11 Nov 2017

## A Machine Puzzle (3 of 3)

Earlier I asked how it could be possible that one cryptocurrency appreciated at 10% a year while another appreciated at 20%, and several people in the comments correctly said that the dollar-price of a coin could adjust accordingly. So the rate of return *measured in dollars* for the two different cryptocoins could be equal, even though one of them grew at twice the rate of the other.

Then I asked how it could be possible for US Treasuries to yield 2% while Japanese government bonds yielded -0.1%. Nobody officially gave the right answer. The answer is that the purchasing power of the USD and the Japanese yen are changing at different rates, so that the exchange rate between the USD and the yen is changing over time. In a simple model where you hold a bunch of other stuff equal, “no-arbitrage” requires that differences in nominal interest rates are explained by counterbalancing expected changes in the exchange rate. So again, the return *measured in dollars* to an American investor is the same, whether he buys Treasuries or Japanese bonds, even though one bond grows at 2% while the other shrinks at 0.1%.

Finally, for our present post: Suppose Machine A can be used to make 10% of itself per period, while Machine B can be used to make 20% of itself per period. Is this possible in equilibrium? Wouldn’t investors dump Machine A and buy up Machine B, until the rates of return were equal?

But as we should realize by now, this way of thinking is faulty, which demonstrated the danger in reasoning from a physical conception.

Because the price of Machine A (and its products, like apples) can change relative to the price of Machine B (and its product, bananas) over time, the rate of return to investors *measured in dollars* can be equal, even though Machine A can make 10% of another Machine A while Machine B can make 20% of another Machine B.

NOTE: There might be more we can deduce about equilibrium conditions in a steady state, but the mere condition of “no-arbitrage” doesn’t pin things down as much as some of you were suggesting in the comments. And I’m not picking on the people who chimed in here on the comments; I think 95% of professional economists would have been falling into the same traps, because they use one-good models as their workhorses in this arena.

#### 44 Responses to “A Machine Puzzle (3 of 3)”

1. Tel says:

The answer is that the purchasing power of the USD and the Japanese yen are changing at different rates, so that the exchange rate between the USD and the yen is changing over time. In a simple model where you hold a bunch of other stuff equal, “no-arbitrage” requires that differences in nominal interest rates are explained by counterbalancing expected changes in the exchange rate.

It’s a nice neat answer with only one small problem that it does not fit the facts. At every stage during the last 10 years, the rate on US government bonds has been significantly higher than Japanese government bonds. Usually double or triple the rate. For this to be explained by exchange rate would require a steadily climbing JPY which did exist before 2011, but after that the Yen got whacked back down again… by Abe-san and his QE money printing.

http://www.xe.com/currencycharts/?from=JPY&to=USD&view=10Y

So if Japanese investors in 2011 had purchased US government bonds they would have made interest on the bonds PLUS also made gains on the exchange rate. However the Bank of Japan is not behaving like a regular investor, they are operating as a political entity. The other big institutional holders of Japanese government bonds are forced to hold them and cannot attempt to sell. This is not a normal market.

2. Tel says:

Because the price of Machine A (and its products, like apples) can change relative to the price of Machine B (and its product, bananas) over time, the rate of return to investors *measured in dollars* can be equal, even though Machine A can make 10% of another Machine A while Machine B can make 20% of another Machine B.

Of course prices can adjust. I’m pretty sure no one said otherwise. If I ever said that prices cannot adjust then I apologize sincerely.

Let’s get back to the original beef which is from your article:

No Murphy, there isn’t a math problem here. Because there are heterogeneous capital goods in the economy, we aggregate them in terms of money-prices, the only sensible thing. (You can’t add up drill presses and hammers to get a single number.) So the units of the x-axis are actually dollars, meaning that when you multiply the vertical y-axis height by the horizontal x-axis width, the dimension of the product is actually a percentage-times-dollars, meaning dollars are what you end up with.

Right, so from a units perspective, if you want to convert heterogeneous capital into dollars then you need a bunch of prices. Totally agree, prices are unavoidable when dealing with capital, and the only question is where those prices come from and how the prices adjust in practice.

But now look at how that price adjustment mechanism typically operates: if bananas are very easy to grow, and apples are much more difficult to grow, and if consumer preference is such that they prefer an equal mix of bananas and apples then prices will gradually tend to reflect that; so the price of apples relative to bananas will go up. Eventually it will balance out until investment in planting bananas gives you about the same return as investment in planting apples. On top of that, unavoidably there are physical factors involved in as much as some land is better for bananas, some land is better for apples, and water, fertilizer, labour to pick and pack, etc, etc.

Thus, once you have allowed for both physical limitations on growth and price adjustment on top of that, you still come back to diminishing marginal returns in the sense of the rate of dollars returned for the rate of dollars invested.

• Bob Murphy says:

Tel wrote:

Of course prices can adjust. I’m pretty sure no one said otherwise. If I ever said that prices cannot adjust then I apologize sincerely.

Tel, this is kind of frustrating when you don’t even remember what you wrote, and when I literally linked to what you wrote in this very post. The part where I said above in the post “But as we should realize by now, this way of thinking is faulty…” and gave a link, takes you right to where you were lecturing me on how an investor would always put his money in Machine B if it could make more copies of itself per unit time.

You don’t need to apologize, but you need to admit that I’m not attacking a strawman. It was your comment there that made me do these last 3 posts.

And FWIW, a new guy just chimed in on the cryptocurrency post, to say only an idiot would invest in the currency that grows at 10%. So again, this isn’t a strawman I’m attacking. You and other people explicitly denied that this could be possible in equilibrium.

• Tel says:

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.

Then Transformer pointed out that although you can come up with an abstract mathematical model of simple exponential growth at fixed return, in the sense that economics is applied mathematics, such a model is physically unrealistic. So he said this:

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 ?

And I barged in, furiously agreeing with the Transformer, to say that you have dodged the issue of diminishing marginal returns in your “short proof”. That is to say, diminishing marginal returns at the physical level. None of the three of us brought up the topic of prices. Here’s what I started with:

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.

Then I started talking about whether people would want machine A or machine B if they were offered for sale:

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.

OK, so I did not start talking about prices there (perhaps I should have but that would have gone to rambling again), and yes those prices would be influential if there’s some sliding exchange rate between machine A and machine B. I was silently presuming that A and B were interchangeable for the consumer, so in terms of whatever you use these machines for it doesn’t matter which one you end up with. Let’s suppose they are general purpose machines. All things being equal, if there is no outside reason to pick A or B and either machine would do the job of the other machine, then you would always pick the one with the greater physical growth rate.

But later on when I was called on the question of prices and exchange rates, I pointed out that the shifting prices will also impose diminishing marginal returns at the economic level. Even though you can have a gold bar which has a physical productivity locked at zero, despite that from an economic standpoint the capital gain on the gold is the result of adjusting prices.

So there’s two things happening at once: physical returns are nonlinear and in most cases you can think of will be the result of many factors such that over-investment gives a physical diminishing marginal return… and also the second thing is that shifting prices and downward sloping demand curves impose a second round of diminishing economic returns. Thus, the very efficient producer who discovers a way to deliver large amounts of product into the market at low cost of production will also sate demand for his own product and thus eat into the profit margin. Monopoly producers are aware of this so they throttle supply, but that gives incentive for a competitor to jump in.

3. baconbacon says:

The simple answer is that Tel is correct, these things aren’t free flowing markets in any sense and there are all sorts of other issues at play*.

So while Bob Murphy’s answer is correct, it is correct in the same way a test question about the economics of how weapons are traded in a video game are correct, an exercise that isn’t particularly illuminating. CBs are acting as market makers on both sides of the equation now, setting the price of bonds and also setting the cost of borrowing for private institutions.

* (iirc) for a while at least the Postal Service in Japan held savings accounts where all the money deposited was invested into Government bonds, but holders of those accounts (up to certain amounts) were guaranteed a return that was higher than the return on the bonds themselves. Long story short the government made up the difference, but those payments were classified differently, so the “interest rate” on the bonds was different from the cost to the government.

• Bob Murphy says:

baconbacon wrote:

The simple answer is that Tel is correct, these things aren’t free flowing markets in any sense and there are all sorts of other issues at play*

Wow this is painful trying to make basic points on this blog. OK guys, suppose I picked the German government, the Japanese government, and the US government circa 2004, before all the QE stuff. Are you saying their bond yields were literally identical? No, and one of the reasons they don’t have to be identical is that people expect the exchange rates to move.

Yes there are other things moving too, but when I have Tel lecturing me in the other post about why physical rates of reproduction on machines are all you need to know for investment purposes, I have to start with really basic counterexamples.

• Tel says:

How about German government bonds in 1922 ?

That was all clean and kosher… nothing weird going on back in those days.

• Bob Murphy says:

Tel wrote:

How about German government bonds in 1922 ?

That was all clean and kosher… nothing weird going on back in those days.

Again, this is very ironic Tel, and I would encourage you to consider the possibility that you are missing something here. I literally wrote my dissertation on this stuff. It’s just possible that if you drop the sarcasm you will see you have been partially saying some erroneous things in our exchanges.

For example, above you seem to think that the German hyperinflation would show how right your analysis on the bond market is, in contrast to my Ivory Tower focus on one particular element. But no, Weimar Germany is a great illustration of the point I was making. Nominal interest rates on German bonds during those years would have been sky-high. So someone who thought, “Investors would obviously buy the thing yielded 15% rather than the thing yielding 10%” would get killed in that environment.

How could it be that the German bonds would yield (say) 10,000% while the US bonds would yield (say) 2%? Because the mark was depreciating against the dollar.

So far from showing how out-of-touch my analysis was, you actually picked a beautiful illustration of it.

• Tel says:

I looked into that, and surprisingly there are examples of bonds from the era with rather low rates of return (see link below). My German is pretty sketchy but I think the coupon rate on this example is a pathetic 4% (two coupons per year, each at 2%) and that was issued early 1922 when estimated of price inflation were already around 10%. Maybe someone else knows how to read these things better than I do.

https://assets.documentcloud.org/documents/351965/german-bond-three.pdf

Of course coupon rate is not the whole story, perhaps those certificates sold at substantial discount. I cannot find any site that gives market rates for the time but governments usually try to avoid selling bonds at heavy discounts because that in itself is often seen as a sign of panic.

As it turned out, the owner of that particular bond certificate later decided not to even cash them in (this example was found in a buried safe) or perhaps the owner intended to come back and cash them in but was unable to return. I rather think people were buying these things out of a belief that the situation would return to normal, possibly even the low coupon rates helped impose a sense of normalcy to comfort people.

Crazy days… far from equilibrium conditions!

• Tel says:

Tel lecturing me in the other post about why physical rates of reproduction on machines are all you need to know for investment purposes

I so totally didn’t say that.

What I said was you can’t dodge the issue of diminishing marginal returns, and any example that presumes a fixed rate of return on capital (be that either at the physical level, or the economic level where prices are allowed to adjust) is a weak and unrealistic example.

• RPLong says:

There is about a 50-50 chance that I don’t understand the issue fully, so please be gentle with me…

I read Bob’s and Nick Rowe’s posts several times before I could finally understand where they were going with things. I don’t think either of them were using an example that assumed “a fixed rate of return.”

I believe a lot of the confusion comes from the fact that the graph is a graph of MPK, rather than a graph of PK. Thus, the y-axis shows us the rate of return on the k-th unit of capital, not the total return on a particular capital investment. If you’re on-board with the typical economic treatment of capital, then shouldn’t you also be on-board with the fact that the k-th unit of capital does indeed have a constant rate of return, even though the (k+1)–th unit of capital has a different, but also constant, rate of return?

Here’s what i *THINK*, and I might be wrong, but from what I can tell, Bob and Nick are making a point about how capital is valuated, i.e. that you can’t look at the MPK graph, think through all its implications, and come to accurate statements about the value of (total, not marginal) capital unless you back up and relate those things back to K and not just MPK.

It’s sort of like how in the classic microeconomic model of the monopolistic firm, we have to graph average cost, total cost, marginal cost, total revenue, and marginal revenue all on the same two axes before we get the whole picture. The problem here is that you can’t really put the total capital graph on the same axes you use for the MPK graph.

That’s where I think the confusion is coming from. Am I wrong?

• Tel says:

At least based on Krugman’s article and my understanding of that particular graph this was always about MPK. Firstly it says “MPK” on the graph itself, but also Krugman’s explanation happens to be quite clear:

Then we can represent the economy with Figure 1, which has the stock of capital on the horizontal axis and the rate of return on capital on the vertical axis. The curve MPK is the marginal product of capital, diminishing in the quantity of capital because of the fixed labor force. The area under MPK – the integral of the marginal products of successive units of capital – is the economy’s real GDP, its total output.

So Krugman not only presumes that a diminishing marginal product of capital, but he spells it out in his explanation. Of course, because Krugman is always about macro, everything is aggregated (GDP is an aggregate, and K is an aggregate) and always in dollars… so by implication a bunch of prices exist in there which Krugman doesn’t explicitly talk about. Those prices are what converts a motley crew of physical units into uniform dollars. Prices (by definition) can convert anything into currency and converts currency back into everything else.

Yes those prices can change over time, thus K measured in dollar terms might shift in ways that are unrelated to any physical capital… macro guys tend to presume that averages out, or they can adjust for it. Doesn’t seem to disturb them.

So I should point out that Krugman throws up the graph as his explanation of the free market argument that he later on goes and shoots down… but this was never a discussion about whether the details of Krugman’s article were plausible, it was about whether such a graph makes sense at any level… Bob’s argument was that the entire concept of getting a GDP value out of adding up all those little marginal returns is itself fundamentally impossible, from a units perspective. Here’s Bob’s original argument:

But if that’s the case, consider the implications of Krugman’s commentary that I put in bold in the quotation above. If we’re calculating total GDP by summing up the contributions of the marginal contribution from each small dose of capital (which is shown along the ­x-axis), then it seems our answer is going to be that GDP is something like “304%.” That doesn’t make any sense.

Well, I still disagree with Bob on that particular point, in as much as you accept GDP to be meaningful at all, you can indeed get the units to come out correctly. Bottom axis is “K” measured in dollars, side axis is a rate measured in units of percent per annum, multiply together and you get dollars per annum which is what economists call a flow, thus in terms of simple dimensional analysis:

Total Capital Stock * Rate of Return = GDP Flow

The units come out OK… presuming you accept the concept of aggregation at all, and if you don’t accept that, then out of consistency you have to also declare GDP to be meaningless, and all macro economics to be meaningless; in which case Krugman probably isn’t your guy.

Even if we imagine a different graph (not Krugman’s macro stuff) where the bottom axis K was measured in real physical units (e.g. head of cattle) and we have a herd living on some ranch and we presume the ranch is fully self contained in terms of water, etc but has finite land boundaries then even in that situation the MPK will be a downward slope because as more cattle fill that finite land the ability of the land to feed said cattle will diminish. If you plot the same graph you will get bottom axis K (meaning head of cattle) and side axis will be rate percent per annum (rate of new cattle being born) and if the rancher chose to keep removing cattle from the herd for sale then it would come to a steady state and the rancher would have a “GDP” which is a flow of a certain number of cattle per year.

So the concept of at least drawing the graph, presuming a diminishing MPK and calculating the area under the graph is valid even in non-macro situations… and yes the units can check out quite nicely as well.

The problem here is that you can’t really put the total capital graph on the same axes you use for the MPK graph.

But in the MPK graph, total capital IS the bottom axis. The whole point of it is that as you put more cattle into that finite slab of land, the rate of return you get back on each cow is reduced. That’s what you are attempting to optimize against.

• baconbacon says:

“Wow this is painful trying to make basic points on this blog.”

Feel free to correct me if I am wrong, but it seems to me that you are making the same mistake that Krugman is making. Your basic point appears to be that if X is a function of A, B and C then you can’t vary X without varying one of A, B or C. From the Mises article

“But if we assume a prevailing market interest rate of 0%, then the “amount of capital” represented by the tractor is \$80,000, while if we increase the annual interest rate to 5%, then all of a sudden the amount of “capital” in the tractor has shrunk to \$61,774.”

This is, I think, incorrect. Lets make it simple and say that the farmer is going to borrow money at the prevailing rate to pay for the tractor. In this case he will be willing to pay (at most) \$61,774 for the tractor, however this does not mean that the capital value of the tractor to the entire economy is \$61,774, it means that the capital value to to the farmer is that number, and the capital value to the lender is the difference between \$80,000 and \$61,774. If you are summing the capital in the economy the interest rate only influences how the capital value gets divided across the economy, but the total value to the economy is the market price of the capital (over the appropriate time).

• Bob Murphy says:

bacon^2 wrote: “If you are summing the capital in the economy the interest rate only influences how the capital value gets divided across the economy, but the total value to the economy is the market price of the capital (over the appropriate time).

That’s a distinction without a difference. When you vary the interest rate, you necessarily change the “market price” of the capital goods. That’s the whole point I’ve been trying to make.

Think of a safe bond. It guarantees a certain flow of monetary payments over time. If I ask, “How much capital is stored in that bond?” you need to know what the prevailing interest rate is. It would be confused to talk about “the amount of capital represented by this bond” and contrast that number with “the market price of this bond.”

• baconbacon says:

“That’s a distinction without a difference. When you vary the interest rate, you necessarily change the “market price” of the capital goods. That’s the whole point I’ve been trying to make.”

Only if you are holding other things constant though. Simply a further step, who is the owner of the capital at the beginning of the example? The farmer goes to the tractor owner and offers to buy the tractor…. only he has not cash. So the Tractor owner offers to loan him the money “at the market rate”. If the market rate is 0%, then the tractor owner demands \$80,000 paid over 10 years. If the market rate is 5% then the Tractor owner wants \$61,774 as the sticker price. Either way the tractor is worth \$80,000 over 10 years to the current tractor owner, correct?

• Bob Murphy says:

Either way the tractor is worth \$80,000 over 10 years to the current tractor owner, correct?

Yes, but the whole point of “valuing capital” is converting future services into a present spot price.

It’s like someone asking an American, “How much is 100 euros worth?” and me saying, “It depends on the exchange rate.” And then you say, “Sure, but it’s always worth 100 euros to the seller, right?” Yeah, but that’s dodging the issue.

• baconbacon says:

This is only true because you are holding other things constant that you can’t (wouldn’t) in reality. You are stating that the physical output in \$ terms of the tractor is identical in a 0% and a 5% interest rate environment*, not only is that not true, the difference in the example should be the same as the difference between the two tractor “prices” over the 10 year period.

*while simultaneously assuming that the marginal cost of producing the tractor is also unaffected by the different interest rate, but that over complicates things.

• Bob Murphy says:

Hey bacon^2 let me try a different approach for you to see the problem:

Suppose an economy has:

1) a tractor that will yield \$8,000 more in crops each year for the next 10 years,

2) a hammer that will yield \$5 more in assembled boards each year for the next 5 years,

3) a factory that will yield \$70,000 more in TV output each year for the next 13 years,

4) a satellite that will yield \$800 more in phone calls per year for the next 28 years,

and

1,000,000) an 18-wheeler that will yield \$3,400 more in shipped goods per year for the next 17 years.

Someone then asks, “How much capital does this economy possess right now?”

I think you want to give the answer back of:

1) a tractor that will yield \$8,000 more in crops each year for the next 10 years,

2) a hammer that will yield \$5 more in assembled boards each year for the next 5 years,

3) a factory that will yield \$70,000 more in TV output each year for the next 13 years,

4) a satellite that will yield \$800 more in phone calls per year for the next 28 years,

and

1,000,000) an 18-wheeler that will yield \$3,400 more in shipped goods per year for the next 17 years.

But do you see why that’s not really an answer?

• baconbacon says:

@ Bob Murphy

The tractor doesn’t harvest \$80,000 worth of crops overt ten years, it harvests a certain tonnage of crops and those crops are then sold for money, and the price they command on the market will depend, in part, on the interest rate. When you say

“Note that we are talking here about the same physical tractor, and we are making the same assumptions about the additions it will make to net income over the next decade.”

When the farmer takes his grain to market and the baker wants to buy it to make bread to sell. Lets say the baker has cash. He can either buy the grain and make bread, or invest his cash at the market rate. In a 0% environment he will pay the amount = the value he will get from the additional bread sales. In a 5% environment he will pay less, because he has to make at least 5% to make it a worthwhile transaction over just investing his money, so he will pay less for the grain in a 5% environment. This means that the amount of grain that sells for \$80,000 in a zero % environment will actually sell for \$61,774 in a 5% environment.

So the value of the capital in the two situations is different because the value of the output in dollar terms is different.

• Bob Murphy says:

Bacon^2,

OK I’m fine with that. I was imagining the farmer was selling finished consumption goods, but sure, I am happy with your clarification. But doesn’t that just make my point even more so, that it will change how much capital (measured in financial terms) you have at any moment, simply by changing the interest rate? Or are you claiming that with your clarification, it perfectly offsets?

• baconbacon says:

@ Bob Murphy

If you will permit me to restate (and ignore some inconsistencies I have written) what I think the general thrust of Tel’s point (and my reason for jumping in) is.

If Krugman makes a claim that you reject, and you come up with an example like the tractor where X = A*B*C and you hold A and B constant but shift C to get a change in X then you have tacitly accepted a hypothetical Krugman rebuttal that goes “Yeah Bob, but it was a blog post not a thesis. In ‘reality’ X = A*B*C*D*…..Q, if you hold A->M constant and let N->Q vary then you get the exact result that I said.” Given his intelligence, the complicated nature of cross border trades and the varied literature on the subject, Krugman not only is it highly likely to be able to find an equation that ‘works’, he will also have a paper published in a ‘highly respected, peer reviewed journal’ to back it up (never mind the variations of the equation or research that don’t).

• Bob Murphy says:

Bacon^2 I’m not trying to be a jerk, but it sounds like you are saying the following happened:

— Krugman claims X.
— I say X isn’t true, and give a counterexample.
— Tel says “Yes X *is* true, because of reason Y.”
— I point out that Tel’s argument is wrong, and give other counterexamples.
— Tel denies ever saying Y has anything to do with this.
— Bacon^2 agrees that my counterexamples show X isn’t true, but wagers that Krugman could make some other statement that would be true.

Do I have it about right? And I’m supposed to be the bad guy here?

• baconbacon says:

I hope I didn’t come across as attacking you Bob! Not at all my intention (though I do not have the greatest knack for diplomacy, so I apologize if I did, I also hope it is recognized that in this coming post I am attempting to summarize 4 different positions am going to misinterpret someone, somewhere unintentionally.). Alright with that out of the way, a summary

1. Krugam: “X, because math and appeal to authority”

2. Murphy: “Not X, Y, because of math with different assumptions. Example Z”

3. Tell: “No Bob, Z happened because of P and Q, not Y.”

4. Murphy: “Ok, fine, but still you have to admit that Y could happen due to math with different assumptions.

5. Bacon: “Yes, but what do you gain from this insight? The assumptions aren’t self evident enough to build the case against Krugman, and you are basically validating his (invalid) approach to econ”

6. Murphy: Bacon, you are as smart as you are handsome*, but still I feel like my main point about Krugman being incorrect should be better appreciated.

Reasonable?

*may not have actually happened

• Bob Murphy says:

bacon^2 that was funny enough that I will say “OK.”

4. Transformer says:

Assume the interest rate in an economy is 5%. One capital good is used to produce itself and always does so at a rate of 20%. It looks like (other things equal) its price would have to fall by 15% per year relative to other goods in equilibrium. It would quickly become so cheap it would be a free good. Which makes sense: If you can hold all other inputs steady and can add additional units of this good for ever and get a net physical return of 20% then it likely will quickly become as abundant as air.

5. Transformer says:

I guess I’m not seeing the value of these examples where capital goods have constant returns (presumably when all other inputs are held steady) as a way of .challenging a theory that says that with diminishing physical returns the interest rate will in equilibrium equal the physical return.

If there was a good with diminishing physical returns where physical output could be measured in terms of itself (goods of these type would be rare or non-existent in the real world) I think market forces would cause both the monetary return and the physical returns to equal (in real terms, and ignoring other complicating factors) the rate of return on capital that prevails in the economy. Would you disagree ?

BTW:. I strongly suspect that I am 100% agreement with you on the fundamental of this this stuff (in as much as I would even claim a full understanding!) , this is just a theoretical curiosity I developed based on Steve Landsburg’s example in the other post.

• Bob Murphy says:

Transformer if you agree that it’s possible for Machine A to reproduce at 10% and Machine B to reproduce at 20% when they are both fixed, because prices adjust, then why do you think if repro rates are flexible, that competition would drive the physical rates to equalize? That would only be true if the prices stayed the same, but why would you assume that to be the case?

• Transformer says:

OK, that’s a good question:

I was thinking of a very simple model where if a physical good had measurable diminishing returns in terms of itself, it would move to the point on its MPK curve where this rate of return was equal to the return on capital in the rest of the economy.

But you are correct that the rate of return could also be adjusted by relative price changes for such a good over time.

However if in equilibrium (for example) the price for A has to fall by 5% per year relative to other goods then it will eventually be a free good. I am therefore still suspecting that to stop this logical absurdity from happening there must be a mechanism to bring output to the point on the MPK curve where return = 5%.

• Transformer says:

I mean assuming the rate of return for the economy is 5%

• Transformer says:

Or to think of it another way: If we have an economy where we hold everything stationary then I would expect in equilibrium for all relative prices to remain the same. If the relative price of Machine A is changing to equilibriate its own rate of return then this will not be true.

6. Bob Murphy says:

So as not to be a hypocrite when I encourage Tel to consider that he has been too obstinate in this debate:

Let me admit (to Tel and bacon^2 especially) that I picked a bad example for my currency point. You guys are right, the negative interest rates on Japanese bonds right now is presumably driven by their unusual monetary policy. I should’ve picked bonds issued by safe governments from, say, 2004 when there wasn’t as much hanky panky going on, to make my modest point that international investors worry not just about nominal yields, but also exchange rates.

• baconbacon says:

Perhaps you could clarify for me difference in our positions. It appears that the out come of what you are saying is “X is a function of A, B and C, if you hold A and B constant then C can still change”, while Krugman is saying that “hold A and C constant then B must change”, while Tel and I are saying “modeling things where you are holding multiple variables constant that are in reality never held constant won’t give you any insight into how the economy actually works.

• Tel says:

Tel and I are saying “modeling things where you are holding multiple variables constant that are in reality never held constant won’t give you any insight into how the economy actually works.

That’s the basis of what I’m saying, but even more than that you have strong reason (based on experience and many examples) to believe that a non-linear relationship most likely exists between each additional unit of effort you put into building more of some particular capital factor, and the unit of reward you get back (be those measured in dollars or whatever).

Thus, because you are expecting non-linearity, to assume that away by declaring a fixed rate of return actually means you are dealing with a different problem at the mathematical level. The non-linearity is what allows the system to adjust real rates of return by shifting the operating point (i.e. the “marginal” cases sit in different positions). The marginal cases are what defines the system gain, so unless those are allowed to shift around, you lack the degrees of freedom necessary to solve it. That is the place where individual time preferences meet up with physical factors of production.

In short: Irving Fisher was right.

• guest says:

“The marginal cases are what defines the system gain, so unless those are allowed to shift around, you lack the degrees of freedom necessary to solve it. That is the place where individual time preferences meet up with physical factors of production.”

Excellent.

“In short: Irving Fisher was right.”

Huh?

• Tel says:

I put a note at the bottom of the Japanese bond example as to why government bonds are always a poor example in discussions over physical capital and interest rates — because government spends the money and does not create any genuine capital (or at the very least capital creation is haphazard and largely unrelated to what the bonds are doing).

But particularly poor example if you pick Japanese bonds under QE scenarios.

More than happy to look at other different examples. I will add some at the bottom here.

7. Tel says:

Example: Physical Constraints Forcing Short Lived Capital

So you and a bunch of the guys are hiking in the woods, you have walked about four hours from your car and you have about two hours hike ahead to make it to your cabin; which is relatively sparse but provides a place to sleep and will keep the rain off. In your packs you have all the basic items: preserved food, bottles of water, change of underwear, etc.

The group are discussing the idea of resting for a while in the next clearing, but astoundingly as you all enter the clearing you see none other than Donald Trump waiting for you with some deep state guys standing behind him in a black helicopter. Although initially worried, Trump assures you that everything is OK, and unexpectedly he hands out ice creams all round, then Trump and his team jump back into the helicopter, shout “MAGA” and fly away.

So the economics question here: “What is the optimal time to consume the ice cream? How much of the ice cream should be saved?”

Just to provide a few additional details: it’s a warm day and no one in the group is carrying any refrigeration equipment, nor anything that would even plausibly operate as such. You check each attachment on the deluxe Swiss Army Knife you are carrying and unfortunately it does not include a refrigerator either.

Every member of the group has similar preferences: their time preference is 5% per annum, and every person finds cold fresh ice cream to be delicious, but none of you enjoy warm melted mushy ice cream. Strangely you all agree that although you don’t much like Donald Trump as a person, you are confident that his ice cream is safe to eat (although you are starting to have second thoughts about the wild mushrooms you ate yesterday).

Be sure to also show how you answer changes should the group have a time preference of 4% per annum, or 6% per annum.

8. guest says:

“Because the price of Machine A (and its products, like apples) can change relative to the price of Machine B (and its product, bananas) over time, the rate of return to investors *measured in dollars* can be equal, even though Machine A can make 10% of another Machine A while Machine B can make 20% of another Machine B.”

So, shouldn’t the question have rather been posed something more along the lines of: “If apples increased 10%, and bananas increased 20%, yada, yada”?

Both the cryptocurrency and the machine puzzles were presented as if we are to compare the two against each other (1 cryptocurrency being worth 1 of the other cryptocurrency, and Machine A producing the same thing as Machine B), rather than against another currency or against subjective preferences.

Had the puzzles been presented in this way, people would probably have said that it depends on how much people value apples vs. bananas, or how much money they could get selling apples vs. bananas.

• Bob Murphy says:

guest,

I agree that if I said what the answer was in the framing of the puzzle, then it wouldn’t have thrown as many people.

In my defense, in the original discussion (in the comments) when I first brought up the machines, I was quite explicit that they produced different goods. (See here for example.) Then someone (whose name rhymes with Gel) told me that people would always invest in the machine that produced more of itself, even though I had been quite clear that it produced different goods than the other machine.

So that’s why I resorted to my puzzle approach.

• guest says:

I see that, now. Thank you.

I’m coming into this having noticed there were three puzzles to solve, and I just read the three puzzles.

9. Tel says:

Example: Physical Constraints ForcingLong Lived Capital
So suppose I talking to my friend Gary Goldbug and he says, “Gold is the thing, I’m stacking for the long haul, I’m expecting some serious gains.”

So I replied, “I dunno, I think Bitcoin is where the action is at, I’ve nearly sold off all my gold, down to one last bar. Hey, you can buy it if you want, it’s right here in my safe just wire me the money at the spot price and I will deliver for free.”

Gary likes the idea and tells me to expect the money. So in the way of these contrived stories Trump wins the election the very next day and of course I’m out with a bunch of friends very drunk and philosophical.

One hangover later I get a message that Gary’s money came through and I figure, “Better get this delivery done” but then disaster hits! Vague memories come back about diving off a jetty in the middle of the night and losing the key to my safe which I normally keep in my boot. Ohhh, regret, should be more careful on those crazy nights. Anyhow Gary will understand, so I call him.

Gary says, “Hey, could have happened to anyone, don’t freak out.”

I explain that my cousin overseas is the only guy with the same key and he will be flying back in 6 months. Gary is willing to tolerate the late delivery but I offer, “Look, I feel bad about this, when I come over to deliver in 6 months, show me your calculations with regards to how much you are out of pocket caused by late delivery (give me a figure in dollars and cents) and I’ll fix you up in cash.”

Sure enough, in 6 months time I make the delivery of one gold bar.

What are Gary’s calculations, based on a prevailing interest rate of 5% PA? How much do I owe him to make up the loss?

Run your calculations again at 4% and 6% interest rates, and explain the change.

• Bob Murphy says:

Tel, what would be more difficult for me than answering your question, is to explain why this sheds light on my original Mises.org post, or any comment I’ve written since then.

• Tel says:

In the ice cream example, the group between them decides to consume all the ice cream immediately (not necessarily distributed equally). That’s because the physical properties of ice cream makes it unsuitable for savings… and that’s completely regardless of individual time preference.

In the gold bar example Gary Goldbug concludes that I owe him nothing for late delivery since storage in my vault is equally as good as storage in his vault over that 6 months (he was just intending to hold the bar anyhow) and the physical outcome is identical whether I delivered a bit earlier or a bit later. By gum! That turns out to also be independent of variation in time preference.

So at least in some cases physical properties do matter.

• Bob Murphy says:

OK. And to quote from your buddy Irving Fisher, we can imagine an island economy consisting of sheep that multiply, or of hard tack that is durable, or of figs that rot. And then Fisher shows that the real rate of interest in those hypothetical economies is pinned down at 10%, 0%, and -10%, respectively. (I might have the 10s different from his numbers.)

So that’s fine. But the way it works is that people adjust the rate of consumption so that in equilibrium they are still optimizing, given the intertemporal tradeoff that is “determined” by the physical facts.

And of course the other interesting thing is that Fisher is using examples of fixed reproduction rates to make a basic point about interest theory, which is what I did (before you sent me to Time Out).

• Tel says:

If you have a situation where someone is choosing between chocolate and strawberry, then preferences come into play. On the other hand, if they are choosing between chocolate and magic dust from Alpha Centauri then preferences become irrelevant because one of those options is simply unavailable.

Now, fair call, I grant you that my examples above are far fetched… but not impossible. If you are stuck with an ice cream on a warm day and storage is absolutely not a possibility then whatever your preferences you eat 100% of the ice cream straight away because anything you don’t eat is guaranteed to be thrown away (OK maybe one of the members of the party might be watching her weight, but then it gets eaten by some other member, but in all cases it gets eaten straight away). That’s not how a normal market economy works, but we would be comforted by believing that the laws of economics continue to operate in fringe situations.

So that’s fine. But the way it works is that people adjust the rate of consumption so that in equilibrium they are still optimizing, given the intertemporal tradeoff that is “determined” by the physical facts.

That will only work in situations where the physical world offers a non-linear curve thus providing the necessary degree of freedom to allow such an equilibrium to align itself with individual preferences. I mean mathematically it isn’t solvable otherwise.

Yes, I accept, this is indeed the most common situation, it happens all the time, we might even be so bold as to call it an “Iron Law” and we expect it to happen.

However, it is conceivable that perhaps such convergence does not happen, the model is not solvable, and in that case the physical world always wins over human preferences. You really cannot modify your degree of consumption to stop the ice cream from melting. It is just going to follow thermodynamics no matter what you ask of it.

Surely whatever this thing is that we call “the world” must necessarily be the thing that you cannot simply bypass because you prefer something different. To say otherwise would be mind over matter, which seems to be the latest “Progressive” concept: you get it just because you wanted it. Preferences are powerful… but not all powerful.