10 Jan 2013

Why Wages–>Labor Is NOT Like Interest–>Physical Capital

Capital & Interest 150 Comments

My last post on this topic was a bit technical, so let me break it down a bit. This post will still probably only appeal to actual economists, whether professional or amateur, because these issues get so nuanced. But I will try to keep the discussion in plain English.

The claim I want to establish is that it is bad economics to walk around thinking that “wages are to labor, as interest is to (physical) capital.” Because of certain modeling conventions in mainstream economics, most economists think this statement is true, but they’re wrong.

Before diving in, let me be clear that throughout this post, I’m talking about real wages and the real rate of interest, as defined in terms of consumption goods. So you pick a basket of consumption goods, and then define the real wage rate as how many such baskets a worker can afford to buy, after selling a time-unit (an hour, say) of his labor. The (gross) real interest rate measures how many baskets of consumption goods in one year you can buy by selling one basket of consumption goods today, and the net real interest rate is just the gross rate minus one.

==> First of all, without workers, there can be no wages, period. So that’s a pretty good reason to think they are intimately related concepts. Yet without physical capital goods, you can still have interest. For example, if there’s an island with coconut trees and no production at all (we’re just harvesting nature’s gifts), people can still say, “Hey, I’ll give you 11 of my coconuts next year, if you let me have 10 of your coconuts right now.” If coconuts are the only consumption good, then the real interest rate is 10%, even though there’s no such thing as “the marginal product of capital” in this scenario.

==> Now the defender of the orthodox treatment might say, “OK sure, in a world without capital goods, you’d still have interest. But all we’re saying is, when you do have capital goods–and where there’s a choice between using the capital to produce consumption goods versus more capital goods–then in equilibrium, the physical ability of the capital good to reproduce itself ends up equaling the real rate of interest measured in consumption goods. For example, suppose there’s only one good, sheep, and you can either consume 1 sheep today, or let it reproduce and turn into 2 sheep next year. This clearly pins down the equilibrium real interest rate at 100%, and this is because of the physical facts concerning the production of sheep.”

==> The above retort is correct, as far as it goes, but I think 99% of professional economists would not see how the rabbit got into the hat. It wasn’t a harmless, simplifying assumption to assume that the same good (sheep) served as consumption and capital good; that was a critical move that guaranteed the result.

==> To see why, consider a slightly more general scenario, where I can use 1 machine today to produce 1 unit of food today, or to produce 2 machines in one year. (In other words, it takes the machine 12 months to make a physical copy of itself. Furthermore, the machines are perfectly durable physically; the owner just performs routine maintenance on them to keep them indefinitely usable.) Now most economists would probably think, “Well, in this case the physical facts pin down the equilibrium real interest rate at 100%. The machine today can produce either 1 unit of food today, or two machines next year, which at that time have the option of producing 2 units of food. So it must be that 1 unit of food today trades for 2 units of food next year, for a 100% real rate of interest.”

==> Not so fast. We are leaving out the fact that the machine can be sold for food on the spot market. I didn’t tell you in the above reasoning what the food-price of a machine was in period 1 versus period 2. Suppose in period 1, the machine could have been sold for 100 units of food, but in period 2, each machine fetches only 49.5 units of food. That means the guy in period 1 can use his machine to produce 1 unit of food and then sell it for 100 more units, for a total of 101 units of food. Or, he can use his machine to produce two machines next period, when he can use them to produce 1 unit of food each, and then sell them both for 49.5 each. This gives him a total of 101 units of food in period 2. Thus the equilibrium interest rate must be 0%, because the owner has to be indifferent between producing 101 units of food in period 1 versus 101 units of food in period 2.

==> The above example shows that when there is a distinct capital and consumption good, you can’t derive the equilibrium real interest rate just by thinking about physical production. You also have to worry about the spot market price of the capital good, measured in terms of the consumption good. If it’s the same forever, then this subtlety falls away. This automatically has to happen in a one-good economy, which is why those models are awful ways to think about capital & interest theory. It can happen too in a “steady state” of a model with distinct capital and consumption goods. But notice that it is a lot more restrictive than mere equilibrium; it has to lock in the real prices of all the capital goods, forever.

==> If people still think “meh” about the above, consider this: I can come up with a model involving robots where, in a steady-state equilibrium, it must be the case that the real rate of interest equals the marginal product of labor. But surely we can agree it would be crazy for me to walk around thinking, “Interest has to do with the marginal product of labor.” Well, the exact same reasoning applies to people thinking, “Interest has to do with the marginal product of capital.”

150 Responses to “Why Wages–>Labor Is NOT Like Interest–>Physical Capital”

  1. Gene Callahan says:

    OK, I’m listening. Can you tell me why my most recent post on this doesn’t resolve this in favor of the mainstream view?

    • Major_Freedom says:

      Isn’t Murphy’s position that interest is monetary, not physical?

      Thought he wrote a dissertation on that.

  2. Gene Callahan says:

    “But notice that it is a lot more restrictive than mere equilibrium; it has to lock in the real prices of all the capital goods, forever.”

    No: Because MPK ought to be calculated in terms of the price of the capital good, not in terms of physical units. And that price, in equilibrium, will set MPK = r. In fact, the way we price capital goods just IS to discount their future productivity by r! And this is real world stuff: that is exactly how we used to write our programs at my trading company, when the capital good was an option.

    • Joseph Fetz says:

      I actually agree with Gene here. Prices are the key.

      • Joseph Fetz says:

        However, in terms of your non-monetary example, those are still prices even though they are listed as units (the unit is the price in a non-monetary economy).

      • Bob Murphy says:

        Bob: We can’t derive interest rates just by looking at the physical productivity of capital goods; we need to look at prices.

        Gene: Bob, you’ve been wrong for 10 years.

        Joe: I actually agree with Gene here. Prices are the key.

        Bob: I’m going to go kill myself now.

        • Joseph Fetz says:

          Hmm, I must have missed something.

          • Bob Murphy says:

            Too late. I’m dead.

            • Joseph Fetz says:

              I will mourn for you, Bob Murphy. But I have a question, is suicide compatible with pacifism?

              • Tel says:

                Only if you take sleeping pills.

              • Yancey Ward says:

                Only if he hires Callahan to kill him.

            • Dan says:

              LOL

        • Gene Callahan says:

          But Bob, how does looking at prices mean r != MPK?! What I’m saying is, once you look at prices, r = MPK.

          • Major_Freedom says:

            “once you look at prices, r = MPK.”

            I would argue that once you look at prices, MPK’s TEND to be equal to r’s.

            r = Difference between money paid now and money received later. For loans, it’s the difference between money paid now is principle, and money received later is principle plus interest (which manifests from originary interest, i.e. difference in temporal valuations).

            MPK = Difference between money paid now and money received later. On capital, money paid now is capital price, and money received later is product sales revenues (which also manifests from originary interest, i.e. difference in temporal valuations).

            I would argue that the MPK’s influence r’s, rather than r’s influencing MPK’s, because if originary interest is the fundamental ground, and MPK’s are more closely associated with originary interest than are r’s, then the direction of influence is from MPK’s to r’s.

            • Major_Freedom says:

              “I would argue that once you look at prices, r’s TEND to be equal to MPK’s.”

              I think that sounds better.

        • Ken B says:

          Can you (Bob) explain why the prices would be 100 and 49.5 ceteris paribus in a sort of steady state. I understand it if the machine becomes obsolete, or half the people suddenly die, but if we are assuming, as you seem to be, that situation 2 is just situation 1 a year hence with or without the duplicated machine, this looks like a deus ex machina.

          Note I am not disagreeing with you Bob.

          • xgsmmy says:

            Ken, I think it depends on what people choose to do in period one.

            If everyone has two machines in period two the demand for machines may fall.

            Old people in period two may want to trade their machines for baskets of goods, but young people with two machines may not want three machines.

            That’s my best guest, anyway. (It seems like there has to be some other way to get food besides machines, though.)

          • Bob Murphy says:

            Can you (Bob) explain why the prices would be 100 and 49.5 ceteris paribus in a sort of steady state.

            !!! Of course they wouldn’t be. In a steady state, by definition, it would be 100 and then 100. In a “sort of steady state,” I guess they would be 100 and then sort of 100 next period.

            We don’t need any of these qualifications when we say “w=MPL.” You don’t need to say, “Assuming preferences don’t radically change next year…” or anything like that. You can even think of it in purely physical terms. A worker in an hour cranks out 10 apples, and that’s what his boss pays him in perfectly competitive labor market.

            But a machine cranks out (say) two future machines. So you can say the owner gets paid two future machines, but that doesn’t tell you what the real rate of interest is. It’s certainly not 100% unless you make some more assumptions.

            What Gene is essentially saying is, “If you tell me the physical facts about the capital goods, and you tell me r, then I can tell you r. Hence, you see why the mainstream guys are right in thinking that the physical facts pin down r.”

            (Now in fairness, Gene’s NOT actually saying that. Really what he’s saying is, “If I totally redefine what everyone means by “r=MPK,” then it’s meaningful.”)

            • Joseph Fetz says:

              “But a machine cranks out (say) two future machines. So you can say the owner gets paid two future machines, but that doesn’t tell you what the real rate of interest is. It’s certainly not 100% unless you make some more assumptions.”

              Thanks, that was helpful in my trying to conceptualize what you’re saying.

            • Matt Tanous says:

              “A worker in an hour cranks out 10 apples, and that’s what his boss pays him in perfectly competitive labor market.”

              Discounted according to the rate of interest, right? I can’t really understand how interest can be a physical result of the marginal productivity of capital if it also applies to monetary loans and affects the wages a laborer can earn. Given the explanation Rothbard presents in MES, it is utterly illogical to attribute interest to productivity, even if – in steady-state equilibrium – they would be equal rates monetarily.

              • Joseph Fetz says:

                Are you referring to the section where Rothbard talks about PPM vs interest? If so, then I certainly have to revisit that one.

              • Matt Tanous says:

                Yeah, I’m referring both to the explanation of interest in general (chapter 6) and the application of the discounting process to such things as the capitalization of future incomes from a factor of production, and the determination of wages as the DMVP.

                It seems to me that, provided you accept that wages and future incomes are discounted by time-preference (and thus the rate of interest in the market), then interest must originate separately from the productivity of anything. Thus, the capitalist return on anything (labor and capital investment both) will be at the rate of interest, monetarily, in equilibrium, but this is not because interest is a result of productivity.

              • Joseph Fetz says:

                As Mises said,

                “Interest is a homogeneous phenomenon. There are no different sources of interest. Interest on durable goods and interest on consumption credit are, like other kinds of interest, an outgrowth of the higher valuation of present goods as against future goods.”

  3. Gene Callahan says:

    “Suppose in period 1, the machine could have been sold for 100 units of food, but in period 2, each machine fetches only 49.5 units of food.”

    Right. And here is where you have become confused: The price of the machine in equilibrium will simply be the discounted value of its food production, and won’t vary like this UNLESS its MPK also varies!

    • Bob Murphy says:

      Gene, I am going to warn you that you’re firing off comments about how I’ve become confused on my doctoral dissertation, and Nick Rowe (who has studied this crap for decades) must be confused too. Is it possible that maybe you’re missing something? Remember when you first confidently said Nick Rowe’s OLG model was incoherent?

      • Bob Murphy says:

        Also, Israel Kirzner is confused. He too rejects the claim that interest is the marginal product of capital.

        • Gene Callahan says:

          I believe Kirzner would agree with everything I have said on this topic. I will ask him when I see him next.

        • Gene Callahan says:

          Because what you are doing is equivocating: I agree with Kirzner that interest is NOT the marginal product of capital. But I contend Kirzner would agree with me that in equilibrium, the RATE of interest will EQUAL the marginal product of capital. (If interest just IS the marginal product of capital, we would not need equilibrium as a condition for them to be equal!)

          And, I will note, Kirzner did not agree with your view of interest in your dissertation.

          • Major_Freedom says:

            Wait, are you saying that for the equation

            r=MPK

            That you think this whole debate was over whether or not that equals sign means “is” or “has a quantity the same as”?

            Paging Wittgenstein.

            • Bob Murphy says:

              That you think this whole debate was over whether or not that equals sign means “is” or “has a quantity the same as”?

              I was nonplussed by that as well. But, it’s not unusual in the Austrian discussion of this stuff to talk about “essential causes” and so forth, so it’s actually not crazy, but I was taken aback too.

        • Gene Callahan says:

          OK, just re-read much of Essays on Capital: Kirzner definitely will agree with me. That you think he would object to what I say IS your confusion!

          • Bob Murphy says:

            Gene, what we have here is exactly analogous to the OLG stuff. You are going to fire off some false statements about my position, we’re going to go back and forth, and when all is said and done, you will settle on a perfectly fine interpretation of the controversy that is not at all what Paul Samuelson (for example) meant when he said physical productivity pins down the rate of interest.

      • Gene Callahan says:

        “Gene, I am going to warn you that you’re firing off comments about how I’ve become confused on my doctoral dissertation…”

        Bob, I do not say you have BECOME confused! I told you you were wrong on this when you first presented it at NYU ten years ago.

        “Remember when you first confidently said Nick Rowe’s OLG model was incoherent?”

        The way he presented it WAS incoherent. It was only when I realized his model was different than his presentation of it that I had to revise my opinion.

        • Bob Murphy says:

          BOB: “Remember when you first confidently said Nick Rowe’s OLG model was incoherent?”

          GENE: The way he presented it WAS incoherent. It was only when I realized his model was different than his presentation of it that I had to revise my opinion.

          Nope, he presented it just fine from the get-go. I thought he was wrong too, but only because I was so sure that debt couldn’t burden future generations.

          I’m not saying he presented it clearly, rather I’m saying he presented it coherently.

          It’s amazing to me how utterly confident you are that if Nick or I say something you disagree with, even though we clearly have more expertise in the particular subject matter under discussion, that it must be because we are incoherent.

          Isn’t there another blogger you hate who acts like this?

          (Obviously I’m not saying I must be right. I’m saying, your dismissive attitude is something up with which I will not put, at least not right now when I have “day job” stuff to deal with.)

    • Transformer says:

      I inderstand how a machine that produces food will be priced at the discounted value of its future food production.

      But what about a machine that produces a copy of itself every period? The only way I can see that its current value could be the discounted vaue of its future output would be if its price was going to fall in the future (as in Bob’s example) otherwise its rate of return would alwys be 100%. But this seems unintuitive as the price of such goods would keep on failing over time.

      Is there a market mechansim to explain the priocng of such goods (in the real world some agrigultural prodcue would be a bit like this) ?

      • Joseph Fetz says:

        What value is a capital good that has no link to consumptive ends?

      • Transformer says:

        Ok, I think I see now.

        There would no point in producing a capital good that just reproduced itself unless at some point it contributed to the production of a consumption good. It will be the discounted value of this consumption good that the price of the capital good will be derived from.

        I think Gene is correcvt on this one.

        • Joseph Fetz says:

          Yes, that is correct.

          I do agree with Gene on the technical point that it is prices, not units that are of concern. However, I do agree with Bob that MPK is not equal to interest. MPK=r is only true in a steady state with no change. And once you allow the movement of prices, and detach them from one another, interest return isn’t dependent on physical productivity, but is instead dependent upon the future valuations and their difference from the actual valuations in the future. Just because a capital good is physically productive, that doesn’t mean that it will yield a positive rate of interest (its value can easily change).

          Essntially, the equation is assuming out time, which in the Austrian view is the most important aspect of interest.

          • Joseph Fetz says:

            Sorry, “future valuations” should be “present valuations of future goods”.

      • Nick Rowe says:

        If a robot breeds new robots (using no other resources) at a fixed rate g, and if a robot produces consumption goods (using no other resources) at a fixed rate MPK, then:

        r is equal to and determined by g

        The price of a robot Pk is equal to and determined by MPK/g.

        (I am assuming robots cannot breed and produce consumption goods at the same time.)

        But those are very special assumptions.

        • Transformer says:

          But what if the robot is also a consumer good itself ?

          That is: it can either be used to produce more robots, or be sold itself as a consumer good.

          I’m struggling to see how it will be priced so that its price will reflect both its role as a consumption good and as a capital good. used to produce copies of itself.

          I’m thinking that a partial answer is that ultimately the supply of all goods (both capital and consumption) will be pushed to the point on the supply line where cost = selling price discounted by rate of interest. But I’m still not sure this fully addresses it.

          • Transformer says:

            OK – I see the answer lies in the fact that the robot would need raw materials to build a new robot and these raw materials would be priced so that one could buy them , let the robot do it work and then sell the new robot either as a consumer good or a capital good for a price that reflects its labor plus it raw materials all discounted by the rate of interest (which as Gene says, in equilibrium will also match the physical productivity measured in money terms).

            • Transformer says:

              But – [ to continue this debate with myself :) ]

              Nick says “If a robot breeds new robots (USING NO OTHER RESOURCES) at a fixed rate g,” so that excludes this answer.

              So the only solution I can think of for how pricing will work for this scenario (a robot that can reproduce itself using no other materials and the robot can also be sold as a consumer good) is that output of this kind of good would keep expanding and force the price of robots down until robots become a free good.

              If the robots produce other kinds of consumer goods then once robots become free goods these goods would be priced purely based upon the discounted value of the other raw materials used.

              • Transformer says:

                this assumes that g > market rate of interest.

          • Nick Rowe says:

            Transformer: What you have just described is Frank Knight’s “Crusonia Plant”. (AKA “Schmoo”).

            It’s a plant, that you can either eat, or leave it to grow at rate g. Let K be the current size of the plant. Every year it grows Y=gK. And you can either eat Y or leave it to grow some more plant, so C+I=Y=gK.

            But that is a very special assumption about technology.

            • Transformer says:

              Thanks Nick,

              I can see how if Crusonia was the only good that an economy produced then g would be the interest rate (in this case the equilibrium level of time preference would shift until it matched g).

              But if Cruonia was one good amongst many and it grew at a rate faster than the equilibrium interest rate for the rest of the economy then I still don’t see how it could be priced to reflect the going rate of interest unless its price fell over time.

              • Nick Rowe says:

                Transformer; correct. It’s price would fall over time.

  4. xgsmmy says:

    Bob, I was wondering if something like this could be used to explain what I think Nick Rowe called the “gizmo theory of the great depression” referring to Stiglitz.

    If demand for food is inelastic (to a point) and demand for cars is elastic. Then if the price of food is falling (because of increased supply), the real income of car makers could be falling faster because the interest rate is higher for farmers in the short-term, but since farmers need to become car makers, you get a deflationary cycle.

    I was thinking it made sense because: 1. everyone has to eat. 2. you could sell (say) a basket of food a day, but only a single car throughout the year.

    (I’m no economist though, so I expect there to be some obvious error.)

    • xgsmmy says:

      I think I should have said the short term real rate for farmers is lower than for car makers while the spot market for farm equipment is more valuable. (The natural rate for farmers is higher.)

      So for farmers the short term real rate is lower and the long term real rate is higher. (Short term natural rate is higher and long term natural rate is lower.)

      And for car makers the short term real rate is higher and the longer term real rate lower. (Short term natural rate is lower and long term natural rate is higher.)

      And this is because the short term spot market for farm equipment is priced higher than the short term spot market for car making capital.

      And since farmers are experiencing a productivity induced supply shock this means the real income of car makers is falling at a quicker rate than the real income of farmers. (Because food demand is inelastic and higher frequency of sales farmers are less forward looking.)

      (Car makers being more forward looking are quicker to downsize.)

      • Tel says:

        The main two “tech shock” components of the time would be internal combustion engines, and electrification. Both of those were on the scene in 1900. The Model-T Ford started in 1913 for example. Tesla’s first motor patent was 1887, the first of the famous “squirrel cage” motors was in 1896.

        These probably were the initial trigger for the depression, but the big crash of 1929 can’t be explained so easily in terms of any technological change at or near 1929, nor can the very extended series of depressions in the decade afterwards.

        I think we have to accept that successful entrepreneurial activity will always be disruptive to an economy. So the sign of a healthy economy is not whether it gets shaken up by these events, but how quickly it adapts and rights itself.

        Hoover tried very hard to prevent adaptation by trying to organize cartels that would deliberately throttle productivity, and with an incentive to discourage upstarts (I’m serious, read Rothbard’s book). On the whole, central planners tend to be worse at adaptation than they are at anything else (even when you ignore the corruption, perverse incentives, unintended consequences, and the rest of it).

  5. Tel says:

    This automatically has to happen in a one-good economy, which is why those models are awful ways to think about capital & interest theory. It can happen too in a “steady state” of a model with distinct capital and consumption goods. But notice that it is a lot more restrictive than mere equilibrium; it has to lock in the real prices of all the capital goods, forever.

    Just wait a moment here, Mises had three types of “equilibrium” condition:

    PSR — Plain state of rest
    WSR — Wicksteedian state of rest
    FSR — Final state of rest as related to the ERE (Evenly Rotating Economy).

    Dare I say it, but the Keynesians use two types of “equilibrium” condition:

    Short run — similar to PSR
    Long run — similar to FSR (we are all dead like Bob)

    See also, LRAC, LRMC and http://en.wikipedia.org/wiki/Long_run_and_short_run

    So Keynes and Mises both described a ficticious state of the economy which is approached asymptotically over time. If you look up exponential decay there’s a bunch of equivalent physics theory. Anyhow, the ultimate resting place for all economic models is the ERE — the Evenly Rotating Economy where prices no longer change. Of course we could argue that new entrepreneurial activity would spring new ideas and new inventions into the world, thus disrupting the ERE, but none of that has anything to do with “equilibrium”.

  6. edarniw says:

    Hi Bob,

    I’m currently reading “Time to Build and Aggregate Fluctuations” by Kydland and Prescott and couldn’t help but notice that their discussion in section 2: “A Critique of Conventional Aggregate Investment Technologies” is very similar to the topic you and Rowe have been discussing. In the context of their paper, they were trying to motivate why you need “time to build” in a model – at the time, the empirical literature suggested that the PPF for consumption and investment goods was not linear, as frequently assumed in conventional macro models. Their solution was to introduce “time to build”. Another way to match the data was to impose adjustment costs, as is frequently done. Both are ad hoc but they’re conceptually closer to the idea of having truly distinctive consumption and capital goods.

    Anyways, I’m not sure if you’ve read this paper before, but I thought it was relevant to point it out.

  7. Tel says:

    I’ve been trying to think of a practical problem to apply this to. So how about this one:

    You have infinite fields of grain, which grows all by itself during the “harvest season” but then it is not available during the “off season” (there are only two seasons and they are cyclic). The only requirement to get grain is to expend labour gathering it.

    You have people who can put their time into some mix of three activities:
    * Gathering grain
    * Building silos
    * Literature and Arts (the highest preference)

    The people also eat grain and there’s a diminishing marginal return, so that if they have no grain they must eat bugs and worms (which makes them unhappy) but as they eat more grain they become happier by smaller amounts.

    Grain silos require no maintenance, and can be built in arbitrarily small increments so the total available silo space is just some real number. We presume that silo owners charge a storage fee (some percent of the grain stored) and we presume all owners charge the same fee at a given moment in time, so there is no advantage shopping around between different silo owners.

    If it starts with zero silo storage space, you can see there’s a strong incentive for someone to put their time into silo building, even though this gives zero present day happiness, because the silo will be valuable later on. However, as more people build silos the advantage of having one diminishes so you might as well just pay the going fee for storage space.

    So how does the silo storage fee settle over time (measured as a percent)? What does the price of buying a silo look like (measured in grain)?

  8. Robert says:

    I have not read Bob’s thesis in years.

    Here is one mathematical explanation of why, even in a steady state, the interest rate is generally unequal to the marginal product of capital:
    http://robertvienneau.blogspot.com/2007/03/interest-rate-still-unequal-to-marginal.html
    http://robertvienneau.blogspot.com/2007/03/interest-rate-still-unequal-to-marginal_12.html
    Can I say that that is an Austrian model of production?

    By the way, I think in a couple of his published papers, derived from thesis, Bob does not make a overwhelming convincing case that the cause of some of Samuelson’s muddled statements is Samuelson’s willingness to adopt a one-good model as an (unjustified) first-order approximation.

  9. Nick Rowe says:

    Wage => labour
    Truck rental => truck
    Land rental => land

    Interest is a relation between the rental rate on a truck and the price of the truck.

    Interest is a relation between the rental rate on land and the price of land

    If there were slave markets, interest would be a relation between wages and the price of a slave.

    Even in steady state, it is not true that the rate of interest is equal to (let alone determined by) the marginal product of a truck, an acre of land, or a slave.

    Listen up guys. Bob is one of the very few people who has his head straight on this stuff.

  10. Nick Rowe says:

    In steady state, where the price Pk and the wage W of the truck/land/slave are constant over time, and assuming no depreciation for simplicity:

    r=W/Pk and W = Marginal Product of the truck/land/slave

    But if preferences were different, then Pk would probably be different, and r would be different, even if W were the same. Unless there were a technology that lets you produce new trucks/land/slaves at a constant marginal cost in terms of consumption goods.

  11. Nick Rowe says:

    Some of the Austrians were very good on this stuff. (I forget which ones were better, but Bob will tell you.)

    Irving Fisher was also very good on this stuff.

    That simple 2-period Irving Fisher diagram is the simplest way to think about it that is also correct (provided you can stretch your mind to see it with multiple periods).

  12. Daniel Kuehn says:

    Is this right (this is where I feel like I ended up working through your appendix the other day):

    1. The interest rate is, in the steady state, equal to the marginal product of capital in producing capital.
    2. In the steady state, this is also equal to the marginal revenue product of capital in producing consumer goods divided by the spot price of capital.

    Of course 1. is really “the marginal revenue product of capital in producing capital divided by the spot price of capital”. but the spot price of capital just cancels out in that case.

  13. Major_Freedom says:

    My two cents:

    Period 1:

    Total money spending = $1000
    Consumer goods spending = $100
    Capital goods spending = $900
    Total money costs (book value of capital) = $900
    Total profit = Total spending – Total costs = $100
    Average rate of profit (marginal efficiency of capital) = $100 / $900 = 11%

    Period 2:

    Total money spending = $1000
    Consumer goods spending = $200.
    Capital goods spending = $800
    Total money costs (book value of capital) = $800.
    Total profit = Total spending – Total costs = $200
    Average rate of profit (marginal efficiency of capital) = $200 / $800 = 25%

    Period 3:

    Total money spending = $1000
    Consumer goods spending = $300.
    Capital goods spending = $700
    Total money costs (book value of capital) = $700.
    Total profit = Total spending – Total costs = $300
    Average rate of profit (marginal efficiency of capital) = $300 / $700 = 43%

    Period 8

    Total money spending = $1000
    Consumer goods spending = $800.
    Capital goods spending = $200
    Total money costs (book value of capital) = $200.
    Total profit = Total spending – Total costs = $800
    Average rate of profit (marginal efficiency of capital) = $800 / $200 = 400%

    Period 9

    Total money spending = $1000
    Consumer goods spending = $900.
    Capital goods spending = $100
    Total money costs (book value of capital) = $100.
    Total profit = Total spending – Total costs = $900
    Average rate of profit (marginal efficiency of capital) = $900 / $100 = 900%

    Period 10

    Total money spending = $1000
    Consumer goods spending = $1000.
    Capital goods spending = $0
    Total money costs (book value of capital) = $0.
    Total profit = Total spending – Total costs = $1000
    Average rate of profit (marginal efficiency of capital) = $1000 / $0 => infinity

    —————————

    The marginal efficiency of capital is (total money spending – total money costs) / (book value of capital).
    Rates of interest are constrained to, i.e. determined by, the rates of profit, in “equilibrium”.

    The more capital intensive an economy becomes, the more will productive expenditures rise relative to total expenditures. The more productive expenditures rise relative to total expenditures, the lower the rates of profit, and thus the lower the rates of interest will be.

    The less capital intensive an economy becomes, the more will productive expenditures fall relative to total expenditures. The more productive expenditures fall relative to total expenditures, the higher the rates of profit, and thus the higher the rates of interest will be.

    Interest in a division of labor society is independent of the productivity of capital, just like it is independent of capital in a non-division of labor non-capital society.

    • Joseph Fetz says:

      Assuming money is neutral. However, if the PPM changes, then that kind of screws up your accounting of interest return. I know what you’re saying, though.

      • Major_Freedom says:

        Yes, I abstracted away from demand for money fluctuations and assumed fixed aggregate spending each period.

        If the demand for money changed, such that total spending went up or down, then this would affect the average rates of profit and thus interest rates.

        I kept aggregate spending constant in order to control for monetary influences on profit and interest.

    • Ken B says:

      Aren’t you assuming capital good wear out completely in one period? Because you have no accumulation, the stock is equal to the spending on it.

      • Major_Freedom says:

        Yes, I am assuming capital is used up entirely in each period. For simplicity.

        If capital is not entirely used up, then the costs are depreciated over time, that is, costs would be postponed into the future. So costs would be lower for a given period, which would raise the average rates of profit and thus interest rates.

        This amendment would not, however, fundamentally affect this model of profit and interest.

        Good eye though.

        • Major_Freedom says:

          In an economy with fixed aggregate spending each period, where the expenditures for capital goods are the same each period, what would happen is that depreciation costs would eventually “catch up” with each period’s capital spending, and it would come to match my model above.

          For example, assume capital lasts 10 years…

          Period 1
          Capital expenditure = $500
          Cost (depreciation, 10 year, straight line) = $50

          Period 2
          Capital expenditure = $500
          Costs = $100 ($50 from first year, $50 from current year).

          Period 4
          Capital expenditure = $500
          Costs = $150

          ….

          Period 9
          Capital expenditure = $500
          Costs = $450

          Period 10
          Capital expenditure = $500
          Costs = $500

          This is equivalent to capital being used up in one period.

          In other words, the addition to profit and interest that comes from depreciation costs would eventually come to an end when there is a fixed money supply and fixed total spending.

          This is why I did not include it initially. It’s a phenomenon that arises because of inflation.

  14. RPLong says:

    Wait a minute, wait a minute…

    Wages are to Labor
    Interest is to Capital
    Rent is to Land

    Right? Which means when we say, “Rent is to Land,” we’re NOT talking about the same kind of “economic rents” that are involved in “rent-seeking behavior.” Right?

    I always understood (and maybe I have been wrong all this time) that “Interest is to Capital” involves something significantly different from “the real rate of interest.”

    Am I just an idiot who never got it right in the first place?

    • Ken B says:

      ” we’re NOT talking about the same kind of “economic rents” that are involved in “rent-seeking behavior.” Right?”

      Right.

      • RPLong says:

        But seriously. I don’t mind embarrassing myself on this one because I am genuinely confused.

        Can someone smart just tell me yes/no “interest on capital” is not actually the same thing as “the real rate of interest,” except by coincidence when they happen to be equal?

        Correct? Anyone?

        • Ken B says:

          Ahhh that’s not the question I answered. That one I do not know. I think you are right but have never really inquired into interest. But as for tyhe term rent seeking, yeah that’s different than rent on land or rent on a car you own and hire out.

        • xgsmmy says:

          RPLong, I’m pretty confused myself, but my guess is that there can be competing real rates for different types of capital so that to get an equilibrium you have to adjust the spot price.

          It might work in reverse though, where a change in the spot price results in a divergence of rates.

          I’m definitely not a smart person though, so maybe someone with the math and modeling skills will show up and set us all straight.

          • RPLong says:

            My question is purely theoretical – I was certain that these two forms of “interest” were two completely seperate economic concepts.

            I thought “interest on capital” literally referred to the price of capital, whereas “the real interest rate” was the price of borrowing/leveraging minus the impact of inflation.

            My whole understanding of the matter was like so: On the one hand, the price of capital was basically the price of financing or buying capital and maintaining it within a microeconomic problem. On the other hand, the inflation-adjusted price of borrowing was either the price of money in a macroeconomic context or the comparative discount rate in a go/no-go microeconomic decision.

            As such, the two numbers may be similar or even closely related, but still two very different numbers.

            I’m trying to figure out if my econ profs totally failed me here and I have the completely WRONG idea about “interest” or whether Bob is conflating two concepts that are totally different, but happen to have the same name.

            But Bob’s a smart guy, so I’m guessing I’m the one who’s confused. I just need confirmation.

            Anyone? Anyone?

            • Bob Murphy says:

              RPLong in everyday language and in models with money prices, the “real interest rate” is the nominal interest rate adjusted for changes in the purchasing power of money, commonly called the inflation rate.

              But if you think about it, what that boils down to is the exchange rate over time between a unit of consumption today versus consumption in the future. I.e. whatever it is that you’re using to define “the price level.”

              So that’s why in a model without money, you define the real interest rate as the intertemporal exchange rate of consumption goods. It’s the same thing, described differently.

        • Joseph Fetz says:

          Interest and discounting is embedded in the valuing of all goods in the present vs in the future. There is no direct relation between what Mises called the “originary” interest rate and that of the interest rate of specific goods or sectors of the economy. This is because the originary interest rate is based upon the subjective valuations between goods today and the future (not any specific goods, per se), and it only manifests itself as an objective interest rate when we view it through the price system.

          Interest is embedded in every price that concerns choosing now or later, which is effectively *every* price in the economy.

          Can the rate of originary interest coincide with the rate of interest found in a certain sector or class of goods within the economy? Sure, this is bound to happen from time to time, because interest in all sectors tends toward an equillibrium. But certainly we should not attribute interest to a very distinct and small part of the economy, nor should we use policy to do such based on such erroneous assumptions.

          Now you mentioned the rea

          • Joseph Fetz says:

            Forget that last line. Bad edit.

          • Joseph Fetz says:

            Now when you talk about the “real interest rate”, that is merely the difference between the nominal interest rate and inflation, which are two very distinct class of interest, or areas of interest, but have very little to do with the source of interest.

          • Joseph Fetz says:

            Remember, money has it’s own interest rate, as do the goods that it trades for (all of them).

          • RPLong says:

            Under my (flawed?) understanding of it, Mises was discussing what I have termed “the price of borrowing” (or “the price of future discounting,” if you prefer), whereas the Production Function refers to “the price of capital.”

            Basically, the question I am asking is this: Is it really true that economists were saying all along that these two things are the same?

            If so, then I agree with Bob. If not, then I am just misunderstanding the whole conversation (which would not be new).

            • Joseph Fetz says:

              No, Mises was discussing the origin of interest, which is simply the discount of future goods vs present goods, and which is manifested objectively in the real world by the ratio of these prices.

              • RPLong says:

                “which is simply the discount of future goods vs present goods”

                “(or “the price of future discounting,” if you prefer)”

              • Joseph Fetz says:

                Right, but you equated this to “the price of borrowing”. One doesn’t need to borrow for interest to arise, and as Murphy pointed out, capital doesn’t have to exist for interest to arise. That is the point that I was making about attributing interest to specific and distinct economic areas, this is not where interest originates.

                ” … the Production Function refers to “the price of capital.”

                No, it is the relation between physical inputs and physical outputs, and then the income is arbitrarily distributed into a big glob of capital called MPK, which is then said to be equal to r.

                My understanding of interest is that it is at root a completely social phenomenon, one that is found in every action discounting the future vs the present. The relation of physical inputs and outputs, or indeed the prices of those avenues, have no direct correlation to the originary interest rate (except in an equilibrium thought experiment, which doesn’t represent real life). Due to this, the originary interest rate is not calculable, but we do see how it manifests itself through the price system, and that is how we make our plans and indeed influence the interest rate in the next time period.

              • Joseph Fetz says:

                The bigger problem that I see is that policy makers will use these identities to inform fiscal and monetary policy, in effect making these conceptual models and their outputs the ultimate ends sought.

        • Scott Angell says:

          RP Long:

          I think people are making this too hard for you.

          The answer *that you are looking for* is “yes, they are the same.” Think about it this way — if you could borrow money (at the ‘money rate of interest’) and use it to buy capital goods (and earn ‘interest on capital’) and make a profit (arbitrage), then everybody would rush in and do it, driving the two rates to identity. Likewise if it resulted in a loss, you could sell capital goods and lend the money out to earn arbitrage. Everyone would do it, and drive the rates to identity.

          At equilibrium, all interest rates are the same, equal to the ‘real rate of interest.’ The problem is, nothing is ever at equilibrium, so you have all these ‘apparent’ discrepancies and need names for all these things. If you’re having trouble with that idea, I wouldn’t even bother trying to follow the rest of the argument here, because it’s probably not going to help you understand anything. They appear to be getting into a whole bunch of ridiculously technical theoretical stuff.

          But I wouldn’t necessarily know, because I don’t think I understand it either.

          • RPLong says:

            You’re right, Scott – that was the answer I was looking for. Thank you! That clears things up at least with respect to where my nutty brain was running afowl. Much appreciated!

  15. Bob Murphy says:

    EVERYBODY: I really do have “day job” stuff and I just can’t sucked into this right now. This area has literally been called the “black hole of economics.” This makes the OLG stuff look like child’s play.

    Gene, I will try to do a follow-up post about your other blog post on this. But let me ask you to clarify it. Here’s the problem:

    You are saying stuff like “if r < MPK then…” Since r is a percentage, that means MPK must be a percentage. But how the heck do you look at a tractor and say, “What is the percentage of its output?” I can look at a worker and say, “How many extra apples per hour can I have picked on my orchard, if I hire this guy?” That is a *physical* technological question. But I can’t look at a drill press and ask, “How many percentage points per year do I get if I incorporate this into my production?” That is a market value question, that can’t be answered merely by physical or technological facts.

    So clearly, there is something qualitatively different between saying in equilibrium “w=MPL” and “r=MPK.”

    Last point: I one time sat in Boyan Jovanavich (sp)’s office and spelled this stuff out for like 15 minutes. He looked at me and said with almost disbelief, “Assume you can transform bananas into tractors one-for-one.” He wasn’t cracking a joke. That was how he dealt with my perspective on this stuff.

    So while you may have a solution that rescues the statement “r=MPK just like w=MPL,” your solution is not at all what mainstream guys have in mind. That’s what I mean about this being like the OLG thing. You eventually settled on a position that was fine, but it was not at all what Krugman and Baker were saying originally.

    • Joseph Fetz says:

      For what it’s worth, I was agreeing with Gene on a technical issue, but I had completely forgotten that what Gene is saying is not what Samuelson was saying (and indeed what mainstream economists are saying). Yes, they do indeed look at physical productivity, I just thought that Gene’s focus on prices was the key to having MPK=r.

      Considering this area *is* the “black hole of economics”, can you cut me a little slack? I’ve never had anybody teach this to me, I have to instead learn everything myself or pick up what I can from blogs and such. I am at least trying, though.

      Glad to hear you’re still alive!

      • Bob Murphy says:

        JF wrote: can you cut me a little slack?

        I was more mad at Gene than you. I was mad that Gene was framing my position and the mainstream guys, such that you thought saying “I agree prices are key” was somehow a point in favor of Samuelson and against me/Rowe, when saying “prices are key” is literally an apt summary of the entire Murphy/Rowe critique.

        It would be like you watched the Ron Paul / Rudy G. exchange and then said, “I agree with Rudy, blowback is key.”

        • Joseph Fetz says:

          So you are or you aren’t going to cut me any slack?
          :)

        • Joseph Fetz says:

          BTW, I wasn’t thinking about in terms of this guy or that guy, I was more trying to think of “how *could* MPK=r?”. The only answer that I could come up with is the price system, along with value imputation and discounting. The whole steady state thing completely slipped my mind, this is certainly not a general theory.

          I’m still working on understanding how this also isn’t true in a steady state (as Nick has stated), but I am sure that it will come with time.

    • Gene Callahan says:

      “But how the heck do you look at a tractor and say, “What is the percentage of its output?””

      If r is per year, then if we have a corn economy, it would be (corn per year / corn cost of tractor).

      • Bob Murphy says:

        If r is per year, then if we have a corn economy, it would be (corn per year / corn cost of tractor).

        I’m not betting my life on it, but I’m pretty sure this is wrong, Gene. In the steady state it’s OK.

        • Ken B says:

          “I’m not betting my life on it, ”
          Of course not. You’re already dead, and poor Fetz has to live with that.

    • Transformer says:

      ‘How many extra apples per hour can I have picked on my orchard, if I hire this guy?” ‘

      In equilibrium won’t we find that the cost of hiring the laborer would be the value of the additional apples picked discounted by the rate of interest ?

      “How many percentage points per year do I get if I incorporate this into my production”

      Isn’t this the same question as above ? And in equilibrium won’t the answer be the same – the price of the the new press will be the value of the additional output it drives discounted by the interest rate (just a bit more complicated if the press will depreciate over a number of periods) ?

      • Transformer says:

        If MPK is defined as:

        the increased revenue produced by a piece of capital equipment divided by the cost of that capital equipment

        then in equilibrium this will always be equal to the interest rate.

        The interest rate itself will be derived from societal time preference.

  16. Rob Rawlings says:

    I think Gene is saying that the physical productivity does not matter (and it sounds like the mainstream guys would disagree ?)

    I think he is saying the following:

    The interest rate is determined by time preference and prices will adjust so that capital and consumer goods reflect that interest rate. If physical productivity increases prices will change to reflect that. That is if the interest rate is 20% per period then a machine will be priced (at equilibrium) at the point where it value equals the discounted value of its future output. If for some reason the machine become more physically productive then its price will rise and the price of its output fall until the same things holds at the new level.

    Likewise changes in demand for the consumer good, or changes in time preference will drive changes in the structure of prices (and production) so that r= MPK.

    • Joseph Fetz says:

      Yes, I think that is exactly what Gene is saying and it is why I agreed with him. I just forgot that that isn’t what Samuelson et al were saying. In fact, Samuelson was only using one good in his example (and the physical productivity of that good), but when you start adding in other goods, it kind of gets a bit jumbled.

      • Joseph Fetz says:

        Also, I think this is why Murphy stressed the whole “capital good reproducing itself to yield a 100% rate”, because it’s obvious that that is not accurate.

      • Joseph Fetz says:

        Oh, and obviously I know that this goes further back than Samuelson, it is just that his conception of it is the most familiar and common (I think).

  17. Ken B says:

    I own a slave. He’s my capital. I can get a certain amount of work from him, less the cost of bull whipping. From those numbers I can get the marginal return on this particular piece of capital right? Well I do own a slave, that slave is Ken B. I can’t sell him though (that bad Mr Lincoln again.) So how do I calculate a marginal rate of return on his lazy ass? i’m not sure I can. So as concepts these are different, right? The next question is, is there some canonical relationship here?

    • xgsmmy says:

      Ironically, in a libertarian world slavery is freedom.

      • K.P. says:

        Where did you get that from?

        • Joseph Fetz says:

          His ass.

          • xgsmmy says:

            This will probably be a case of “don’t explain the joke”, but what I’m saying is that:

            1. Libertarians are not “at liberty” because they renounce “positive” violence (a part of human nature), including against property. (Although, I’d argue it’s impossible to be an “anarcho-capitalist” and not a pacifist.)

            2. If you did want to be free, what then is the easiest way? “Sell yourself” (or get conscripted into) slavery. Now you’re truly free.

            • Joseph Fetz says:

              1. I am an anarcho-capitalist, and I am most certainly not a pacifist.
              2. This line of reasoning makes no sense. Not logically, nor in terms of libertarian theory.

              However, I must say that we are discussing economics here, not political philosophy. So I am confused as to why you’re injecting your opinion on libertarianism into a purely economic discussion.

              • xgsmmy says:

                Joseph, I made a joke in response to Ken B’s funny post, which you said I “pulled out of my ass”, and when I respond to explain myself you get offended?

                I’m not trying to derail, but this is a threaded comments section, so I hope the disruption was minimal. I’d respond to the points you raised in response to my critique but I’m afraid you would not take kindly to it.

                (I’m bogged down right now, though, so I may be rationalizing. In other words, if I find the time I’ll probably risk being labeled a troll by responding.)

              • Joseph Fetz says:

                I didn’t get offended, I just think that you’re full of shit. Big difference.

              • xgsmmy says:

                Joseph, here’s a explanation of the kind of thing I was talking about:

                http://bleedingheartlibertarians.com/2012/11/black-hearted-or-bleeding-hearted-it-would-be-irresponsible-not-to-speculate/

                As far as “anarcho-capitalism” not being compatible with self-defense: self-defense and punishment both suffer from the economic calculation problem that so bothers Bob Roddis.

                So counter-cyclical self-defense should create “malinvestments” and an inevitable “blowback”.

                But that’s not all: contract enforcement and debt slavery are “retroactively” determined acts of aggression. Creditors and contractors, if consistent by logic, should accept the risk of losses they take on voluntarily.

                And we haven’t even got to the non-sense about trespassing, natural resources, and the utter lack of a commons.

              • xgsmmy says:

                You might ask yourself, where does all this lead? Probably Gandhian-style anarchism, but logically you’re probably committed to Jainism.

              • Joseph Fetz says:

                You’re attempting to mix and form entirely disparate things such that it is now getting quite difficult to take you seriously.

              • Dan says:

                JF, the dude is either a troll or too ignorant to realize how ridiculous his position is. Either way, he’s not worth your time.

              • xgsmmy says:

                Guys, I’m am for better or worse serious.

                And just to be clear, I’m not saying I believe Libertarian, Austrians, and Anarcho-Capitalist believe what I’m saying.

                However, if you have any feedback about the myriad ways I’m mistaken, I would actually appreciate your comments.

                Saying “you’re full of shit” doesn’t really do it for me.

              • K.P. says:

                “self-defense and punishment both suffer from the economic calculation problem that so bothers Bob Roddis.
                So counter-cyclical self-defense should create “malinvestments” and an inevitable “blowback”.”"

                All organizations suffer from the calculation problem. Now, I don’t think that’s the libertarian call to eliminate all forms of organization. It’s not special for defense nor anarcho-capitalism.

                “contract enforcement and debt slavery are “retroactively” determined acts of aggression.”

                That’s true today as well.

                “Creditors and contractors, if consistent by logic, should accept the risk of losses they take on voluntarily.”

                Also true today.

                “And we haven’t even got to the non-sense about trespassing, natural resources, and the utter lack of a commons.”

                Honestly, for someone who appreciates having their mistakes corrected you’d think you’d hold off on comments like “non-sense” and be a bit more humble about something you clearly know little about.

                For starters, look up Long on Commons.

      • Major_Freedom says:

        Selling yourself is selling your freedom.

        Freedom includes the option to remove it. Suicide for example is permitted in a libertarian world. The fact that you are free to end your life in a libertarian world, doesn’t mean a libertarian world contains non-freedom of life.

        The only permitted “slavery” in a libertarian world is voluntary slavery. But some might call that an oxymoron, and not slavery at all.

        If I agree to let my girlfriend tie me up, and “do stuff” to me, then I am not able to move all that much. I am “trapped.”

        Am I free or am I not free? If I am free because I chose to be tied up, then it isn’t too big of a leap to lifelong slavery. The only thing that happens is that instead of one night, it lasts days, weeks, years, etc.

        • xgsmmy says:

          Woosh.

          • Major_Freedom says:

            Then unfunniest joke EVER.

        • successfulbuild says:

          Basically the loon major_freedom admits Libertarianism is tyrannical.

          The “freedom” to sell yourself into slavery is based on property norms and institutions that are entrenched before you’re even born. So basically this nut is saying that it’s fine to sell yourself into, say, Glenn Beck’s commune because Glenn Beck owned all the property before you were born.

          And it is indeed a big leap to say you have to agree to already constructed property norms versus personal possessions. This is because Libertarians don’t understand that property norms themselves vary from person to person.

          This “Major_freedom” has also claimed everybody has to be paying insurance agencies because people who don’t are “lazy” anyway.

          Notice how Libertarianism is not only tyrannical, but it precludes real freedom.

          If I wanted to set up a democratic community, it would be violating the Libertarian definition of “coercion” because democracy is based on rational debate, not property norms.

          • Major_Freedom says:

            “Basically the loon major_freedom admits Libertarianism is tyrannical.”

            it’s not “tyrannical” to be able to choose what happens to your body. Yes, even if a person’s choice for themselves is something you don’t like. Yes, even if your emotions lead you to antagonizing another’s choices for themselves.

            If I agree to let my girlfriend tie me up, then that is not tyrannical against anyone, not even me. But because you don’t agree to it, you want to merely DEFINE the argument that it should not be stopped by force by you or anyone else, as a “tyrannical” ethic.

            OK, if you want to DEFINE voluntary behavior between consenting individuals as “tyrannical”, then so be it. Yes, I fully admit that libertarianism is “tyrannical” the way you have defined it.

            But I don’t care how you define tyranny. What matters is what people are DOING with each other, to each other, and around each other.

            If, in terms of actions, one person agrees with another to be tied up, then to me that is perfectly justified. I choose to not call that “tyrannical”, but if you do, then that’s your propaganda agenda that is clearly designed to invoke an emotional resentment towards libertarianism, because you know you can’t convince people through reason and logic.

            “The “freedom” to sell yourself into slavery is based on property norms and institutions that are entrenched before you’re even born.”

            No, it’s based on human action that exists before, during, and after one is born.

            The “freedom” to have a gun pointed at you by a thug, to “voluntarily” stop you from doing to your own body what you choose to do, to stop you from “coercing” your own self, is based on property norms and beliefs that existed before YOU were born, by the world’s thuggish socialists who can’t stand individuals doing to their own bodies what they choose to do to their own bodies, laws or norms be damned.

            It doesn’t matter what the “property norms” and “institutions” happen to look like or be, when it comes to current thug behavior in pointing guns at people to stop them from doing to their own bodies what they choose to do. It is always going to be violence to point guns at people to force them to do something they otherwise would not have done and what they otherwise would have done is non-violent (such as agreeing to let someone else tie them up).

            “So basically this nut is saying that it’s fine to sell yourself into, say, Glenn Beck’s commune because Glenn Beck owned all the property before you were born.”

            I’d rather be a nut to you, than a non-nut, or even a friend. You’re a thug who believes pointing guns at people who are not engaging in any violence, is justified, just because you don’t like what they are doing to themselves.

            “And it is indeed a big leap to say you have to agree to already constructed property norms versus personal possessions. This is because Libertarians don’t understand that property norms themselves vary from person to person.”

            Then you have no grounds to stop those who agree to have themselves tied up by another. If you argue it is “tyrannical” to agree to be tied up by another, then you are claiming it’s just your subjective opinion, because, after all, “property norms vary from person to person.”

            “This “Major_freedom” has also claimed everybody has to be paying insurance agencies because people who don’t are “lazy” anyway.”

            I never claimed that.

            “Notice how Libertarianism is not only tyrannical, but it precludes real freedom.
            If I wanted to set up a democratic community, it would be violating the Libertarian definition of “coercion” because democracy is based on rational debate, not property norms.”

            You cannot set up a democratic commune and impose it on people who never even agreed to be a member of it and be subject to the democratic outcomes.

            Not only that, but by even postulating a commune, you are tacitly claiming the justification for private property rights, namely, only those who are in the commune have the exclusive right to control its resources.

            The only difference between your property rights ethic and mine, is that whereas you would deny respecting the property rights of individuals, but not groups of individuals, I would not deny the property rights of individuals or groups of individuals.

            You are a thug to individuals, whereas I am not. You are wanting groups of people to have their property rights respected, but you don’t want individual people to have their property rights respected.

            Your position is inconsistent and arbitrary. Mine is consistent and not arbitrary.

            If you want to go live in a commune, then convince your thug friends to do so, and because I respect property rights of individuals, I will not point a gun at you to stop you.

            You, because you are a thug, will not afford me the same courtesy if I chose to live on private property as an individual. Then you sense I am alone, weak, and your thug-like mentality leads you to pounce and point your gun at me.

            You’re a tyrannical thug who does not want to act peacefully with his fellow human beings.

            • successfulbuild says:

              Wow.

              So after ALL that, we learn, indeed, it is justifiable for a Libertarian commune, which exists because of force and property rights, and excluding others to use the land, to force people into slavery in order to come onto their land (and presumably force their children into slavery).

              And a democratic commune is indeed un-Libertarian, because you have to accept the changes they make even if you don’t agree with them. Libertarian institutions are only those where people acquire the property before hand and force others into their feudal relationships.

              Thank goodness most people aren’t convinced by this Matt Tanous/Major Freedom logic.

            • Dan says:

              Don’t feed the trolls.

              • successfulbuild says:

                Yes, it’s “trolling” when people don’t agree with your slave society.

                What a fool.

    • Tel says:

      Well I do own a slave, that slave is Ken B.

      Yeah, but you didn’t take out a loan to buy him, so you didn’t have to calculate the interest that you would be willing to pay.

      • Bob Murphy says:

        And if you try to divide by the market price of Ken B, you blow up because you can’t divide by–

      • Tel says:

        On second thoughts… student loans?

        How to correctly calculate the rate of interest you should be willing to pay on a student loan… presuming you had knowledge of what you are buying in terms of productivity boost.

        • Dean T. Sandin says:

          The interest rate on a student loan would be based on the marginal product of the education, not the whole person. The whole person includes the capital good from the previous stage of production.

          • Dean T. Sandin says:

            Thought not in equilibrium, because the cost of the education should increase to absorb the extra earnings.

          • Major_Freedom says:

            Even when the loan is guaranteed by the state? Can’t see how the rate would be a function of the student only.

          • Tel says:

            Let’s suppose you borrow P dollars on a student loan (ignore inflation) and for every dollar you spend on education, you get back x dollars every year in higher wages for 50 years. The interest rate r is what you pay on the student loan (suppose yearly payments).

            Now if( r > x ) then you are screwed because you can’t even cover the first year’s interest payments, and the loan gets worse and worse.

            But if( r = x ) you exactly make the payments, but never get the loan paid off and anyway there’s no benefit to you in the whole exercise. You also can’t resell the “capital” good at the end of it.

            Thus no student in their right mind would accept a higher rate than x minus whatever pays back the loan over 50 years. Some students may accept a lower rate, if such a thing is on offer. In a competitive market, if all potential students were otherwise the same, they would bid up the available loans until r was getting close to x.

            Seems to come out pretty close to rate of interest equals marginal return on capital (with an adjustment because of finite capital lifespan).

            We might also have a supply/demand happening between people saving money and offering those savings to student loans, and the total number of students out there who are interested in borrowing… so if there are lots of people wanting to save, and not many students the rate will be driven down below the “worst case” rate.

            If education becomes more expensive, then x will get smaller, if the education process improves and teachers become more productive then x should get larger.

            • Major_Freedom says:

              Seriously, what student makes these discounted future cash flow estimations?

              Most of them just want to get a degree, and are willing to take out student loans to do it.

              They almost always worry about wages and incomes after they graduate.

              That’s how I explain the massive student debt bubble bursting. Many students found out that doing what students before them did, did not work out.

              • Tel says:

                Seriously, what student makes these discounted future cash flow estimations?

                A student smart enough to take some of the excellent value courses at mises.org before wasting their money on a lesser educational establishment.

                But anyhow, I was working it through as a theoretical exercise in economic calculation, if people make mistakes, then they make mistakes… every model is idealized in some way.

                Also, I doubt anyone really knows what they are going to earn for the next 50 years — there’s a prediction horizon in the calculation.

  18. Adrian Gabriel says:

    Robert Murphy = Genius. Great blog, you are right, like always.

  19. John Hawkins says:

    Here is my understanding of the discussion and why its so problematic – I think it’s obvious that the spot prices matter, perhaps what we need is a deeper understanding of why the spot prices change?

    I remember a very similar debate with David Glasner a while back on Uneasy Money, I think this was the same problem back then too.

    What really needs to be concrete is the definition of a certain kind of equilibrium where spot prices can still be evolving. Without that, I think it’s like one side is arguing in latin and the other side is arguing and greek and we wonder why we can’t understand each other or why this becomes a black hole.

    Post Script – I think the aside conversation about the “Crusonia plants” with different natural growth rates was onto something in the regard of the kind of model I’m thinking of. Would love Bob’s input on that train of thought if at all possible.

  20. Rob Rawlings says:

    Bob,

    I just read the appendix to your dissertation and have a comment.

    You describe a scenario where the interest rate as zero as follows:

    “the rate of return on financial assets is zero,
    despite the obvious physical productivity of the machines. What happens is
    that the total market value of the capital stock K declines with each successive
    period, so that the rental payments accruing from ownership of the machinery
    exactly offset the decline in market value of the stock”.

    This seems wrong to me. Surely if interest rates are zero then people will always prefer a larger amount of consumer goods in the present to a smaller amount in the present. They will adopt infinitely long production techniques. In equilibrium all capital goods would be used to produce more capital goods. These capital goods would be sold with a revenue that exactly matched the prices of inputs and any money that was needed to facilitate this would be lent at a 0% rate of interest. So no matter what the physical productivity of capital both the money interest rate and the rate of return on capital goods would be zero.

    The only thing that might change this is if the supply of money did not keep up with the demand for money (the productivity of a commodity money did not keep up with productivity generally, or the CB did not increase the money supply at the appropriate rate) in which case there would be an inflation or deflation premium on the interest rate.

    • Rob Rawlings says:

      Correction: “Surely if interest rates are zero then people will always prefer a larger amount of consumer goods in the PRESENT to a smaller amount in the present”

      should be

      Surely if interest rates are zero then people will always prefer a larger amount of consumer goods in the FUTURE to a smaller amount in the present

      • Rob Rawlings says:

        Having thought about this some more I now see that the only way that sales revenue = sales costs in an economy where the physical output is increasing is if prices fell.

        As prices fall so the value of the capital stock will fall and with them rental values

        So I now see that .

        ” the rental payments accruing from ownership of the machinery exactly offset the decline in market value of the stock”

        is correct, its just not the full story of what would happen in an economy in equilibrium under zero time preference.

  21. Scott Angell says:

    But surely we can agree it would be crazy for me to walk around thinking, “Interest has to do with the marginal product of labor.”

    Really? That would be crazy? I would think that was right. Interest does have to do with the marginal product of labor, doesn’t it?

    For example, if I could borrow money (and pay ‘the money rate of interest’) and hire guys to make X product (and pay X market wages) and make a profit (a (admittedly convoluted) form of arbitrage), then everyone would rush in and do it, driving X market wages, the price of X product, and the interest rate into equilibrium.

    The whole market interacts in this way, to reallocate capital, labor, etc., so that all returns are the same — the rate of interest. That’s why it’s hard to ‘beat the market,’ in pretty much any sense of the word, i.e. almost no matter what you are talking about (wages, interest, rents, etc.). Admittedly, there are concrete effects which will push things out of equilibrium, so that there will be (exploitable) discrepancies between various particular market rates, but the tendency is to push them all to the same value in the long run.

    And isn’t that why the FED lowers the interest rate — to boost employment and production?

    • Major_Freedom says:

      Productivity of labor is in real terms.

      But you are treating it in terms of spending. If workers can be hired to produce X at a profit, then you are introducing demand for those products. That demand will depend on what you are selling. Consumer goods or capital goods? If consumer goods, then you are saying that time preference is such that that much money is being made available by people to consume those products. If capital goods, then you are saying that time preference is such that that much money is being made available by people to invest in those products.

      The demand for your products will be a function of people’s time preferences. The productivity of labor is not related to this.

      • Scott Angell says:

        Productivity of labor is in real terms.

        Yes, that is true. But I do not see how my argument assumed that the terms were not real. Workers will move where wages are highest — and presumably wages would be highest in a field for which demand was growing, i.e., for which the market rate of interest was lower than that implied by the price differential spanning a particular stage of production.

        I didn’t introduce demand, I assumed it. I basically assumed “Ok, let’s say Bob’s argument was true. Wages are independent of the rate of interest. What would that imply?” It would imply that certain situations would exist as I described — that (convoluted forms of) arbitrage profits were available. But it stands to reason that profit seeking would obliterate any such situation. By lowering the interest rate, the FED creates manifold such arbitrage opportunities, at least temporarily, and in nominal terms. Once things begin to approach equilibrium, of course, things fall apart.

        Sorry, it just seems to me that pretty much everything about the economy is tied to the rate of interest. The productivity of labor is tied to the availability of capital — which is tied to the time preferences of a society, which is tied to the rate of interest. If you want to make a lot of money (wages), its best to be located in an economy with lots of accumulated capital — one with low time preferences.

        That just makes sense to me.

        • Major_Freedom says:

          “Yes, that is true. But I do not see how my argument assumed that the terms were not real.”

          Nothing in your argument assumed that the terms were real, but the fact that you were comparing a nominal concept (interest rate) with a real concept (productivity of labor) is why I chimed in and made it clear that the productivity of labor is a real concept.

          You don’t see a problem with trying to find a real based concept to explain a nominal concept?

          Are you aware of the problems with productivity theories of interest?

          “The productivity of labor is tied to the availability of capital — which is tied to the time preferences of a society, which is tied to the rate of interest.”

          Not sure what direction of causality you’re going with here, so I’ll just say that interest rates are caused by time preferences. Time preferences are not caused by interest rates.

          I would say

          The productivity of labor depends on the availability of capital, which depends on investment, which depends on time preferences, which manifests itself in nominal interest rates on loans and in nominal profits on capital invested in a division of labor, monetary society.

          • Scott Angell says:

            Interest rates are a nominal concept?!? Now you’ve totally lost me…

            I could’ve sworn they were real! Just because the FED fakes it doesn’t mean it isn’t faking a real thing.

            Are you aware of the problems with productivity theories of interest?

            Nope. I have no idea what you’re talking about.

            I would agree with your last paragraph. I did not mean to imply causality (or, at least, a direction of causality) by using the words ‘tied to.’ Only that they ‘go hand in hand.’ Or ‘they all go together.’ The accumulation of capital would cause the rising real productivity of labor, obviously, but I could also say that rising real productivity of labor is associated with (or tied to, or whatever) the accumulation of capital.

            Basically, they are not independent of one another. All of these concepts come as a packaged deal. Wages are ‘tied to’ the rate of interest — all returns to whatever are tied to it, as equilibrium pushes all returns to a uniform level. Which is the ‘real rate of interest.’

            • Major_Freedom says:

              Alley-oop sarcasm aside, if you want to find a connection between everything, which is admirable, it is very difficult, because our minds are only able to grasp a finite set of concepts, and ultimate truth with a T contains little truths in between concepts such as “real” factors like productivity of labor and “nominal” factors like interest rates.

              The connection, if there is one, is probably not direct, but indirect, in that one affects a set or variables, which then affect other variables, and so on, and then, there is a change to the variable in question.

              It’s one thing to say “they are not independent”. It’s another to say “they are dependent in this particular way.”

              For me, I have rejected the theory that productivity (of labor or capital) is related to nominal interest rates in the sense of causality, because I put all causality on grounds of the individual actor, not non-acting concept to non-acting concept.

              So if productivity of labor is related to interest rates, there MUST be human action in between somewhere as at least a mediator. But, having said that, because human action DETERMINES productivity of labor, and because human action DETERMINES interest rates, I think the connection between productivity of labor and interest rates is only connected in the way one tree branch is connected to another tree branch on the same tree. It’s by way of the tree trunk, and they can only change if the trunk changes, which may seem like one branch influencing the other branch.

              The way I think of “connecting everything” economics related is by grounding it all on human action.

              Tell me a story of how increased labor productivity, or decreased labor productivity, will influence me as an actor to change the way I set interest rates with borrowers and lenders. I know you talked about that above, but it wasn’t clear to me.

              • Scott Angell says:

                Well, you’ve gone all metaphysical now! :)

                But yes, that’s right — theory is just theory, it is a simplification of the concrete in order to make the concrete intelligible. That is what abstraction is all about. People act like abstraction is a complex thing; actually it’s not, it is the concrete which is complex. And any particular concrete example can certainly go against the abstract theory which attempts to describe it, which is I think what you see with the divergent rates in different markets. Reality diverges from the abstract ideal, pretty much always. I have been speaking (mostly) in the abstract, because that is the general way people talk & think, even when they don’t realize it. So of course, I’m very much simplifying.

                Now, if you want to ask about the exact ‘mechanical connection,’ between all these things, really you are just asking to have someone recite something like Man, Economy, and State to you. That would kind of be a waste of time. But it is fairly easy to see how an increase in a person’s real income (i.e., by an increase in productivity) could cause his time preferences to fall — he has started to have access to consumption goods above and beyond what he considers an acceptable minimum, and now is trying to build up capital so that he can be lazy (i.e. work less and still enjoy the same level of income).

                In fact, I think that is more or less a paraphrased example directly from MES. Most highly developed economies have much lower real interest rates than less developed economies. Probably the causation is not all one-directional. Probably it is a sort of feed-back system. Poor people are barely getting by; they don’t want to save as much because life would just be too miserable for them.

                But give them some extra income (by increasing their productivity, say, by maybe allowing foreign investment or whatever) and suddenly they may start saving at higher rates. In such a case it would be equally true to say that the economy became wealthy because time preferences were low, allowing an accumulation of capital, and that an increase of productivity allowed for the fall in time preferences. They will have worked together to produce the concrete observed outcome, not simply uni-directionally (from pre-existing low time preferences to increased productivity.)

  22. successfulbuild says:

    Btw… Libertarian Glenn Beck, who the guest commenter describes as one of the better Libertarians on Fixed News, is trying to set up a Libertarian commune now. so you have three attempts: The Free State project, some other Libertarian’s whose name I can’t remember, and Glenn Beck.

    I wish it well. Finally we can see if there is such a thing as “equilibrium,” because if genius Libertarians can’t establish a free-market commune operating under equilibrium conditions, than nobody can.

    • Adrian Gabriel says:

      What equilibrium? Who wants a commune when we already live in one? All countries are communes, which are areas of land owned by the state, but which everyone feels they have rights to the land. As is evident, it is impossible to own land, because the government owns it all. A democratic society is just, and that is what MajorFreedom was talking about. A democratic society where everyone is voting for themselves through majority rule…one vote which influences one’s own life. This is voluntaryism. But let me harken back to the equilibrium quibble. When has there ever been an appropriate equilibrium, when those ideas are artificial and never exist. There will never be an equilibrium in even our own lives with our choices…..otherwise we would not act. The natural process of human action is what will make voluntary actions come closest to this artificial equilibrium many statist economists attempt to calculate through numerical and unrealistic jargon.

      • successfulbuild says:

        I don’t see how the non-existence of “economic equilibrium” helps your case at all as this very thread is predicated on its existence. As a concept I agree it is bad. But that just gives credibility to the argument that economic power is based upon power.

        Democratic communities are unLibertarian because they are not predicated on the belief that you have to “homestead” land to use it. Even if you could somehow convince millions of people that “homesteading land” gives them the right to implement arbitrary tyranny, you’d still have the problem of different “agencies” fighting over its very definition. You believe in the state in the sense that you want this principle, and others, universally applied to all people. You are thus no different from the state who has a set of pre-conditions that you must meet to own the land.

        This isn’t even controversial, even mainstream economics texts note how capitalist is based on laws, grants, property norms, and other such things. That is one area where an economics text states something that is true.

        • Adrian Gabriel says:

          Incorrect. This thread is arguing whether or not an equilibrium is calculable and each person is taking their position on which variables are used to determine an equilibrium. Austrian economists, Rothbardians that is, make the Misesian claim that there are various praxeologocial elements that can determine equilibrium. Each of these elements is traced back to an individual, and their subjective value scales. The various elements are time preference, and scarce means. Each person is attempting to attain his desired end according to his environment. Since all humans are never satisfied, that means they are always thinking about some end to achieve, and thus they will never stop acting. If they were satisfied, they would not act. Thus various ends are attempting to be attained in the process of the human actor. He uses means to attain these ends. The incalculability lies in the fact that his preferences are only expressed in his actions, thus his life is incalculable. He can change his preference at any moment to arrive at another end with various means. This is why there is never any equilibrium in the orthodox sense. What is occurring in life is that people are constantly making choices that never stop and thus what is known is simply a range of an equilibrium in society.

          Take for example the price of a good. We may only be able to know the spot price, but in so looking for the spot price, we must be aware that it will again change quickly. As I mentioned, we will never know exactly what the price will be, but we do know that it will be set by bargaining somewhere at or below the maximum buying price of the most capable buyer and above the maximum buying price of the next most capable buyer. These various prices are set on a large market in larger quantities with the medium of exchange making this process more efficient and quicker. The “market clearing” price is the equilibirum price. But as I keep mentioning, the market will never clear. Suppliers will supply goods when they see their stock is depleting, while demanders will stop demanding if their wants become satiated. Further, prices will rise if people demand a low stock, while prices will fall if the stock is high. These efficient market process keep occuring until there is a spot price for the moment, but again “only” at that moment.

          Many people are taking the orthodox mainstream position and making broad assumptions with constants. They are using formulas and absurd generalizations on factors of production to assume they can calculate the interest rate by grouping factors of production into these mathematical assumptions. For this reason they are wrong and always will be. The world is too diverse and complex to make such assumptions. Not only does this lead to grave error, but it also makes people think they can calculate the future or allocate scarce resources more accurately than consumer preferences can. This is a Keynesian fallacy, and all the university kids fall into this category of vast absurd assumptions. Since the basic Keynesian determinants of income — the consumption function and the level of investment — cannot remain constant, they cannot determine any equilibrium level of income, even approximately. There is no point toward which income will move or at which it will tend to remain. All we can say is that there will be a complex movement in the variables of an unknown direction and degree.

          In regards to your quibble with democratic communities, I just told you they exist in a Libertarian world. The democratic processes of people deciding by majority rule (one vote only for themselves and their own choices which influence their own personal lives), allows for the most efficient outcomes to abound. And there is no need to predict people that homesteading land gives them right to it, it is what naturally occurs in society. Someone able to produce upon an unused portion of land, could thus attempt to register a private agency with that land, and this would give that person the right to continue to use and produce upon the land. If another attempted to use the land, then the person that registered the land with a private agency has the right to use the available means to stop that other person from doing so. Communist or socialistic ways always fail in that due to the lack of private property rights, land will be abused and people will be tyrannized by physical force on that land. Communistic and socialistic methods actually lead to more bullying and tyranny than do capitalistic approaches. By owning land the rightful owner has a vested interest in up-keeping it with capital. People could use it, if they paid for its services. It is a simple process of realism that should not seem tyrannical in any way.

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