The inequality thing, I am thinking that the issue is boiling down to the “rational” actors one, or possibly a “free market”, which is a bit of a can of worms. If everyone has a choice to spend or save, then I am coming round to your view that it is not logical to tax interest. In our simple example world, almost no-one would choose to forgo all the future benefits of saving. If you did choose to do so, one assume you must have a good reason: perhaps you knew you would die very soon. If you turned out not to die, then you could get on the saving bandwagon, just a bit later than everyone else. This only becomes a problem if some people are unable to get on the bandwagon- either because they must spend all their income, or are unable to understand the benefits. I think this is a totally different point, and all economic discussions could end up here, if we let them. That is not to dismiss these arguments, just that they are for another time.

I am still unsure quite why this works. If we take the real world, then somoeone who has pots of money and derives $1000 per month from it – it looks like income. Why should they not pay tax on theirs, when I have to pay income tax on mine! This is, of course, a rhetorical question, or we will be back where we started, and was the point from where I started. It takes a bit of working through to get from there to here, so thanks particularly to ryan yin for bearing with me. I have satisfied myself that there are no inconsistencies within the argument. If I wanted to challenge it, I would have to go further back into the theory.

I still don’t see why the changing inequality is a huge issue per se. If I always think apples are better than bananas, and you the opposite, then we should trade. This would lead to huge apple inequality (I would have them all) and huge banana inequality (you have them all). Does this mean I should be mad that you have all the bananas? That seems like more of a feature than a bug — we are better off precisely because I traded my bananas for apples. So if I prefer stuff today way more than you, then why shouldn’t I also trade some of my future stuff for some of your current stuff? Isn’t that trade also the whole point?

Or to put it another way, suppose we start with the same amount of money and we face the same prices and we get the same return on investing. Then in a lifetime sense, we have exactly the same wealth — in other words, we have the exact same lifetime options. If you choose to invest more than I, you will have more stuff in the future, but this isn’t actually inequality of wealth — it’s just that you were more willing to give up future stuff than I was. In that case, both of us made the right decisions and we were equally wealthy.

My revolution talk was meant to be tongue in cheek – a result of some having nothing and the rest being infinately rich may lead to revolution. It is only an illustration that the “bad” outcome of extreme inequality has a bad outcome for everybody. This is in the model world, which exists in our heads only to exagerate outcomes to illustrate points.

People tend to have less problem with inequality itself than with being on the “wrong” end of it. Thus people do not give their money away when they have more than average, but would willingly take it if offered.

In our imaginary world, we could see that the inequalities could be very rapidly amplified. We could also see that these inequalities could be addressed by transfering some money from the saver to the spender at the start. I could see a problem arranging that payment. This is because to “desired” outcome is to ensure that everybody saves. However, why should you pay me just because my outgoings are higher? At what rate? What if you pay me enough to save, but I go and spend it anyway? These are not un-solvable issues, but not trivial either.

However, I like the idea. If it were offered to everyone now, a tax on all capital, to be distributed equally, then no further tax on capital intertest ever, would that be popular?. In the imaginary world, you would have to be completly stupid not to invest the extra you recived, and rapidly your pot would grow.

My ponderings were I suppose about what outcomes do you get from the application of this economic theory, and do you need to do anything about it. It seems that you might possibly want to do something about capital income to prevent rampant inequality. Only one way to do this is to tax interest, but this may not be the best way.

However, I have thought of a completely different point – not thought it through fully yet, but bear with me. Is there not an economic “rule” that future is valued differently from today? In effect, we care less about our future selves than our current self. I came accross this in particular about the Stern Report on the economic costs of global warming. There was quite a discussion about the appropriate rate of discounting. If the future scone is not worth a scone, but less than a scone, perhaps we need to tax it more to tax it equally?

I think the source of your paradox is the unrealisticly high 100% interest rate, not the capital tax rate.

A) With a capital gains tax rate of 50%, none of the situations you described are eliminated; they’re just pushed back a day or two.

B) The situation you described does actually happen in the real world. People do work until they can collect enough savings to live comfortably on the interest, then they retire. It just takes thirty or fourty years of work to get there. :)

I don’t understand why “how to arrange that initial payment” is a puzzle — you seem to be assuming taxes on wealth are always possible, except at time zero. For that matter, “time zero” can just mean “just right now”, so that would seem to imply you should only tax capital today but never in the future — which, again, is the “don’t tax different goods at different rates” result.

If people really do prefer equality to money, then I’m not clear why you think we need taxation to achieve this — presumably people should give away their money when they have more than mean income, right? No fair inferring revealed preference or a “this is optimal” conclusion from the results of a political process!

I’m not sure what to take from the “revolution” argument. On the one hand, it seems like we were discussing what is optimal and now we’re discussing what is politically necessary — again the “is vs. ought” distinction seems important. And it also makes me wonder whether it’s literally true that ongoing capital taxation is really the easiest and most efficient way to avoid violence. But even that seems to be missing the point. If someone is making an argument to the effect of “we would all be better off if we had policy X instead of policy Y”, how can the argument be “well, yes, but then there is violent resistance”? Or rather, how can that be the only argument? If Y actually isn’t better than X, or if there isn’t a mutually improving alternative to X, then that seems like the argument that should be made against the policy proposal. But if the argument is purely the violence question, how can that make sense — i.e., isn’t it like saying, “yes, I would prefer this new policy, but we shouldn’t do it because eventually it will mean I kill you”? Is this like a commitment problem — e.g., the reason we should tax savings indefinitely is because those who would choose to save less than most cannot commit to refraining from confiscating savings in the future and/or violence?

Second point – the consumption does not max at 1 – it carries on rising. After 2 days they start to get more, and they keep on getting more. It assumes they value higher rates of income and leisure. The paradox arises in that after 2 weeks the consumption has risen to 500 scones a day per person, and nobody is making scones any more because the baker has retired to live on his interest.

Point 3 – the result is not optimal because it results in revolution! Bananas = scones today, apples = scones tomorrow. In the above example, if I prefer bananas, (i.e my kids have eaten the scone), I have no way of getting any apples. If you prefer apples (you can forego your scone today), then in two weeks you can have 500 bananas a day and just about an infinate number of apples. The system in this obviously too simple world results in diverging wealth, which is itself a bad result. We know it is a bad result because people prefer to have less and be equal than to have more and be relatively poor.

I have now considered the last paragraph, and yes, I see it now. In the above example, it would be much better if we could arrange for you to pay me some of your money from day 1, so I could save a bit and still feed my kids. Then we can all enjoy the benefits of the amazingly good 100% interest rate. However this still leaves us the original problem of the paradox. And quite how to arrange that initial payment.

Second, and much more importantly, I don’t see why you disagree with my claim that if you supposed that people had such preferences where they really would ever choose to stop working entirely, then such a scenario would be ideal. You say you’re creating a paradox, but I don’t see this at all. It seems like your model implies people value consumption and leisure, and that the utility from consumption maxes out around 1 scone: ok, so if in that world after 2 days they literally get everything they ever wanted, so much better for that world!

Third, I agree that some people might prefer to save more than others, and that this can generate the result that over time, stocks of wealth diverge. What I don’t agree with is why you think this is obviously bad. Think of it this way: suppose you and I both like apples and bananas, but I am always willing to trade more apples for a banana than you are. Surely you would agree that we can arrange a Pareto improvement where I eat more bananas and you eat more apples. This is what we want markets to do. So why if I say “by ‘bananas’ I mean ’scones today’ and by ‘apples’ I mean ’scones tomorrow’” would you suddenly say this is NOT optimal?

But suppose you also think there should be some redistribution from the high-savers to the low-savers. That’s possible. Ok, but we already established that the low-savers prefer (or need) consumption more in earlier periods than later periods, and vice versa for the savers (we know this from the revealed preference — by definition, a saver is more willing to forgo consumption today to get a given amount of consumption in the future). So if we’re going to transfer between them, we should do it as early as possible — that’s the consumption that “costs” the savers the least (in utility terms) and is most valued by the non-savers. That is, make a single lump sum tax at time zero on those people who would tend to save. This has the added bonus of, again, minimizing distortion — true, we would be taxing the people who save more than the people who don’t save, but for any given person we would be taxing all their goods equally. So again, even under the assumption that we want to tax savers more, it seems to turn out that we really shouldn’t tax savings.

None of this undermines the point of the scenario – to demonstrate that taxing interest breaks the tax everything equally “rule”. My concern is that it is easy to go from a proven rule in theory to assuming that it applies in the real world. This thought addresses the “they are free to make other arguments” part. Of course, given the scenario of the made up world above, it would be great if everyone could have almost infinate consumption with no work, and this is what would rapidly happen. This is, of course, impossible, so therefore the world as set up cannot exist. By creating a paradox, we are alerted to the need to question a bit deeper.

Keeping the “tax everything equally” rule bangs up against other “rules” or desired outcomes. The world above is designed to be simplistic to illustrate a point, and I am now using the same simplistic set-up to illustrate another point.

Lets say in this world there are two types of people, those who can go 2 days working without eating, and those who cannot or will not – this perhaps includes the feckless and those with small children. Those who consume all they earn will remain with a consumption of 1 scone a day. Those who managed to go without at the beginning soon have an almost infinate amount of money. You can imagine the scene: “Jeeves – throw some more money on the fire, I am a bit cold” “Cirtainly sir. How about a pay rise so me kiddies can eat more than 1/4 a scone each a day, sir?” “Cirtainly not, you have already shown that you will work for $2 a day or you would be as rich as me!” At which point Jeeves hits the master over the head with a poker.

So by keeping to this rule, we run up against other rules and rapidly end up with revolution. We increase differences in income to a point where any eventual benefit in total output is undermined by the cost of the perceived unfairness. We would rather be a bit poorer than treated unfairly (as studies of giving money to be shared have shown). This is the same point as made above several times, so I am really just repeating others. Ultimately, I suppose it is the old argument that markets are already distorted, so you need to introduce new distortions to correct for them.

My third question is perhaps most fundamental: suppose for the sake of argument that real interest rates are constant at 100% (independent of labor supply) and that no one would ever want more than one scone per day. I agree that in such a world, you’d eventually have zero work and everyone living off of interest (though I think if we wrote this down mathematically, “eventually” would be “after an infinite amount of time”). But so what? Why is that bad? It seems to me, given everyone’s implied preferences, that would be the best of all possible worlds — once we get to that point, everyone really is as happy as they possibly can be.

In other words, I agree that wealth effects make people work less, all else equal, but I don’t see why this is a bad thing per se. Being richer is a good thing, and one reason why it’s a good thing is that it allows us to have more leisure when we want it.