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Why Time-Preference Must Be Positive

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CaptainMurphy Posted: Wed, Aug 25 2010 7:13 PM

I was thinking earlier about positive time preference.. even though it seems intuitive that people should value present goods over future goods, I didn't entirely understand the praxeological justification.  Thinking about it in terms of marginal utility helped me understand why time preference is necessarily positive.  I know that I'm walking through stuff you are probably familiar with, but I think it helps sometimes to actually write it out.

We know that marginal utility must diminish with each subsequent unit of a good obtained.  This is because you will use the first unit to satisfy your most urgent desire, the second unit to satisfy your 2nd most urgent desire, etc..  That we satisfy our wants in order of their rank priority is proven by the actions we take to satisfy those wants.  For example, if you get $10 and spend it on a sandwich, then get another $10 and spend it on gas for your car, then get another $10 and spend it on a CD, your actions prove that your top priority was satisfying your hunger, your second priority was satisfying your desire to be able to drive in the near future, and your third priority was (an investment in) achieving the psychic profit you get from listening to music.  You cannot logically argue "no, I actually prefer the CD to the sandwich" because if that were so, then you would've spent the first $10 on the CD, not the sandwich.

The above proves that each subsequent unit of a good you obtain provides less satisfaction than the previous unit did, because each subsequent unit is used to satisfy a lower ranking desire.  The corollary of this truth is that each subsequent unit of a good you lose necessarily harms you (in terms of opportunity cost) more than losing the previous unit did.  To see this, we go back to our example but this time you start with the $30.  You earmark $10 to be spent on a sandwich, $10 to be spent on gas, and $10 to be spent on a CD.  Now suppose you lose $10 before you go out.  Are you going to abstain from purchasing the sandwich, the gas, or the CD?  You will of course give up the CD because the CD was the least valuable of the three according to your own subjective preferences.  Now suppose you lose another $10.  You will give up the gas and buy only the sandwich.  So while losing the first $10 carried an opportunity cost equal to the satisfaction you would've received from achieving your third ranked priority, losing the second $10 cost you the satisfaction you would've received from achieving your second ranked priority.  This is why the marginal cost of losing units of a good is necessarily increasing for each subsequent good lost.

For us mere mortals who only have a finite amount of time in this world, time is an economic good.  We can't stop it's passage, therefore we can't prevent ourselves from "consuming" time.  The more time that goes by, the more our supply of remaining time dwindles.  Like any other economic good, the marginal cost of each additional unit of remaining time lost carries a greater opportunity cost than the loss of the previous unit.  Therefore, consumption of present time provides greater satisfaction (lower opportunity cost) than consumption of future time from the reference point of individuals in the present, meaning that people acting in the present-- the only people who can act-- discount the value of future time, thereby proving that time preference must be positive.

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Fantastic post, thank you.

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That explanation in the last paragraph is off.  Consuming now is better than later from the now point of view because the desire is felt now.  Not because your life is time limited.  What life expectancy does is cap your plan length.  You won't save to consume after death.

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I like this, it says a lot. I just have one question about;

That we satisfy our wants in order of their rank priority is proven by the actions we take to satisfy those wants.  For example, if you get $10 and spend it on a sandwich, then get another $10 and spend it on gas for your car, then get another $10 and spend it on a CD, your actions prove that your top priority was satisfying your hunger, your second priority was satisfying your desire to be able to drive in the near future, and your third priority was (an investment in) achieving the psychic profit you get from listening to music.  You cannot logically argue "no, I actually prefer the CD to the sandwich" because if that were so, then you would've spent the first $10 on the CD, not the sandwich.

In what context are you saying that?  Perhaps the sandwich shop is closing, he is closer to it, or he was given the first $10 on the basis that he buy a sandwich with it.  He may still prefer the CD, but is obligated (by these, or any other of an infinite number of possibilities) to buy the sandwich.  Would it still be prudent to say he actually preferred the sandwich to the CD?

I guess that's 2 questions lol

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That explanation in the last paragraph is off.  Consuming now is better than later from the now point of view because the desire is felt now.  Not because your life is time limited.  What life expectancy does is cap your plan length.  You won't save to consume after death.

I would argue that urgency of desire is a symptom of time scarcity.  For instance, even if we imagine a person who never dies, time is still limited and scarce for him because each individual unit of time still carries an opportunity cost.  Even someone with an infinite amount of total time on this planet would have to economize time because he can only be in one place at a particular point in time.  Therefore, time is still a limiting factor for him and still carries a marginal cost.  The only scenario in which time would not be scarce would be if each individual point in time was infinite, which I'm not even sure is theoretically possible.

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chloe732 replied on Wed, Aug 25 2010 11:35 PM

Epicurus Ibn Kalhoun:
In what context are you saying that?  Perhaps the sandwich shop is closing, he is closer to it, or he was given the first $10 on the basis that he buy a sandwich with it.  He may still prefer the CD, but is obligated (by these, or any other of an infinite number of possibilities) to buy the sandwich.  Would it still be prudent to say he actually preferred the sandwich to the CD?

The context is, I believe, that the person obtains $10 and that is all he has.  In a 2nd example, he instead obtains $20, in a 3rd example, $30.  His actions reveal his preferences regardless how he may feel about things.

If he desires a CD with his last $10, but instead buys a sandwich because the shop is closing and he is closer, then his preference was to buy a sandwich at a shop that was about to close because he was closer...it does not matter what he desired, he acted by choosing the sandwich.  His preference is revealed. 

If he was obligated to buy a sandwich, then that really wasn't a choice revealed by the presence of a value scale.  He was following an order. 

"The market is a process." - Ludwig von Mises, as related by Israel Kirzner.   "Capital formation is a beautiful thing" - Chloe732.

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Azure replied on Thu, Aug 26 2010 12:01 AM

I would argue that urgency of desire is a symptom of time scarcity.  For instance, even if we imagine a person who never dies, time is still limited and scarce for him because each individual unit of time still carries an opportunity cost.  Even someone with an infinite amount of total time on this planet would have to economize time because he can only be in one place at a particular point in time.  Therefore, time is still a limiting factor for him and still carries a marginal cost.  The only scenario in which time would not be scarce would be if each individual point in time was infinite, which I'm not even sure is theoretically possible.

Let us imagine then, a purposefully acting creature which lives forever and has the ability to parallelize tasks infinitely, so it basically does exist everywhere at once. Would it still experience time preference?

Yes. There's a simpler proof: Time preference is a feature of purposeful action itself, not a consequence of scarcity. If our immortal infinitopus didn't experience positive time preference then it couldn't act.

First, let's imagine the case of negative time preference, and attach cardinal utility values for the sake of illustration. If the present preference is 1, and time preference is -1, then its preference evolves over time as 1,2,3,4,5... It can always gain by waiting, so it would never do it, ever.

Now let's imagine the case of the absence of time preference. Then its preference would evolve as 1,1,1,1... it doesn't care at what time it is done, therefore it cannot do it at any time. For a being to act at all, it must have a preference, even an arbitrary one.

In both cases it couldn't act unless it, arbitrarily, placed a preference on the action at some unit of time which is greater than the preference on all the future units. That is, its time preference is made positive.

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chloe732 replied on Thu, Aug 26 2010 12:10 AM

CaptainMurphy:
I would argue that urgency of desire is a symptom of time scarcity.

Let's say I am hungry, hungry for marshmallows.  I am given a choice: I can have 10 marshmallows right now, or 2 marshmallows in 15 minutes. 

Example 2: I can choose between 10 marshmallows now or 10 marshmallows in 15 minutes.

Example 3: 10 now or 30 in 15 minutes. 

Why would I ever choose the same or fewer marshmallows in the future when I can have the same or more in the present (all things equal)? 

It seems it is as McKibbin said; desires satisfied now rank higher than the same desire (all things being equal) satisfied in the future.  I don't see how the urgency of any desire is a symptom of time scarcity.  Can you provide another example?

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In what context are you saying that?  Perhaps the sandwich shop is closing, he is closer to it, or he was given the first $10 on the basis that he buy a sandwich with it.  He may still prefer the CD, but is obligated (by these, or any other of an infinite number of possibilities) to buy the sandwich.  Would it still be prudent to say he actually preferred the sandwich to the CD?

I'm saying that he prefers the sandwich to the CD given the specific realities of his situation as he understands them at the point in time his preferences are evaluated.  Changing the context does not change the fact that his preferences are what they are for a given scenario.

To use an analogy inspired by Robert Murphy:  If I claim that marginal utility is necessarily diminishing, that can be likened to me claiming that gravity on earth always exhibits a downward force on objects.  Your changing-the-context objection is akin to saying "well if an object is placed on a stable surface it stops falling down.  Doesn't this prove that gravity doesn't necessarily pull stuff down?"

 The answer of course is no, because when you changed the context of the problem by introducing the stable surface into the environment, you added another independent variable to your experiment so to speak, and so your hypothetical argument would not prove that gravity doesn't apply to objects at rest because gravity wasn't isolated as an independent variable in your hypothetical thought experiment.  Likewise, when you change the context; whether it be a change in the sandwich shop's hours of operation or a change in how close the sandwich shop is to you, you are no longer holding marginal utility as the only independent variable.  Therefore, your objections can't disprove my claim that for any given scenario, marginal utility necessarily diminishes.

In other words, the marginal value I assign to a specific unit of a good can be higher or lower depending on how much of the good I start with.  But once you stipulate a starting point, it must be true that ceteris paribus, each additional unit consumed provides less satisfaction than the previous unit consumed.

 

Edit: looks like Chloe732 gave a  much less convoluted answer.

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Let's say I am hungry, hungry for marshmallows.  I am given a choice: I can have 10 marshmallows right now, or 2 marshmallows in 15 minutes. 

Example 2: I can choose between 10 marshmallows now or 10 marshmallows in 15 minutes.

Example 3: 10 now or 30 in 15 minutes. 

Why would I ever choose the same or fewer marshmallows in the future when I can have the same or more in the present (all things equal)? 

It seems it is as McKibbin said; desires satisfied now rank higher than the same desire (all things being equal) satisfied in the future.  I don't see how the urgency of any desire is a symptom of time scarcity.  Can you provide another example?

But your examples don't hold all else equal, because you are not comparing the same desires.  You are comparing "my desire to eat when I haven't eaten in X minutes" to "my desire to eat when I haven't eaten in X+10 minutes", with the implication that your hunger would be more intense from postponing consumption by 15 minutes.  To that end, present marshmallows and future marshmallows are different economic goods because the degree to which something is a 'good' is a value judgment based on the satisfaction it is expected to provide.

 To borrow an analogy from Robert Murphy (although he may not endorse the context I'm using it in):  If I'm given a choice between having a beer when I'm 5 years old versus having a beer when I'm 18 years old, I would prefer to have the beer when I'm 18 because as a 5 year old beer tastes gross but at 18 it tastes smooth.  This doesn't disprove positive time preference, because the goods being compared ("a beer at 5" vs "a beer at 18") are different goods in that they provide different amounts of satisfaction.  In this same vein, I believe your reasoning does not hold all else equal because you are evaluating different goods.  If my logic is correct, then your argument quoted above doesn't isolate time scarcity as the only independent variable, so it can't disprove my claim. 

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I didn't quite follow your example but I can respond to this part:

Let us imagine then, a purposefully acting creature which lives forever and has the ability to parallelize tasks infinitely, so it basically does exist everywhere at once. Would it still experience time preference?

Yes. There's a simpler proof: Time preference is a feature of purposeful action itself, not a consequence of scarcity. If our immortal infinitopus didn't experience positive time preference then it couldn't act.

If time scarcity is eliminated in the manner I describe in the post you quoted, our immortal infinitopus would engage in every possible action that could improve itself (of which there would be an infinite amount) simultaneously and instantaneously.  This may sound like a cop out, but a thought experiment that involves putting the infinitopus into our reality is like a thought experiment that involves constructing the Penrose Stairs in our physical world; it doesn't make sense, not even in theory.  

Time progresses in a linear manner.  Sure we can slow down time by traveling near the speed of light, but it is impossible to travel fast enough to bring time to a stand-still or cause it reverse direction.  Because of this, time is necessarily scarce in our reality. 

 I want to quickly go back to the example of a hypothetical person that lived in our world but couldn't die:  while it's true that his supply of time remaining doesn't dwindle in terms of # of years remaining, it does depreciate as time goes by, and to that extent his time is still scarce.  Basically, "infinity minus five" is still a smaller number than "infinity" and so his demand curve for time-preference is necessarily downward sloping, meaning that he discounts the future and exhibits positive time preference.  It's just that his demand curve can never hit zero because he would have to either be dead or he would be the theoretical impossibility mentioned above that could condense infinity into an instant.

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 I'm going to bed now and I probably won't be able to check this thread for a few days.  I didn't make this thread to convince people that the viewpoint presented is correct, it was more just a fun idea to run with.  Anyways, when I come back I'll check to see if there's any interesting discussion still going on.

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abskebabs replied on Thu, Aug 26 2010 3:21 AM

What life expectancy does is cap your plan length.  You won't save to consume after death.

 

Unless you have inheritance, or altruistically care about the long run consequences of your actions on others. I think you're right to an extent but there are caveats associated with your statement.

 

Also @Captain and even more so Azure, your thoughts somewhat echo some that I've had recently (Indeed I am a little upset now that I've lost my originality!). I've even thought of taking some of the draft notes I've made so far and producing a paper on the subject. I'll keep an eye on this thread

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Azure replied on Thu, Aug 26 2010 3:31 AM

If time scarcity is eliminated in the manner I describe in the post you quoted, our immortal infinitopus would engage in every possible action that could improve itself (of which there would be an infinite amount) simultaneously and instantaneously.  This may sound like a cop out, but a thought experiment that involves putting the infinitopus into our reality is like a thought experiment that involves constructing the Penrose Stairs in our physical world; it doesn't make sense, not even in theory.  

Time progresses in a linear manner.  Sure we can slow down time by traveling near the speed of light, but even it is impossible to travel fast enough to bring time to a stand-still or cause it reverse direction.  Because of this, time is necessarily scarce in our reality.

My main point was a proof of positive time preference need not rely on any scarcity at all. We can toss out the infinitopus if you'd like, and my proof still works.

Anyway, the infinitopus couldn't perform every possible improving action at once: What about those that have to be done in a sequential order? Parallelization also doesn't mean it can do everything instantaneously either.

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msinia replied on Thu, Jun 2 2011 9:29 PM

 

Great post! Sorry for reviving it, but I'm somewhat confused by time preference as well.

I can grasp the principle intuitively and pretty much accept it as a generalization or tendency, but I'm having a hard time understanding it as an universal law.

I think my confusion can be illustrated on this point. Why couldn't an individual arbitrarily decide that prefers an end fulfilled in the future rather than in the present? Now I'm not asking why couldn't this be the modus operandi, but why not just once, arbitrarily? If the time preference law is universal, this is supposed to be impossible, yet I can't see why.

I've read Mises argument on this issue on a Human Action chapter (echoed on some other parts of the net too). It goes "if humans always desired to act in the future rather than in the present, there would be no action". This is true, but to my understanding only proves that future fulfillment of wants can't always be preferred to present fulfillment. However, it does not prove that present fulfillment is always preferred to future fulfillment.

Hope this makes sense, and thanks for the assistance!

 

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I agree that the statement of time preference may be confusing, as to be absolutely universal, it relies on certain assumptions, which usually remain implied.

E.g., you can keep the received good indefinitely with 0 costs (unrealistic for goods) and use it at any future moment after receiving (unrealistic for services).

There is another caveat. Let's take the archetypical good for which the statement holds always: a get option with unlimited execution date. On the first sight, it is beneficial to get this option earlier (A) than later (B), because A allows its holder to do everything that B allows, plus additional ability to execute it earlier. However, as shown by Schelling (and others), it is not always beneficial to have more options - sometimes one demonstrably destroys his options to create a credible commitment. See http://en.wikipedia.org/wiki/Chicken_%28game%29 for an introductory example of how having less sooner can be beneficial.

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