06 May 2014

Showing Problem With Piketty Using Neoclassical Models

Austrian School, Capital & Interest 24 Comments

I am an Austrian economist. My understanding of capital & interest comes (originally) from Mises, but then it was refined in grad school when I studied Bohm-Bawerk, Fetter, and Fisher.

In case I haven’t been clear: One doesn’t need to be an Austrian to understand what’s wrong with Piketty’s conceptual remarks about capital & interest income. The reason I personally can “see” this is because of my background with the Austrian School, but a true student of the history of economic thought and neoclassical theory (which includes Paul Samuelson but not Paul Krugman) would understand the problem with Piketty’s remarks. So here are some links:

==> Nick Rowe has a great post today walking through standard two-good diagrams with PPFs and indifference curves, to show that interest is not “determined” by the marginal (physical) product of capital. This is standard stuff from Irving Fisher.

==> If you understand formal notation and modeling (like the Solow growth model), then check out the appendix (starts on page 178) to my dissertation. I show that in general, the equilibrium real rate of interest is not equal to the derivative of the production function with respect to K. It’s only under very special conditions that the general formula reduces to “r=MPK.”

==> Finally, go look at Paul Samuelson’s referee reports on my two journal articles where I fleshed out the appendix. I took Bohm-Bawerk’s verbal analysis and put it into a neoclassical model. I showed “with math” that Bohm-Bawerk was right and the naive productivity theory was wrong. As you will see, Samuelson had some quibbles with the conclusions I drew etc. (in particular he denied that some authors were advancing a “naive” theory), but he told them to publish the papers (which they did).

Let me say something in closing: Thomas Piketty isn’t stupid. He is aware of some of these issues. But it’s like the classical economists who adhered to a labor- or cost theory of value. Adam Smith understood full well that if you spent 10 hours making a mud pie, nobody would buy it. Yet it is still correct to say “the labor theory of value is utterly muddled” and to use simple thought experiments to get people to see why it’s utterly muddled.

24 Responses to “Showing Problem With Piketty Using Neoclassical Models”

  1. Matt M (-Dude Where's My Freedom) says:

    I’m starting to worry, Bob. If you keep making so many posts about Piketty, Krugman may start to get jealous… He’ll have to post some REALLY ridiculous nonsense in order to try to re-gain your attention.

  2. W. Peden says:

    Piketty is a genius. Every book has to be flawed in some way, and a book with his thesis must be very flawed, but if you’re going to have a flaw that is very hard for people to criticise, then capital theory is the area to have the book’s flaw. I’m just starting to get my head round some of these issues; goodness knows how it’s possible to argue this stuff with most of Piketty’s fans, most of whom (a) will not be interested in economics and (b) will not be keen on dealing with criticism of the book in good faith in the first place.

    It’s a fundamentally different problem than The Spirit Level, which had flaws that were very easy to explain to people. This book is here to stay.

    • Major_Freedom says:

      So to be a genius, one needs to believe in serious flaws?

      Well that explains a lot.

      • W. Peden says:


        • W. Peden says:

          Incidentally, even if believing in serious flaws was SUFFICIENT for being a genius, it wouldn’t follow that believing in serious flaws was NECESSARY for being a genius. Some basic logic there.

          • Major_Freedom says:

            So given that you just exposed a serious flaw in my assessment of what you wrote, would that mean you think I am a genius?

            If not, what makes Piketty a genius again?

            • W. Peden says:

              “what makes Piketty a genius again?”

              I dunno; maybe he’s good at getting sarcastic points?

              • Major_Freedom says:


                I think I hear Krugman saying that his talk about a housing bubble was just a joke.

          • Major_Freedom says:

            Also, if I were to treat your initial comment as a book, as it is a piece of writing that you published, wouldn’t that mean that it contains a serious flaw?

            If not, would putting what you wrote on paper and selling it to me make it have a serious flaw?

            Logic is pretty fun, isn’t it?

  3. Transformer says:


    If I understand Nick Rowe’s post correctly he shows that MPK is just one of the factors involved in deriving r. However (if these other things remain equal) there will be a correlation between MPK.and r.

    Do you accept that conclusion ?

  4. Anonymous says:

    Doesn’t Piketty’s idea imply that the future is better off with less capital investment and more conspicuous consumption by the rich? That keeps them from getting ever richer. Isn’t that obviously wrong when you look at history?

  5. Tel says:

    I like Rowe’s post, and he has done an excellent job on the diagrams, but I must disagree here:

    It’s only under very special conditions that the general formula reduces to “r=MPK.”

    Count the third diagram from the top in Nick Rowe’s post and look at the green box. You can’t store apples so eat them now, or lend them to someone else, or throw them away. Physical capital in this situation simply cannot exist. Financial capital may exist as an agreement between two people; but you remember that German case where one guy voluntarily agreed to be eaten by the other guy. I’m not saying that’s wrong, because I believe in individual freedom but preferences can be hard to explain at times.

    What Nick is essentially saying here is that when no capital is allowed to exist, then capital cannot be the determining factor in deciding interest rates. Well I guess flying pigs cannot be the determining factor in aircraft control either, but I’m tempted to say that the model where capital does not exist at all is more of a “very special condition” than the model where at least some sort of physical capital does exist. Am I way out in space to see it that way?

    Let’s move on to the blue line in the diagram, where apples may be stored so some very primitive physical capital is allowed to exist. There’s a warehouse and you can store apples in the warehouse, very handy. Better than a slap with a fish as the saying goes. But in Nick’s model, that warehouse is always empty. Sure we let you have capital, but no one ever actually uses it, everyone leaves the warehouse empty. Why does that feel a bit like I’m missing something?

    Suppose they did use the warehouse. Suppose at least one single apple was stored. Why that would automatically lock the “budget line” at the same slope as the physical property of the warehouse itself… which I think is the whole point here. Should I get back to the phrase “very special condition” and ask if it is more special that economic agents deliberately avoid using the opportunity of physical capital when it is available to them; or whether the more common or garden situation is that overall it is more likely that the opportunity to take advantage of those warehousing facilities will be attractive to at least someone?

    • Tel says:

      Ahhh crap, I managed to bugger up my quoting, there you go.

    • Bob Murphy says:

      Tel I’m not going to go back and re-read it, but I think he is saying:

      (a) You can have interest with no capital goods at all.


      (b) Even when there are capital goods, you also have to worry about their market price changing when computing the total financial rate of return to their owner. So physically productivity of capital goods does not, by itself, tell you what the interest rate is.

      I’m going to tweak my Mises Canada example and show just what Nick is talking about.

      • Nick Rowe says:

        Bob understands me correctly.

        Tel: the only conditions under which MPK determines r is when the intertemporal PPF is a straight line, and the PPF between C and I is a straight line with a slope of minus one.

        Suppose there were a plant, that grew at a constant rate g, and we could either eat part of that plant or let it grow. The size of the plant is K. C+I=Y=gK. In that case, MPK is a constant, g, and MPK determines r. That is a very special model of capital.

        (Frank Knight’s “crusonia plant”?, or has my memory failed?)

        • Tel says:

          The store-room situation is the same as that, but the plant just sits in the warehouse and neither grows now shrinks. Of course any linear model of capital gives you a straight line, and in most applied mathematics we start with a linear model (knowing that it isn’t exactly right) because the territory is well known and easy to work with.

          At least a linear model of capital is some sort of model that includes some capital. I’m just pointing out that your model of capital (from the third diagram) is saying that people have the opportunity to stockpile capital, but because of their preferences they all decide not to, and the warehouse is perpetually empty.

          It’s a pepperoni pizza but can I have that without any cheese or tomato, and ummm hold the pepperoni as well. Yes, I guess I am asking for a slice of toast.

          • Bob Murphy says:

            It’s a pepperoni pizza but can I have that without any cheese or tomato, and ummm hold the pepperoni as well. Yes, I guess I am asking for a slice of toast.

            Tel, what are you driving at here? Is Nick’s example somehow annoying you?

            If somebody wrote a 600 page book called “Pizza” and said, “All food is determined by the toppings on the pizza” then yes it would be fine for Nick to say, “Actually sometimes people just eat toast.”

            • Tel says:

              Yeah it annoys me. Heck yeah!

              You have yer basic model of capital which has been setup so that it contains absolutely no capital whatsoever. Toast is still toast and pizza is still pizza, but toast is not approximately a pizza when the whole discussion was about pizza toppings.

              • Bob Murphy says:

                Tel wrote:

                You have yer basic model of capital which has been setup so that it contains absolutely no capital whatsoever.

                No no no, a thousand times no.

                We have our basic model of interest, to show that it is not directly tied to the physical productivity of capital goods. So when someone comes along and says interest is the marginal product of capital, we can show, “No it isn’t.”

              • Tel says:

                Go back to the link and check out the diagram. The green box “PPF Without Storage” implies that no storage of apples is even possible… physical capital is outlawed.

                The blue line “PPF with storage” shows a gradient of -1 and in this situation storage is physically possible, but Rowe has placed the equilibrium point right on the corner meaning that we have big, empty warehouses but preferences being what they are no one ever puts any apples in those warehouses.

                Thus, operationally the green box and the blue line are giving the same result — zero physical capital.

                Yes, I understand you can still have contracts between individuals, and thus financial capital, and even some rate of interest stipulated in those contracts. However, Nick’s system is not constrained by physical capital in any way, for the very simple reason that there is no physical capital in his system anywhere.

                Personally, I find that a rather unsatisfactory explanation of the effect that physical capital has on an economy.


                See link to diagram. Note the equilibrium point sits are 100% consumption every period. Zero saving.

  6. guest says:

    consultingbyrpm blog tag piketty

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