis (love those Greek words!) of time preference. Hyperbolic discounting of course is conceivable only in the context of 3 or more different values. If you were to look at a curve of the discounting factor of someone who exhibits hyperbolic discounting, you could see this phenomenon, but the curve that joins only two points cannot be ascertained at all - it could even be a linear curve, but nobody has claimed that we actually exhibit linear discounting.
In light of this then, I applied my thought to it and read the sections on time preference in Human Action and my (first) volume of Man Economy and State (I know, to a certain extent the same thing, but sadly my library isn’t large enough to do any really extensive reading, and i don’t have Boehm-Bawerk’s book) as well as Mises’ analysis of Bawerk’s view in his appendix in Human Action.
Unfortunately none of my friends have the relevant experience in praxeological reasoning to really test my ideas against, and so i turn to you all in order to try and settle this question.
So, first of all, when we act, we necessarily conduct action via the dimension of time, if you will. We cannot but act in time, and time is always passing us by. It is however something that needs to be economised. It is natural that the economisation of resources in our actions that take place via time, and the analyses of this, have not taken into account temporal flow (as it were, i’m sure there is a more proper terminology) as separate from action because in no conceivable world would the economisation of time be separate from that of resources. The choice to put the first horse to work on the most important need inherently contains the concept of “first” in a temporal sense. In a sense man is economising both time and resources at one and the same time. The fact that neither of these things can ever be separated in the realm of actual action is the reason no one has referred to the “simultaneous” but separate economisation of time AND resources.
References to these phenomena (Rothbard) have stated that a man for whom time was scarce would cease to be able to act because time preference would fall to zero. This however is, in my opinion, the result of a lack of separation conceptually between the economisation of time relative to the economisation of other resources.
As in all metaphors or examples, we have to suspend some specific factors to make the model believable. It is clear that here the theory is most likely to err, and so I shall try to be very careful in my wording, but this is the part I need some help on. Consider a man for whom time was not a scarce resource. He would live forever and his health would in no circumstance deteriorate. This of course would affect the judgments he would make as to his values, (such as questions of nutrition) but the ends themselves are not currently relevant. Despite his time being infinite, in a sense, he would still necessarily act in a certain temporal order. His resources would still have a diminishing marginal utility. Time’s infinite nature to him would not allow him to act twice simultaneously. His needs are dealt with in order of their importance to him.
The obverse of the same is the question of a man with “infinite” resources, but limited time. In such a case he would still tend to his most important ends FIRST. Notice that the action itself has not changed, but in each case he is economizing each resource separately. In each case, the finite resource is being economised, whereas the infinite resource cannot be, it does not need to be. Once we see this, then, time can be considered the same as any other resource. It is the fact that it constantly passes us that confuses us in this judgment, but this does not change the nature of its role as a resource.
Another way of looking at it becomes a little more abstract. Consider a man who was outside time, but had time as any other resource. In order to conduct an action, he would take means x, y and z, and put them together to produce his end. Now imagine any of these resources as being time. It is of no importance which one it is, but this conception could be used to more clearly view time as a resource just like any other.
If the previous reasoning is consistent and correct (that’s your job, to help me analyse it!) then time also has a diminishing marginal utility. Constant marginal utility would be shown by “exponential” discounting, that is a constant rate of discount between time points x, y and z. A diminishing marginal utility (which we understand as the nature of any good) is reflected (as the mathematicians put it) as a hyperbolic discount rate, that is, an increasing discount rate over time. Therefore, the action axiom contains within it the assumption of hyperbolic discounting.
I appreciate the length of this post is not conducive to casual reading, but I greatly appreciate the time of those who sit to read all of it, because I think it could be useful, and also it’s a nice way of testing my own reasoning against others who have more of an understanding of praxeological reasoning. I don’t mind if this all gets blown to bits by more consistent logic, I’m just curious as to whether it could be useful as an exposition of hyperbolic discounting.
tl,dr: hyperbolic discounting is inherent in the action axiom, because time is a resource like any other. It just doesn’t look like it.