Two Approaches to Criticizing Krugman on Kapital
Nick Rowe and I have both known that something was unsettling in Krugman’s recent posts involving capital theory and the corporate income tax. (BTW this isn’t ideological: I would’ve written the same thing about Steve Landsburg’s diagram except he had too much extra stuff going on, and it would have distracted from my point.)
So Nick writes a really long post that is very polite.
In contrast, I wrote a short, snarky post that has so far gained me 3 emails, all negative. (They were all along the lines of, “I agree that Krugman can often be annoying, but no you messed this one up, Murphy.”)
So you be the judge.
P.S. I’m writing the current blog post tongue-in-cheek, but I am actually wondering what the best approach is. I worry that Nick’s post will fly under the radar, whereas my provocative claim was *so* provocative that nobody believes me–even allies.
Bob, maybe I’m missing something obvious, but doesn’t the dimension of integral X dY equal the dimension of X times the dimension of Y? And so doesn’t the dimension of integral r dK equal the dimension of r times the dimension of K, which is simply equal to the dimension of K since r is a percentage?
That is the normal way to do it, except that interest rates are percent per annum with units of 1/year.
People are lazy not to write the time component of the unit, but it’s in there.
Keshav, isn’t that exactly what I said a purist would say? So I had two levels of critique: A big picture blunt one, to shake people and say, “Hey! A rate isn’t the same thing as a widget or a dollar. Something is screwy here if you’re thinking of capital being analogous to labor.”
Then the next level is to deal with your response.
Oh sorry, I didn’t see your “A note for purists” section. Somehow I thought the post ended before that.
Tried to post this at Mises.org but couldn’t get past the gatekeeper:
There are machines that make widgets. The horizontal axis is “number of machines”. The vertical is “widgets per machine per year”. The areas are “widgets per year”. Does your objection come down to saying that there are many types of machines in the real world and we shouldn’t lump them all together? If so, then why are we allowed to talk about the demand for cookies in a world that has both Oreos and Chips Ahoy?
There’s a hidden presumption that Oreos make a very good substitute for Chips Ahoy, therefore the approximation of treating them as a single commodity does not significantly mess up your answers.
Attempting the same presumption claiming that (for argument sake) underwear is a good substitute for lawn mower fuel, is going to result in a much rougher estimate. Going ahead and presuming that all economic produce can reliably be substituted for everything else at any time would result in a very crude estimate indeed.
We could perhaps wave a magic wand and presume that all economies are self balancing and will deliver exactly the right ratio of all goods therefore only the total is important. I’m happy enough for the macro guys to speak up and admit that’s what they believe, providing they also admit that this assumption is so powerful that a large chunk of economics just vanishes completely when you do that.
Tel,
If I intend to consume either underwear or lawnmower fuel then you’re right they are very poor substitutes. But, if I am an investor (i.e. a consumer of capital) looking for a return (or a claim on cash flows from future production) then lawnmower fuel may be a very good substitute for underwear and the capital to produce either may be very good substitutes from my perspective.
The problem with the ‘magic wand’ assumption is it breaks several other fields of macro economics. Specifically, public goods theory, externalities (positive and negative), and monopoly theory all fall apart if you assume the market is correctly producing in the right ratios.
I disagree that Krugman’s graph has the units wrong. It’s quite clear that his X axis is in dollars, and his Y axis is an interest rate, thus the units of the area on the graph is simply the units of one axis multiplied by the units of the other axis… which would match GDP. Don’t make the rookie mistake of presuming that interest rates are a simple percentage, actually time sneaks in.
https://en.wikipedia.org/wiki/Dimensional_analysis
Thus, Krugman’s X axis is what economists call a “stock” measured in dollars, and the area of the graph becomes a “flow” measured in dollars per year. So in a nutshell:
Stock * Rate = Flow
You could make the same argument against GDP itself, and then argue against macroeconomics even in principle, which is not to say that the units are wrong.
Clearly we can (mathematically speaking) just go around adding up the market value of anything and everything, just like we can go around adding up the total income all over the place and call it GDP. Does it end up meaning anything? Dunno… lots of people seem to think it does.
Clearly we can (mathematically speaking) just go around adding up the market value of anything and everything, just like we can go around adding up the total income all over the place and call it GDP
Tel, I don’t think you are understanding the critique. It makes sense to say, “How many apples will be sold at $3 per pound? How many apples will be sold at $2 per pound?”
But it wouldn’t make sense to talk like that, if your definition of “1 apple” depended on its price.
I think it’s all part of the same conceptual problem, but see my rather rambling examples below. Yes I understand there’s a circular feedback loop in terms of each thing using each other thing as a reference round and round it goes, but real economies are just like that (each thing does affect every other thing) and real accounting is also like that (e.g. banks basing their asset collateral on house prices, which in turn depends on bank loans which are backed by housing collateral).
Normally in a feedback situation, you test an open loop by running part of the system in isolation, and then run another part of the system in isolation, and only when you have all the component parts measured up do you close the loop. You can’t do that with an economy because it’s by definition a process of exchange and the concept of exchange as an “open loop” operation is kind of meaningless.
So pricing everything in money simplifies the multidimensional economic calculation down to a one-dimensional price system which provides both a common reference and a common communication mechanism between all participants. It’s a very clever trick, but you can see there is no way to convert a multidimensional object into a single dimension, therefore the price system destroys information by necessity (quite likely, as per Hayek it also localizes information, which makes the complex problem more solvable). We hope nothing important is destroyed in this process.
I can see from an Austrian perspective that Krugman is wrong to say that r = MPK but I don’t see what is wrong (in the context of this discussion) with saying that if the x-axis is the $ value of all capital and the y axis is the rate of return on capital that you can multiply the two to get a dollar value for the return on capital.
I can’t quite see why that would be GDP but that’s a different issue.
Actually I think once you stop seeing the curve as MPK it stop being GDP- so I may be agreeing whit Bob.
Yeah I think you’ve got it, Transformer. If you want to make it GDP, then you have to be thinking of it as physical capital goods. Like, tractor-hours that produce 100 units of wheat in Unit 1, 80 units of wheat in Unit 2, etc. But then you can’t make sense of the y-axis being a percentage.
On the other hand, if you want to make it coherent that the y-axis is a percentage, then you can’t think of the capital as physical things, but rather as bursts of money. But then the GDP interpretation makes no sense.
I’m assuming I was unclear on this one, since I am getting really sharp people arguing with me heatedly on email. But I think my underlying critique is solid, I just should’ve been clearer.
Of course you can make sense of the y-axis being a percentage. If one machine produces 8 widgets a year, and if it takes 100 widgets to make a machine, then the MPK is 8 widgets per machine per year, which we express as 8%. Or more generally, if one machine makes enough widgets per year to trade for 8 gadgets at the going price ratio, and if it takes 100 gadgets to make a machine, then the MPK is 8 gadgets per year, which we express as 8%.
None of this has anything to do with time. It has to do only with physical processes taking place in the present. You’ve got a machine. It produces stuff that can be used to make more machines (either directly or by trade). In a given period of time, one machine produces enough stuff to build x% of a machine. That defines the MPK with **no reference** to time (also with no reference to money, contra to what somebody on tne Mises site is saying).
This all seems perfectly clear and I don’t understand the problem.
In particular: One tractor produces 100 units of wheat, it takes 1000 units of wheat to make a tractor (or to trade for a tractor); the MPK is 10%.
One tractor produces 100 units of wheat per annum.
The MPK is 10% per annum.
Those 100 units of wheat were not produced instantaneously.
Tel: Yes, absolutely. Thank you for the correction.
The problem I see is this:
There are probably other ways of producing tractors that will allow you to produce a greater volume of wheat per unit of input. But these other ways will take longer to actually get the wheat.
Example: You could build a tractor in 100 labor hours that produces 1000 units of wheat, or a better tractor in 200 labor hours that produces 2200 unit of wheat.
Which one you choose depends on whether at the point you start production you value 1000 units in 100 hours over 2200 units in 200 hours.
It is likely that across the economy as a whole there is an infinite number of possible capital structures the one that will emerge will be the be that reflects the productivity/waiting time preferences of the participants. The price structure will adjust to provide the incentives to produce the right goods for this optimal capital structure.
It will be impossible from these relative prices to come up with a meaningful ratio that could be called the MPK as the ratio of capital goods prices to output prices reflect the incentives to own these capital goods, and have nothing to do with physical outputs.
So in the widget example the prices and output levels of widgets and machines would adjust so the money rate of return on a widget machine would be the same as other capital goods in the economy.
Most situations you find there are multiple factors of production and investing too much in any one factor results in diminishing marginal returns.
Therefore as the capitalist keeps putting investment money into one particular factor, the productivity is not a constant rate, but instead it sweeps along a nonlinear curve and the productivity goes down until it isn’t worth investing any more. That equilibrium point should, in theory, be just tangential to the prevailing indifference curve (which in this case is the time preference of savings).
Therefore, we would expect the physical productivity of each factor to equal time preference — but there’s prices involved as well and they also adjust. Thus, investment in a lot of tractors will tend to drive DOWN the grain price, and drive UP the price of fuel, tyres, and mechanical repairs, which in turn makes every tractor appear less productive (in terms of dollar value ROI) even though physically none of the tractors have changed at all. With those prices taken into account you will be seeing even more nonlinear diminishing marginal returns, allowing the physical system to converge with time preferences quite rapidly.
Tractor-hours and “bursts of money” are interchangeable. The value to the investor of a tractor-hour depends which unit it is (because the product varies). But the price he pays for it does not (vary in the same way). The price he pays per tractor-hour is a (more or less) fixed sum determined by the interest rate discounted present value of the marginal product of the next highest use in the broader market. The difference between the value and the price is the reason for making the investment. If enough units are bought to bring value and price together then investment ceases.
Craig wrote: “Tractor-hours and “bursts of money” are interchangeable.”
Well they are in some ways, but not in others. You can’t use bursts of money directly to harvest more crops.
Actually if you click the James Galbraith link at the end of my post, you’ll see him spell it out. (Of course I don’t endorse everywhere he goes in the discussion, but his focus on the physical/monetary distinction is the same as mine.)
From Galbraith link summarizing the Cambridge Capital Controversy: “Third, a more subtle point: as the rate of interest falls, there is no systematic tendency to adopt a more “capital-intensive” technology, as the neoclassical model supposed.”
So, given the the above here is what I’d like to ask of Dr. Murphy or anyone who might favor me with a response.
If an existing firm is realizing an existing rate of profit that is partially taxed would that firm respond to a reduction in its tax rate by increasing output and capital investment? Or do you believe there is no reason to suppose that it so?
If you do believe an individual firm would respond to tax relief by increasing capital and output do you also believe that all firms would behave similarly?
If all firms would behave similarly why wouldn’t the Krugman-Landsberg MPK diagram be a meaningful representation of that result?
No way to predict the outcome in the general case; even in a particular case it’s a question of psychology as much as economics.
Reducing costs, either by reducing taxation or by technological innovation, does provide an incentive to increase output and investment. This is only one of many factors that will go into the decision. With taxes in particular, the obvious question will be how long the tax cut will last, and how long until a replacement tax is levied. If the businessmen think the tax cut will be effectively removed before the new investment starts producing revenue, they’re likely to just sit on the extra income, or pay dividends. Even if they think the tax cuts will last long enough, they have to believe there would be sufficient demand at the lower price to maximize their profits. On the other side of the coin, the increased capital investment would have to yield a sufficiently large increase in output to justify the additional expense. For example, incremental expansion of a factory is often impossible. If the taxes were lower the whole way through, the company might have built a larger factory, but once the factory is built, the fixed costs for remodeling are often high enough that the expansion won’t pay for itself in a reasonable length of time.
Another reason you can’t expect to measure the impact of tax cuts as increased output is because they might make the output stay steady, or decrease slightly, instead of decreasing sharply. If a business has ceased being profitable, or if the owners think it will shortly cease being profitable, the odds are very high that that business will drastically cut output. If, before the output is cut, a tax break comes down, it may resolve the issue, leading to little or no change in output. This, of course, will not be detected in any gross statistics.
Regarding Steve’s ‘Of course you can make sense of the y-axis being a percentage. If one machine produces 8 widgets a year, and if it takes 100 widgets to make a machine, then the MPK is 8 widgets per machine per year, which we express as 8%.’
I can see how MPK is 8 (that the number of additional widgets you get if you add a machine and hold everything else constant. But why is this 8%? Surely to calculate the return on capital you also have to include labor and other inputs not just the widgets ? To do this you have to introduce a unit of value (such as dollars) so I don’t see how money can be kept out of the discussion.
The MPK by definition holds other inputs fixed.
yes, I agree the MPK is 8. Probably I am misunderstanding but its when you say that is 8% that I get confused. Sure , its 8% of the total widgets used in a machine but that seem meaningless as a return on capital if other inputs are used as well.
For example a widget machine has a MPK of 8 widgets (with a value of $1 each), but it costs $200 ($100 of which is attributed to the 100 widgets used in it construction and $100 to labor and other stuff). Is the return on that machine 8% or 4% ?
Perhaps you mean “it takes inputs equal to the value of 100 widgets to make a machine”. Then I see where the 8% comes from, but then that would make the ‘no reference to money’ claim invalid as far as I can see.
Currently we have 100 machines, we work 100 hours a week, and we produce 1000 widgets a week. The assumption is that if we have 101 machines and work the same 100 hours, we can produce (at our option) either 1008 widgets or 1000 widgets plus 8% of a machine. The meaning of “it takes 100 widgets to make a machine” is that by doing this for several weeks in a row, we get to choose between one new machine and 100 extra widgets. As for your question, I’m not sure what you mean by the word “return”, but all of the assumptions are spelled out so that whatever “return” means to you, you ought go be able to calculate it.
Thanks. I know you are probably busy and have better things to do than answer my stupid questions but if you have some time:
By “return” I meant the same as “rate of return” on the chart in your post on the matter from a week or so ago and that when you say MPK is 8% that will correlate to rate of return at the relevant points on the curve.
Regarding: ‘The meaning of “it takes 100 widgets to make a machine” is that by doing this for several weeks in a row, we get to choose between one new machine and 100 extra widgets’.
So after those several weeks you have a pile of 100 widgets. If you can barter them for a new machine then it makes sense to say (given our assumptions) “the rate of return (in a situation where it equals MPK) on a machine is 8% measured in widgets”.
But if the 100 widgets have to be combined with labor and other stuff to actually produce a machine then the statement: “the rate of return (or MPK) on a machine is 8%” does not make sense.
The reason I am interested in this is that as someone who has learned economics mostly by reading Austrian text books I am trying to get my head around the view that return on capital is somehow related to its physical output (which is what I take you to be describing?) and not time preference (as Austrian text books tend to conclude).
Actually, I see I didn’t read your first sentence carefully enough – I think that explains what I was missing.
Okay, I think you’ve largely got it. Just for further clarification: It does not make a bit of difference whether you produce (over 12 and a half weeks) 100 widgets that can be traded for a machine, or whether you just directly produce the machine. All that matters is that adding one more machine (without adding any additional labor) allows you, each week, to produce *either* 8 more widgets that can be traded for 8% of a machine OR literally 8% of a machine. Either way,the MPK is, by definition, 8% per week.
In equilibiriium, the MPK has to be the same in all industries, and in equilibrium it has to equal the (after-tax) interest rate.
Steve, just to give you a flavor of the kind of thing I worry about–when moving from a simple one-good model like Solow’s to a more general framework–consider the following statement you made:
In equilibirium, the MPK has to be the same in all industries, and in equilibrium it has to equal the (after-tax) interest rate.
Imagine an economy with N different types of capital goods and N different consumption goods, and where, for each consumption good, there is one and only one machine that helps labor to produce it. Furthermore, each machine can make more of itself (but no other machine).
You can pick an appropriately weighted basket of consumer goods, and then define the real interest rate as the premium on that basket at t compared to the basket delivered at t+1.
But in general, your condition will not be possible to fulfill, if we are thinking in physical terms. Maybe machine 1 can make either 3 apples or 8% of another machine 1, while machine 2 can make either 8 bananas or another 13% of machine 2, etc. If we define “MPK” in monetary terms it all works out, but it won’t in physical terms. What has to happen for equilibrium is that the spot prices of apples versus bananas change over time.
So I’m not saying your statement is wrong per se, but I think most economists believe it means a certain thing when in fact it only holds for a weaker condition.
And yes….the MPK is defined in terms of physical output. The relation to time preference is an equilibrium condition, not part of the definition.
Thanks a lot for the clarification.
In this case the same machine can be used
either for making widgets or making widget-making machines. So its pretty easy to see the ratio of widgets to machines (and even when widgets are traded for machines the same ratio holds.)
But what if no widgets are used in machine production and totally different machines are used to produce machines versus producing widgets? You can still say “we have a choice of adding one more unit of capital and producing either 8 widgets or 8% of a machine” but in this case you are choosing a different unit of capital rather than just a different type of output.
Can this complication be handled in the “physical output” MPK story (for example by specifying that both type of capital goods contain the same qty of labor) ?
Transformer, make sure you read my comment to Steve on this stuff. I think I’m echoing your concerns.
It was my first thought that Steve’s machine that can produce either a certain type of good or itself (using the produced good as an input) was a sophisticated version of the single good models where everyone seems to agree that the “physical output” MPK story holds.
But I am sure Steve’s thinks it holds beyond that so I look forward to his reply to your (or my) comment.
I do sort of think I see how in your model of ‘N different types of capital goods and N different consumption goods, and where, for each consumption good, there is one and only one machine that helps labor to produce it’ and where MPK in physical terms can be calculated like Steve describes then it might be possible to set the production levels of all the goods so that the physical ratios are the same for all good – but I’m still trying to think that through.
When you introduce more mix-and-match types of capital goods and break the circular link between capital goods and the goods they produce it becomes really, really hard to see how “physical output” MPK story holds – but that might just be because its really, really complicated!.
Short proof: If MPK is a physical thing, and in a unit time machine A can produce 10% of machine A while machine B can produce 15% of machine B, then it can’t possibly be true that the rate of interest equals the MPK.
But is the return on A and B fixed at 10% and 15% no matter what the mix of capital to other inputs is? Won’t it vary as more units of capital are applied ?
In Steve’s example an addition of one machine adds 8 widgets and 8% of a machine to total output. But the next unit might add a different number of widgets and a different % of a machine to total output.
While I don’t necessarily see why MPK will decline with output (which may be an issue) I don’t see why there can’t in principal be levels of capital applied to A and B (holding steady other inputs ) that will equalize MPK between them.
Yes Bob is attempting to dodge two things: firstly diminishing marginal returns, which is to say Bob is presuming a fixed rate of return and in practice that doesn’t happen.
Secondly, Bob is ignoring the marketplace where if machine A and machine B were offered for sale side by side, everyone would buy machine B and we would not even be talking about machine A because no one wanted to invest in that. Seriously, who would invest at a 10% return when right next door they are offering 15% ? What would you do?
At least, they would all buy machine B, up until those diminishing marginal returns started kicking in, and it wasn’t delivering 15% anymore.
#1: In Steve’s example, he didn’t talk about a diminishing rate of return. He talked about 8% of a machine and how that related in equilibrium. So I’m pointing out that it would be an interesting fact of engineering if you could get the technical rate of capital good reproduction IN PHYSICAL TERMS to be identical across millions of different capital goods worldwide.
#2: Tel you completely miss the point about physical goods versus market prices. I’m glad you are illustrating the danger in thinking like this. Look, if I buy a flock of sheep, it will multiply every year. If I buy a gold mine, it just keeps shrinking. So did I just prove nobody in his right mind would ever buy a gold mine, when he has a flock of sheep available for purchase?
Steve aid ‘Currently we have 100 machines, we work 100 hours a week, and we produce 1000 widgets a week. The assumption is that if we have 101 machines and work the same 100 hours, we can produce (at our option) either 1008 widgets or 1000 widgets plus 8% of a machine.’
Isn’t there an implicit rate of diminishing returns in that ?
So I see no reason in principal why you couldn’t get the technical rate of capital good reproduction IN PHYSICAL TERMS to be identical across millions of different capital goods worldwide.as long as they had the attributes of Steve’s widgets/widgets machines.
Transformer wrote:
So I see no reason in principal why you couldn’t get the technical rate of capital good reproduction IN PHYSICAL TERMS to be identical across millions of different capital goods worldwide.as long as they had the attributes of Steve’s widgets/widgets machines.
And you also think it would line up perfectly, so that the amount of consumer goods we wanted from each of these millions of different options was optimal too?
E.g. right now, you think we have the exact number of hammers, drill presses, backhoe loaders, 18-wheelers, telescopes, MRI machines, etc. etc., so that one more hammer can produce x% more hammers, and one more backhoe loader produces x% more backhoe loaders, etc. etc., across all industries? And it all works out that this optimal amount also balances out with our subjective preferences to line up with how much carpentry we want performed, how many ditches need to be dug, how much stuff needs to be shipped by truck, how many stars we want to look at, …?
Again, if you are thinking of MPK as “the market value of the stuff we’re producing” then of course it works out. But it seems when people stress “physical output” that they mean in terms of physical things. So to your question, no, I think it is inconceivable that that would all happen to work out.
What would happen if aliens gave us a machine and people didn’t know how to make more? Would the financial markets blow up? No. And yet the rate of return in investing in that alien machine would equal the risk-adjusted rate of return on investments in terrestrial machines.
I was half trolling people with my latest post about cryptocurrencies. Do you see my point in that context?
To be clear: I’m not endorsing the physical productivity theory of the interest rate – I’m just trying to explain my interpretation of Steve’s simple model.
I do not think in the real world all (or probably any) goods are like Steve’s widgets so I agree with you.
OK, I should more correctly have said BOTH Steve Landsburg AND Bob Murphy have been dodging the issue of diminishing returns. There you go, I’m an equal opportunity heckler and I apologize for my earlier failure to adequately spread the blame around.
This is longer than it should be, I’m taking over from Major Freedom (presumably he finally got hired or something).
But there’s two layers to it (mentioned already above): the physical layer and the money/price layer. BOTH of those layers independently point towards diminishing returns. When you put them together you get even stronger diminishing returns because one multiplies by the other.
You can understand I’m a tiny bit frustrated here, because last month you were praising “MRUniversity: The Solow Model and the Steady State” wherein they declared the IRON LAW of diminishing returns. Iron is the most unbreakable thing known to man. I mean, once we start building laws out of iron, I simply have no choice but to step in and prevent you attempting to break that… you could hurt your hand or something. This is for your own good!!
In all seriousness though, let’s look at the physical layer first. If you buy a flock of sheep do you intend to put them out on your balcony? You probably need some land, you also better make sure that land has plenty of grass, so the sheep have food, they will need water too so you want a dam, also fences, maybe some dogs, a gun in case there are wolves out there. Since you cannot use the sheep as-is you also need additional factors like a shearing shed it you want wool. You need a slaughterhouse and a butcher if you want meat. The wool isn’t much use either you need to spin it into yarn, then knit socks and jumpers… all of these require skilled labour, and suitable tools. The meat requires cooking, which needs a kitchen and fuel.
You find yourself in the “I Pencil” situation where everything rapidly links to everything else.
So the answer is, NO absolutely those sheep will not simply multiply every year. The world does not work like that. The growth will rapidly be curtailed unless you cater to a surprisingly complex web of additional factors. The sheep could eat the grass down to the roots, the land will be overgrazed, next big rain washes away your topsoil and leaves you with a slab of rock so the grass never comes back. Soon you have no sheep and worthless land because you poorly managed it.
But, let’s go ahead and look at the money/price layer. Let’s totally ignore the entire physical world, skip right past all the farmer’s woes and allow you to go back to square one where you were putting the flock of sheep out on your balcony, and they somehow produce more sheep.
Not only do you have all the sheep you can use for yourself, but you can sell and exchange sheep for whatever else you want. OK… run with that… pretty soon other people will also have sheep on their balconies too, the numbers of sheep will go up and up.
The market supply of sheep will exponentially grow and outstrip demand for sheep; besides almost everyone already has them, and there’s only so many things you can do with sheep, so there isn’t a whole lot of demand for sheep any more.
The market price of sheep will fall. Egats! Now you no longer get the same price you used to get, so when it comes to exchange you have to exchange more sheep for less of whatever else you want.
The price system is adjusting here (i.e. negative feedback) and imposing diminishing returns in an economic sense. If you were exchanging sheep for gold then you discover that the price of gold (as measured in sheep) keeps going UP. Hey, gold is making an economic return. The price system is forcing that to happen. Since there are some situations in the physical world where you really need gold, and just cannot substitute a sheep; when people discover sheep are very easy to get, so all of the jobs that require sheep are done now, the people will focus their efforts on the remaining jobs that require gold. Suddenly the guy who purchased the gold mine is making a good return, because of the price system imposing a penalty on sheep.
So both the physical layer, and the money/price layer are working against this concept of a simple fixed rate growth model… but that’s no accident because the money/price layer is doing the task of coordinating the complex multidimensional structure of the physical layer. The two layers are tied together by supply and demand. That’s the mechanism by which the ultimate decision maker (i.e. consumer preferences) imposes itself on that physical world of economic production.
Look at it another way… if we believe that the world works like a fixed growth rate where you just own capital and it grows, then people like Thomas Piketty and his socialist buddies would be 100% correct. The socialist calculation problem would be solved very quickly — you have capital and it grows. Voila! No problem optimizing multiple factors, no coordination to worry about, just stand back and let it grow. That would be a zero sum world… but it’s all wrong. Mathematically such a world might conceptually exist, but we don’t live in that world.
The main point of capital it to increase labor productivity. To take Steve’s example ‘If one machine produces 8 widgets a year, and if it takes 100 widgets to make a machine’ then the only point of doing using these machines (assuming the machines were only used for widget making) would be to get more net widgets from the total labor used on machines + widgets than if widgets were made with no machines.
So capital allows more or better stuff to be produced than without capital, but if all one got back for owning and renting capital goods was the price you paid for them there would be no incentive to own capital goods. Therefore the return on capital has got to be rate of return that motivates people to hold the existing capital stock. And as it quite possible that purely subjective changes in the way people feel about holding capital can cause the required rate of return to vary totally independently of the productivity of capital itself I do not see how it can be equal to MPK.
Yes, completely agree, and that’s where the time preference will control the point at which people just give up investing in more capital and decide to consume instead.
No, because the incentive will push it toward equality. Suppose I have a capital project that can earn much better than your time preference, would you invest in that? Sure you would.
Thus, the subjective way people feel about holding capital is what decides whether the capital gets built in the first place. All of those capital items that don’t achieve the return that investors are looking for, also don’t get built and therefore don’t exist (other than one or two trial attempts abandoned after the entrepreneurial error is realized).
Bob, I’ve been thinking about this business of self-referential asset valuation. Here’s the example I came up with:
You are a factory manager and the accounting team wants you to list the factory assets for the annual report for the stock holders. So you make some notes:
* 1/2 Acre of land.
* 1 Steel shed (large).
* 582 lineal yards of aluminum pipe.
* 130 pounds of ball bearings.
* 5 drill presses.
* 4 welders.
* 2 long work benches.
* 27 hand tools (various).
The accountant says, “No you idiot, we need to add them all up!”
So you point out actually it’s mathematically impossible to sum a lineal yard of aluminum pipe with a pound of ball bearings. So the accountant explains that by using prices, all the items can be converted to dollars and then we add the dollars to get a total, and stick that in the annual report.
Fine. So where do those prices come from? Well… you could use the prices you paid for everything, and then apply some kind of depreciation schedule based on typical estimate of age. In the USA that’s known as the “historical-cost principle” of asset accounting, and obviously any economist would see that’s going to give a wrong answer. But it does have some useful properties… companies need to figure out their profits, and the cost you paid for the asset is the cost that will need to be accounted for when it comes to calculating those profits. Also, the standardized depreciation schedules are helpful for providing some kind of consistency when it comes to taxation.
You don’t like the problem that these costs tend to be unrelated to market prices? Besides, some assets don’t depreciate at all (e.g. the land) and anyway, standardization makes no sense when each business is unique. OK, I offer to you “mark to market” accounting. Ta Da!
So with “mark to market” we take each asset and figure out what it would be worth if sold at auction. Maybe you paid $3000 for the drill press 5 years ago but recent Chinese imports mean you can buy a roughly equivalent drill press at $500 today, so although your press is not significantly damaged it still won’t get much of a second hand resale price. Banks in particular very much like the “mark to market” idea when they own the title deeds to land as security on mortgages, and the land prices often go up, because “mark to market” means they can claim strong collateral to back all their loans, therefore low risk you see. The slight problem being that market value in real estate is itself determined by bank lending which in turn is determined by the bank balance sheet and strength of their collateral. Hmmm, almost like the thing we are measuring is being measured with reference to itself.
Oh did I mention that the banks quietly suspended any “mark to market” valuations when they saw the possibility of real estate going DOWN in value? Yes, they really changed accounting rules mid stream in order to get the answer that suited them. Who does that?
I should point out that you cannot use your method of accumulating all future returns on a given factory asset then applying a discount to present value. It won’t work because you do not know the specific return that comes from drilling a hole in an aluminum pipe (because there is no market for a pipe with one hole drilled in it), you only know the market value of the finished product (resulting from many operations). For that matter, you don’t actually know how many holes that drill press can drill, but perhaps you can average it out. If you really were to auction the drill press then the buyers would be a bit conservative and offer you a low-ball price even when you know it’s worth more… auctions are like that.
So what’s the point of this example? Accountants regularly use dodgy asset valuations, but they do the best they can. There isn’t actually a neat answer to this.
We regularly run into arguments over what counts as an asset. For example, in a normal business the cost of labour is considered an expense, isn’t it? Thus the cost of labour is subtracted off before profits are calculated (i.e. labour is normally a tax write off).
But in the oil industry it takes a lot of labour to drill an oil well, and once drilled you have a capital asset. By gum, they have figured out a way of converting labour into capital… we cannot let them just get a tax write off when they are converting labour into capital. That would be dreadful! We must count that labour as capital, surely.
What if the oil well turns out to be no good? Then it becomes an “intangible drilling cost” and it has no capital value so labour turns into an expense once more (but the various Green groups will not call it a subsidy to the oil industry). All very strange.
Gosh, I hope these guys never start to look at labour in the software industry. Could get ugly.
Let’s look at the stock market and we have some notions such as “Market Capitalization” and “Price/Earnings Ratio”. So the Market Cap is kind of an asset price as determined by the market, except that it changes regularly as the share price changes (even without any physical asset in the corporation changing) and none of the market participants really believe that the Market Cap is what you would get it you attempted to sell all the shares in the company (because the price would crash). Then there’s “Price/Earnings Ratio” (units are Years) which is kind of the reciprocal of a rate of return (units 1/Years) … but some types of shares keep a steady price and pay regular dividends, while other types of shares just go up in capital value but never pay dividends. Which is real capital, and which is real return?!?
You see the sort of problems, and that’s just in the private sphere. We haven’t even started attempting macroeconomics yet.
Bob, you twisted my brain all inside and out for this one, but at the end of it, I think you’re right. The key is what you say at the end:
Krugman’s diagram is solely a graph of MPK. In other words, we only get to see how MPK changes for the k-th unit of capital in response to a given change in r. What we cannot see from Krugman’s graph is a situation in which r changes but K — the total stock of capital — does not change. In other words, we can’t see what happens to output when we “independently vary” r and hold K constant, just like you said.
Now, I understand why there are reasons we might skip over this part, e.g. there are long-run effects on K and r as they interact with the international markets. I think Nick Rowe’s post covers this, but as usual I found his explanation really hard to follow and I feel like he’s making me do all the thinking on my own, without his help. I couldn’t really understand his post until after I had understood your point, Bob.
So which is the better approach? Probably the two of you needed to co-author one! I needed both posts to grok the issue!
Thanks for the feedback RPLong.