When we teach students economics, we sometimes use numerical examples to help them understand general principles. Sometimes we make them work through those numerical examples by themselves, as an assignment. It's the only way they will really get it, and see what's really going on. But once they get it, they don't need the numbers any more, they can see the general principle that doesn't depend on any particular numbers.
As an undergraduate at Stirling I took a course on Merleau-Ponty's Phenomenology of Perception. One book for one course. Looking back on it, I have no idea what it was about. I think I learned something, but I couldn't really tell you what it was.
But I remember (I think I remember) one of Merleau-Ponty's examples. There is a row of light bulbs. The first bulb lights up, then goes out. Then the second bulb lights up, then goes out. Then the third, and so on. And we see a light moving from left to right along the row, even though none of the bulbs is moving.
I think it was Roger Farmer who first explained Samuelson 1958 to me, back in grad skool at Western. He used a numerical example. I think it went something like this:
1. Imagine an infinite line of people, each holding one beer. One equilibrium is where each person drinks one beer. But there is a second equilibrium, where each person gives his beer to the person in front. The person at the front of the line drinks two beers, and everyone else drinks one. The second equilibrium is Pareto Superior to the first, because the person at the front of the line drinks more beer, and everyone else is the same. You can imagine the first person in line giving the person second in line a bit of paper, in exchange for the beer. That bit of paper (money) travels down the line in exchange for the beers traveling up the line.
2. Now change Roger's example, so there is one person first in line, two people second in line, four people third in line, and so on. The population doubles every generation. If every individual gives his beer to the person in front, every individual can drink two beers. The paper money becomes twice as valuable every generation, or pays 100% interest per generation (same thing). But if the population ever starts to decline, somebody is going to be stuck drinking less than one beer.
3. Now change the example again. Let the population be constant, and assume each person lives two periods. He produces 100 beers when young, and none when old. He would like to save half his beer to drink when old, but beer does not keep. If each young person gives 50 beers to the old person in front, everyone is better off. The old people at the front of the line get to drink 150 beers over their lifetime (100 when young, and 50 when old). Everyone else gets to drink the same 100 beers over their lifetime, but now drinks 50 when young and 50 when old, which they prefer.
The total number of beers consumed over one's lifetime tells us something, but it doesn't tell us everything. If beer has diminishing Marginal Utility, and if people do not discount future utility, they will always prefer drinking 50 when young and 50 when old to any other combination of drinking 100 beers over their lifetime. For example, let:
lifetime utility = log(beers consumed when young) + log (beers consumed when old)
4. Now change the example again. Same utility function, constant population, but now assume people produce 50 beers when young and also produce 50 beers when old. If each individual consumes what he produces, and consumes it when he produces it, it looks like this:
A 50 50
B 50 50
C 50 50
D 50 50
E 50 50
etc.
Each row represents a generation (or cohort). Generation A is followed by generation B is followed by generation C and so on, forever.
Each column represents a period in time. By assumption, each column must add up to 100 beers, because it is impossible to make beers travel in time. You are not allowed to move beers horizontally.
But you can move beers vertically. You can take 10 beers away from the young in generation B and give them to the old in generation A. And you can imagine that you give the young a bit of paper in exchange for their 10 beers. And you can repeat this, so that the young in generation C give 10 beers to the old in generation B. And then stop, so that the young in generation D give no beers to the old in generation C (the debt is redeemed).
You can make it look like those 10 beers are traveling back in time from generation C to generation A. Just like Merleau Ponty's row of light bulbs.
There are two ways to aggregate: aggregate by columns (years); aggregate by rows (generations). You get different perceptions of reality depending on which way you aggregate. You can't see beers travel back in time horizontally, but you can see beers travel back up the generations vertically.
[Update: if we use natural logs, then lifetime utility is 7.824 for every row; and the aggregate utility in any period (if you are comfortable with adding two people's utilities) is also 7.824 for every column.]
Play with this numerical example by yourself. Because I can't teach you anything. You can only teach yourself this stuff. And the best way to teach yourself is by playing with numerical examples. That's how I learned it. That's how Bob Murphy learned it. See what happens to the lifetime consumption, and lifetime utility, of future generations, if you use debt to finance transfers to the old in generation A. There is no way you can do it without making some future generation have lower lifetime utility.
[The equilibrium rate of interest in this model will be determined by:
1+r = (consumption when old/consumption when young)
Because Marginal Utility of consumption = dlog(C)/dC= 1/C
At the initial equilibrium drawn above, r=0. But if the debt is positive, r will be strictly positive.]
I would be indebted to anybody who knows how to set this thing up on a spreadsheet, with the lifetime utility calculator built right in, and can put it up on the web somehow. Young people can do that sort of thing, right? [Update: thanks to rpl for creating this spreadsheet; which you should be able to copy and edit! I think rpl used base 10 logs, which is why his utility numbers are different from mine.]
Have fun.
Worthwhile Canadian Initiative 
“See what happens to the lifetime consumption, and lifetime utility, of future generations, if you use debt to finance transfers to the old in generation A. There is no way you can do it without making some future generation have lower lifetime utility.”
Assuming it stops, right?
(i.e. analogous to tax / primary surplus)
Nick, is this the kind of spreadsheet you were looking for?
[Link Here NR]
NB: The shared doc itself won’t be editable (e.g. to change the generational transfer amount) by people other than me, but you should be able make a copy that you can edit (I think…)
If everyone in line has a beer and passes a beer forward ,for the first person to have two doesn’t that mean she must retain her beer? Doesn’t it then follow that the last person will have no beer, having passed her beer forward? The last person will merely have the scrip.
Two questions:
1. “There is no way you can do it without making some future generation have lower lifetime utility.”
Does that also hold when you introduce the production of real capital like a beer-producing machine in addition to just changing the distribution of consumption goods?
2. How would public debt be any different here from private debt?
Vladimir – it’s an infinite line, there is no last person (by definition of infinity).
Nick: “I can’t teach you anything. You can only teach yourself” Is this self-evidently true? Those 10 words merit a blog post in their own right.
What happens to the lifetime consumption, and lifetime utility, of future generations, if you use sawn-off shotguns to enforce transfers to the old in generation A? Am I right in thinking that there is no way you can do it without making some future generation have lower lifetime utility? If that is so, do we need a treatise on The Burden of Shotguns?
JKH: “Assuming it stops, right?
(i.e. analogous to tax / primary surplus)”
We don’t need to assume it stops. If you try to run a Ponzi scheme in this model, r rises above g (the growth rate is 0%), you will eventually get to a point where the debt can’t grow any more, because if it did it would be bigger than 50, so the young would be drinking negative beers. It has to stop.
(It would be different if I assumed r < g, for example by having the young produce 60 beers and the old produce 40, which would make r < 0%.)
rpl: that’s exactly what I had in mind (I think), if people can find some way to copy then edit it. Thanks!
Vladimir: it doesn’t work if the line is finite. It also doesn’t work if someone breaks the chain.
Odie: you can play with the model yourself, or change the assumptions and see how the answers change. That way you will really learn it.
Frances: Hmmm. Probably not self-evidently true, and not 100% true, but from experience (as student and teacher) I think there’s a lot of truth in it, especially when it comes to OLG models.
Kevin: we do use sawn-off shotguns. Or the government does. To collect taxes. Debt and taxes are related. If r < g, there need be no taxes, and there needn’t be a burden of the debt.
Kevin: want to call it “the deferred burden of deferred taxes? OK.
Nick, I’ll stick with the answer I gave you in comments at Mainly Macro: The Perils of Aggregation.
There’s no good reason why a policy which benefits Generation A and screws Generation Z should be called a burden, nor why the reverse policy should be called a boon.
Nick
“We don’t need to assume it stops.”
Can’t you sustain it with primary surplus of 0?
In which case you do have to assume it stops (with a positive primary surplus)?
JKH: “Can’t you sustain it with primary surplus of 0?”
No. If the debt is positive, then (Cold/Cyoung) > 1 so r > 0, so you need to run a primary surplus to pay the interest and stop the debt growing over time.
Oh right .. got that backwards
I guess I intended a primary surplus equal to the interest
thx
Kevin: if the government puts a tax on apples, is it the seller of apples or the buyer of apples who bears the tax burden? And is there an excess burden of taxation? That’s how we normally talk about tax incidence. We use the word “burden”. I don’t see why I’m not allowed to use the same word the same way to talk about intertemporal taxation.
Odie: “How would public debt be any different here from private debt?”
There’s no way Generation A can borrow from Generation B, since they only coexist for one period. But of course government can tax Generation B and subsidize Generation A and then repeat the process until (in Nick’s example) it decides to not tax Generation E or subsidize Generation D (the one that gets screwed).
In other words, we can get exactly the same result with no debt at all, public or private. Taxes and subsidies will do just as well. Public debt is neither necessary nor sufficient for an intergenerational stitch-up such as this. That’s probably one reason why Paul Krugman is ignoring Nick Rowe & Co.; he knows a red herring when he sees one.
You can’t force future generations to pay your private debts, unless you leave thenm an asset in return.
You wait Kevin. Any day now, Paul will see The Light, and will be converted to The Truth.
My Phenomenology of Perception course was taught by Dreyfus. It was very good. Speaking of times past:
“Nick, I might ask something else, but this puzzles me:
“because the domestic and foreign central banks want to push interest rates lower, but can’t.’
I don’t understand why the Fed couldn’t”
1) Add a fee to these bonds
2) Discount them over time
In other words, add a disincentive to buy and hold them.
Posted by: Don the libertarian Democrat | February 03, 2009 at 04:51 PM
“Hi Don: it’s technically possible. But people would just hold cash under the mattress, or in safety deposit boxes, and get zero interest rates that way. (There are various schemes always floated to tax cash, or make it expire, etc., but they always come across as a bit sci-fi.)
Posted by: Nick Rowe | February 03, 2009 at 05:27 PM”
Welcome to the future:
Don! The one person who might read this and know if I’m talking nonsense about Merleau-Ponty! (My course was very good too, but man that was a difficult book.) I just Googled and found this. I don’t really understand it, but bits of it are very slowly coming back to me, out of a 40 year old haze.
Yep, if there are costs to storing currency (fear of fire and theft) you can get interest rates a little bit negative. Until someone figures out a cheaper way to store currency. (I think they are already onto the “pay your taxes in advance” gambit.)
Am I missing something obvious here? Since you have diminishing marginal utility in beer in each period, additive utility across individuals, and an equal division of beer consumption across time periods in the initial state, a transfer of beer consumption from one time period to another, even between different people, is utility-reducing. This is more or less tautological. The transfer of beer from Gen B to Gen A in the second column (period) is a dumb idea. The model shows that you can compensate the Gen B’s loss of ten beers in the first half of its life by getting Gen C to donate 10 beers in the following period, but it can’t be fully compensating in utility terms, nor can subsequent compensations to Gen C, Gen D etc.
Similarly, with the same utility functions, if people are more productive in the first half of their lives, producing 60 beers in the first period and 40 in the next, you would get an aggregate utility boost from the same transfer program, assuming an infinite time horizon.
So the moral of the story is, if the old and young are equally well off, don’t force the young to transfer some additional portion of their consumption to the old. I’ll buy that.
If the old owns everything, let’s say an apple tree (there is no beer trees I know of). Let’s say he needs to pay the young a price to pick the apples (a market clearing price) – assume the old cannot pick the apples.
The old wants to sell the apple tree to buy some extra apples as he knows he will be soon gone. What is the price of the apple tree? I think there is no such price because after the trade there is no market for apples anymore. What is the price of government debt? I think it is zero, the young will not buy it at any price. The young knows he would be worse off. The old cannot hand over a piece of paper to make the young comply. The young will get everything by just waiting.
The old needs more than economical means to get extra amount of apples. This is not an economical model at the micro level?
This is not exactly Nick’s model but does it give any insight? Can we relax the assumptions that the old cannot pick the apples?
OLG with an infinite number of agents is done well in Romer’s Advanced Macroeconomics (an upper year undergraduate text). The Welfare Theorems are violated when you expand to an number of infinite agents. What you are talking about in this post is the possibility of dynamic inefficiency.
The best way to learn this is NOT by numerical examples, it’s by writing down the specification and working out the Pareto efficient equilibriums. As I learned in high school, numerical examples confuse, they don’t help. Units disappear making it impossible to track mistakes, and the arithmetic is just mechanical. Insight comes from understanding relationships, that’s why we use algebra!
This is a useful exercise for undergraduates so that they can see how it is possible to get a Pareto efficient outcome that a competitive market cannot reach.
“get a Pareto efficient outcome”
It looks to me as an inefficient outcome? And I think competitive market will do better.
@Peter
I think you are exactly right, the young will not buy the burden (it can be forced, by taxation but not in voluntary terms).
“Imagine an infinite line of people, each holding one beer. One equilibrium is where each person drinks one beer. But there is a second equilibrium, where each person gives his beer to the person in front. The person at the front of the line drinks two beers, and everyone else drinks one. The second equilibrium is Pareto Superior to the first, because the person at the front of the line drinks more beer, and everyone else is the same.”
This illustrates the danger of reasoning from infinities. The amount of beer drunk is the same in each “equilibrium”, yet one more beer is drunk in the “Pareto Superior equilibrium”. Economies are finite, and there is no reason to think that reasoning from infinities applies to them. Besides which, it matters how the infinity is generated.
Let us start with two people and two beers. In one “equilibrium” each person drinks a beer. In the other “equilibrium” the first person drinks two beers and the second person drinks none. The second “equilibrium” is not Pareto Superior to the first. Now let us add one person and one beer. In the first “equilibrium” each person drinks one beer. In the second “equilibrium” the first person drinks two beers, the middle person drinks one beer, and the last person drinks none. The second “equilibrium” is not Pareto Superior to the first. Now let us add another person and one more beer. It is obvious that the “equilibrium” where the first person drinks two beers and the last person drinks none is not Pareto Superior to the other one. If we keep on adding people, we will never reach a situation where one “equilibrium” is Pareto Superior to the other. That relation between the two “equilibria” is always the same, and it remains the same in the limit.
So is the second “equilibrium” Pareto Superior to the first or not at infinity? There is no way to tell. The original reasoning assumes that when you have an infinite number of people and beers, there is no last person. But that assumption is not justified. It is perfectly possible to have an infinity of people and beers with or without a last person. The reasoning from infinity of the quoted argument is fallacious. Reasoning from infinity is dangerous.
But reasoning from infinity is fun.
Nick constructed a model which is not infinite because r>g (g=0). I’m not sure this is a consistent model because with certainty (no volatility) and zero growth I think r == 0. If r>0 this is a ponzi scheme, so who is willing to buy the bond in the first place? Both r>0 and r==0 cannot be true – market doesn’t clear?
Hmm. it might be infinite but the effect kicks in at some point of time. This happens when a generation recognizes the ponzi scheme. Assuming rationality it will be the first and second generations.
This illustrates the danger of reasoning from infinities.
It is perfectly true that reasoning from infinities has many pitfalls for the naive; that is why an innocuous-looking series like Grandi’s series diverges. It is also true that the reasoning given in the post is fallacious.
But it is possible to reason about infinities and in fact your inductive approach is the right way to go about it: construct a sequence of arbitrary length and then ask whether it converges, and if so what to? But I don’t agree with “no way to tell”; every term in the series is Pareto Inferior, assuming convex utility. The average utility converges (from below) to the original average.
But once they get it, they don’t need the numbers any more, they can see the general principle …
Your posts so often make me nostalgic!
The introduction to the textbook for my first exposure to abstract algebra (“Modern Algebra with Applications”, by Gilbert) ran, in paraphrase:
And so the path was opened to Stone’s representation theorem and all that followed.
Kevin wrote: “If that is so, do we need a treatise on The Burden of Shotguns?”
If a Nobel laureate in firearms kept writing blog posts saying, “It’s impossible to shoot yourself” then yes, we would definitely need such a treatise.
Kevin wrote:
“we can get exactly the same result with no debt at all, public or private. Taxes and subsidies will do just as well. Public debt is neither necessary nor sufficient for an intergenerational stitch-up such as this. That’s probably one reason why Paul Krugman is ignoring Nick Rowe & Co.; he knows a red herring when he sees one.”
And yet, Krugman has never once made this particular argument, Instead, he keeps saying “we owe it to ourselves,” which is utterly irrelevant if he has been trying to make the point you bring up here. One almost gets the sense that Krugman thinks “we owe it to ourselves” is the crucial factor, since he keeps saying it is. Nick is simply taking Krugman at face value, rather than inventing arguments for his position that Krugman has never made.
Phil Koop: “But it is possible to reason about infinities and in fact your inductive approach is the right way to go about it. . . . But I don’t agree with “no way to tell”
IMO, for scientific purposes the inductive approach is correct, as a rule. However, it is quite possible for something to be true for each finite instance and yet false for the infinite case. But if you reason from infinity there is no way to tell if that is so. IOW, you have to make an assumption.
Bob Murphy: “Krugman has never once made this particular argument, Instead, he keeps saying “we owe it to ourselves,”
I don’t follow Krugman, so I am not exactly sure what he means. But as far as future debt is concerned, people in the future owe it to other people in the future. If both the future debtors and future creditors belong to “us”, then “we” do owe it to “ourselves”. (“Do” in the sense of the timeless indicative. ;))
Peter: “Similarly, with the same utility functions, if people are more productive in the first half of their lives, producing 60 beers in the first period and 40 in the next, you would get an aggregate utility boost from the same transfer program, assuming an infinite time horizon.”
True. But in that case, r < 0. With a negative interest rate, an increase in the debt would imply no future taxes. Ponzi finance would be sustainable, because the debt would diminish over time by itself. All future generations would gain (and you can make that statement without adding interpersonal utilities).
And where does this case leave “We owe it to ourselves, so debt doesn’t matter at the aggregate level”?
Odie said: “2. How would public debt be any different here from private debt?”
With private debt, entities have a pretty good idea who will/should pay the interest and principal and when the principal and interest will/should be paid.
With gov’t debt, not so much.
rpl, thanks for the spreadsheet. It appears the key in this particular scenario is B2,C2 and E5,F5.
Anyone, is there “money” in this model?
Min, if you look carefully at what my statement again, you’ll see that I didn’t argue, “Krugman is wrong when he says we owe it to ourselves.” Rather, I said that that is irrelevant to the argument Kevin Donoghue was making about why the debt is a red herring.
It’s like Krugman has been running around for 3 years saying, “Whales are actually mammals, not fish, because their name starts with ‘w.'” And all the biologists are saying, “Yep, good job, clearing up that confusion with the public.”
(I realize I destroyed any comprehension you may have had, with that analogy. My audience is Nick at this point.)
@ Bob Murphy
No, you didn’t destroy anything. What Krugman says may be irrelevant to what Donoghue is saying, but Krugman is addressing fears of the public and propaganda that has been around as long as I have been alive. Maybe everybody needs to go to an Esalen weekend retreat and communications workshop. 😉
Nick,
I’m just wondering, why do you only tax the young and not the old in these models?
Suppose, for example, that the government taxes the public and uses the proceeds to fund Public Television for one period. Don’t the old also watch TV? But they were not taxed when young to watch TV in the current period — Public Television was only provided in the current period, not the past. Wouldn’t this be a transfer from the young to the old? Exactly the same kind of transfer as if the government sold bonds to pay for public television for one year, and then redeemed the bonds in the future. In other words, the transfers you describe are due to a poor taxation system, whether this is part of pay-as-you go or part of coupon redemption. In this case, you may want to pay for public TV by imposing a tax on consumption that is paid for by both the young and the old, rather than a tax on labor income that is only paid for by the young. A tax on consumption, in your model, is identical to a tax on savings as the old consume all of their savings and only their savings.
You have only shown that with a bad taxation policy, it’s possible for government debt to result in a transfer. Just as it’s possible for a pay-as-you go government expenditure to result in an intergenerational transfer! The financing method is not the culprit here, but the taxation policy.
But you have not shown that it is required. E.g. that by taxing both the young and the old, an intergenerational transfer necessarily arises. It does not arise with an optimum taxation policy, regardless of whether the spending is deficit financed and redeemed in a distant future period or pay-as-you go.
Nick,
In your original post (this year’s) you make the basic point about intergenerational distribution.
Which you label as “time travel”.
But you do not talk about utility there, until subsequent posts.
I’m trying to piece these together – versus Krugman for example.
These are analytically separate pieces aren’t they?
Independent? Interdependent?
Is Krugman denying both of them?
“True. But in that case, r < 0”
But Nick in your example r > 0 and it is a ponzi scheme, why do you assume someone is buying ponzi-bonds in the first place??
JKH: adding utility to the model doesn’t really change the model, but it lets you see additional things. It lets you see that debt can make someone worse off (or better off, if r < 0) even if their lifetime consumption is unchanged. It’s a better, more accurate way to talk about the burden of the debt.
rsj: there are two ways for the government to implement my 10 beer example:
1. Set up an unfunded pension plan where each period the government taxes the young 10 beers and gives 10 beers to the old (then stops doing it after 2 periods).
2. Issue bonds to borrow 10 beers from the young in the first period and give them to the old. The rate of interest will be (60/40)-1 = 50% per period. The government taxes the old 5 beers to pay the interest. Next period the old sell their bonds to the young. Then the government pays off the debt.
Both 1 and 2 give exactly the same result. A national debt is like an unfunded pension plan.
Yes, it is possible for the government to tax the old to benefit the young in each period. That’s like a negative unfunded pension plan, or a negative national debt. A student loan program is like a negative national debt, because students owe the government. Funding for high schools is like a negative unfunded pension plan. Lots of things are possible.
JKH: but if you say that debt makes people worse off if it reduces the Present Value of their lifetime consumption, then adding utility to the model doesn’t really let you see much more. You get the same answers with PV as you get with Utility, for small changes in debt. (For large changes, the sign of the effect is the same, but the magnitude is different.) So if you want to think in terms of PV of lifetime consumption, you are fine. (It gets tricky for large changes, because r will change too.)
“A national debt is like an unfunded pension plan”
right
which is why those who are saying this is not about debt are introducing a straw man
the “time travel” idea obviously requires/assumes a time period longer than zero
and some form of liability over that period
an unfunded pension plan still has a liability, which amounts to contingently structured debt
Many thanks to Bob Murphy for giving me some idea what it feels like to be Paul Krugman. Against uncharitable readings the gods themselves contend in vain.
Sez Bob: Krugman has never once made this particular argument, Instead, he keeps saying “we owe it to ourselves,” which is utterly irrelevant if he has been trying to make the point you bring up here.
My point being: “we can get exactly the same result with no debt at all, public or private. Taxes and subsidies will do just as well. Public debt is neither necessary nor sufficient for an intergenerational stitch-up such as this.”
Here’s Krugman making precisely that point:
He goes on to argue that it doesn’t.
http://krugman.blogs.nytimes.com/2012/10/12/on-the-non-burden-of-debt/
The infinitely long line of beer holders, each passing his beer forward, ignores the effect of time. This is a serious departure from economic reality.
Assume the infinite line of beer holders, each with a beer in hand. The first in line shouts the order to “Pass Beer Forward!” The order travels down the line at the speed of sound . As the order travels down the line at the speed of sound, each beer begins movement when the order reaches the beer location. It is obvious that beer movement begins later in time when the beer holder is farther from the front. The effect can be considered as a traveling hole . Each beer holder becomes beer deficient when he makes the transfer of his beer.
The effect of debt is the traveling hole that each person in the line experiences. Except for the first in line, there is always a period where the beer holder actually has no beer.
Nick,
I think the deficit/surplus intergenerational transfer and the utility intergenerational transfer are separate analytical issues.
Because utility is still an issue (I think) even if there is no “stop” effect from a surplus as otherwise assumed at the far end of your model.
And I think this is one point of confusion – e.g. it shows up in comments in Murphy’s post.
A sub-point is that some people seem to believe that the front end deficit alone is enough for an intergenerational transfer – which it is not in terms of intergenerational transfers from the future to the present, which is the point of your model – which also leads them to think that debt (liability more generally) is not an issue, which is also wrong – again this shows up in comments in Murphy’s post.
And then there’s the extremely basic point that some people don’t seem to understand that a steady state GDP is assumed in the model – to make the other points clearer. It is absolutely no revelation at all to understand that aggregate consumption in a period is unchanged, notwithstanding the intergenerational analysis that is done beyond that. It is a simplifying assumption – not a Eureka insight – as to what’s going on. Similarly, Krugman’s “we owe it to ourselves” should be obvious enough to anybody who understands that a government debt obligation is somebody’s asset. For those to whom that is not obvious, Krugman shouldn’t be making sweeping generalizations that are incorrect in other specific ways.
The key strike against Krugman is still the very last sentence in his post, which is what your model addressed.
What a mess, still, after 3 years.
JKH: “Because utility is still an issue (I think) even if there is no “stop” effect from a surplus as otherwise assumed at the far end of your model.”
Yes. Utility can be reduced, if taxes to pay interest are positive, even if the debt is constant over time. But then Present Value of lifetime consumption is reduced by those taxes too.
Nick, I haven’t followed this closely, but Krugman is obviously smart enough to understand what you are saying. He would have grasped the point more quickly than I did. It seems to me that either:
1. He hasn’t read any of your posts on this.
2. He has, but prefers to think in terms of the consumption of cohorts alive at various dates (is that the right term?), not generations.
Nick,
If PK were led to the Truth after reading your posts over a light lunch of apples and beer, he might feel duty bound to say “If I define intergenerational transfer in a particular way, as a transfer between old and young at the time they coexist on this earth, then debt can transfer wealth across generations. However, 125 years later, this debt will have no impact on the aggregate wealth of old and young combined.” Would that end the debate on this particular topic, or is there something deeper that I ( and others asking the same question) are missing?
I realize it is frustrating for you when multiple people ask the same question, as though some new phrasing of it will suddenly make you change your mind. I am just trying to understand.
I have played with the arithmetic as you advised, and am no clearer. I cannot create a cascading loss of wealth or utility.
Michael
“Play with this numerical example by yourself. Because I can’t teach you anything. You can only teach yourself this stuff. And the best way to teach yourself is by playing with numerical examples.”
And, I may add, the best way to play around with the numbers is with computer simulation. I just did a quick web search, and I do not mean the sophisticated computer programs that solve massive systems of equations, or those that compute equilibria, but something like NetLogo, which lets you create simple models and run them. 🙂
“And then STOP, so that the young in generation D give no beers to the old in generation C … you can make it look like those 10 beers are traveling back in time from generation C to generation A… just like Merleau Ponty’s row of light bulbs”
A deficit starts the process.
Time elapses
A surplus stops the process.
The intergenerational burden is due to:
a) The initial deficit
b) The passage of time
c) The surplus tax event
Krugman simply doesn’t address this
utility is a separate measurement dimension, IMO