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Red (base) money is an asset of the central bank no? Isn't (base) red money any liability to the central bank? Since central banks hold a lot of government bonds, you could say that most of the red money is held by governments (on behalf of the people). Then broad red money would be debt.

So in simplistic terms in the falling population model with no time preference the optimal thing to do is for the young to consume everything produced by both age-groups as this will always be greater than the per capita production of a single age-group in both its time periods ?

Actually I suppose utility will be the same as long as they transfer at least the extra production produced by the older generation compared to the youngers

This is making me confused. You are right, red money is an asset of noone. You almost have to start with the stock of red money as some kind of baseline and a central bank pulling out red money would be an asset to it.

For model 2, wouldn't the interest rate be negative with green money also? When you are young you take a loan to buy a bit of output with green money. When you are old, you sell some output back to pay back your loan but since total output is lower, real rates have to be negative.

Red money just prevents you from having to have a bank to make that loan?

Benoit: "For model 2, wouldn't the interest rate be negative with green money also? When you are young you take a loan to buy a bit of output with green money."

Who do you borrow from? The only people you can borrow from are the old, but they will be dead when you are ready to repay the loan. Unless red money exists, with a negative value.

MF: "So in simplistic terms in the falling population model with no time preference the optimal thing to do is for the young to consume everything produced by both age-groups...."

No, because then the old would consume zero. Agents are indifferent *at the margin* between a *small* amount of extra consumption when young and when old, starting from a position of equal consumption when young and when old. But the U = logCy + logCo means they have diminishing marginal utility, so won't want to consume everything when young (or when old). If we instead assumed U = Cy + Co then we would get your result.

Thanks for the clarification. Looks like the time may have come when I need to find out what weird things like "U = logCy + logCo" actually mean !

Diminishing Marginal Utility. If U=log(C), then dU/dC=1/C, which is a decreasing function of C. Every extra apple you eat per day gives you less and less extra utility. So you would rather eat 10 apples every day, than 9 apples on even days and 11 apples on odd days. And 0 apples on even days and 20 apples on odd days, would be even worse. We want to smooth our consumption across time periods (and across states of the world, because insurance is motivated by the same thing).

In model 2, is a young person consuming more than an old person?

Thinking of your apples I have a trivial counter example to consumption smoothing: thanksgiving (and chinese new year and feast days generally).

On Thanksgiving I consume far more turkey and food generally than average. If Utility=log(consumption) measured daily, I should prefer to eat slightly less on Thanksgiving and slightly more every other day of the year. However, that would significantly lessen the impact of the holiday but not significantly increase my happiness on other days (my food marginal utility is pretty small most days). I think this preference is true for most humans (look at how high real consumption is in villages on festival days!). It's probably trivial though - increase the time period enough (to a year?) and the effect should vanish.

Odie: yes. Y (production per person per period) is assumed constant, and the same for young and old, and the young consume more than they produce and the old consume less.

Squeeky: Yep, diminishing MU doesn't always work. The biggest counterexample I can think of is leisure; we consume a big bunch of leisure called "retirement". Thanksgiving and Christmas might be state-contingent (date-contingent?) preferences though.

Thanksgiving is an example of a coordination problem. We don't just consume turkey on Thanksgiving, we also consume fellowship and camraderie, either personally with friends and family or symbolically by participating in a shared cultural ceremony (even if alone).

The former can only happen when everyone else is free; the latter gains its significance from its rarity.

Still, it's a fair point to make. That's why consumption smoothing is a better assumption for broader categories of goods and broader definitions of periods; here we're consuming "stuff" when "young" and "old", rather than "turkey" at "individual hours of the day."

I was thinking about this model a bit more. When the population growth is negative then lifetime utility can be maximized via transfers from the old to the young. [typo fixed NR] This makes sense for everyone apart from the first generation to have to make the transfer (who make a transfer to the young without having themselves received one).

So to get to the optimum state you need either an act of altruism on behalf of an older generation or an act of compulsion by the younger generation. A utilitarian could probably justify the latter on the grounds that all future generations benefit at thee expense of just one generation (or a few , if the transfers are phased in gradually).

Its not clear to me though why such a complex mechanism as red money would be better than just a tax and transfer model, or just a social convention that doing it this way makes everyone better off over their lifetime.

typo: "old to the young" not "young to the old"

MF: I fixed your typo.

"This makes sense for everyone apart from the first generation to have to make the transfer (who make a transfer to the young without having themselves received one)."

Good point. I missed that one. In Samuelson's model, the first generation to start money is better off too (much better off, because it gets the transfer when old but makes no transfer when young.)

"Its not clear to me though why such a complex mechanism as red money would be better than just a tax and transfer model, or just a social convention that doing it this way makes everyone better off over their lifetime."

It's not clear to me either. In a simple model like these, where everyone is identical, it should be the same either way. But it might be easier to decentralise the red money equilibrium, if individuals are different.

I think Samuelson's model is mostly about relying on forward infinity (otherwise you are just stealing from the last unborn generation and are no Pareto optimal) and your model similarly needs backwards infinity. Since it's hard to posit backwards infinity for us agents, except maybe along a flat circle, it's hard to think about a Pareto optimal equilibrium that introduces a negative value "pay it forward" reverse chain letter, right?

dlr: I tend to think you are right.

But think about a hybrid model. Like my model 1, except that x% of the people work when young and retire when old, and 100-x% study when young and work when old. Let x start out near 100%, so we get samuelson's green money model, with a small amount of red money (that we call debt). Now let x fall over time. If we ran that model in real time, would it converge to my model?

Or, let the population growth rate start out positive (Samuelson) then fall over time, and become negative. Do we (could we) converge towards my second model?

Yes, you seemingly could converge toward a red paper world, but all agents wouldn't be better off. I think you are just imposing a transfer from the first generation of agents to be stuck with the red paper against their will. So why is that more interesting than just talking about debt-as-money if it is not a Pareto optimal solution to an infinity problem? Would Samuelson 1958 be interesting if all it said was "hey, here's a model of a chain letter that would allow us all to screw a particular future generation if we canceled it immediately after giving it to them."

Side note, preventing defections seems like it would be tricky even if this backwards infinity allowed this model to be Pareto optimal. In model 1, for example, the young would be motivated to change the law about destroying red paper immediately after receiving theirs (and perhaps create an entirely new monetary regime), since unlike debt there is no one around to enforce their asset interests.

" the first generation to start money is better off too (much better off, because it gets the transfer when old but makes no transfer when young.)". Much better off but they invented a useful scheme. It's their just compensation.
Asset of noone? Maybe but asset of everyone. It's a useful scheme. It has value and so is an asset. To everyone as a network.
Musing of a humble I/O guy hoping he is not making a fool of himself...

Jacques Rene: not making a fool of yourself. In fact, that's sort of my answer to dlr.

If we imagine each person behind the Veil of Ignorance, and given the choice of being born into an economy with red money, or being born into an autarky economy without red money, they would prefer the former. You can think of the social institution of red money being an "asset" to the community in the same sense that law and language are assets. But that is a different sense of "asset" than the usual one.

Asset, like liabilities are on a spectrum. On a balance sheet, they are ranked by liquidity and its counterpart exigibility.
You can even move the dividing line. When Air Canada discovered that Aeroplan points weren't a liability to be redeemed (that is putting obstacles to their redemption so as to never pay them) but a marketing asset that could be sold... (the Milton maneuver)

Isn't the red money an asset of the central bank, in the same way green money is a liability?

There has to be some way for these red notes to get into circulation, and it seems to me that in our system a central bank expands its balance sheet by exchanging green money for privately owned assets (mostly government debt). In the green/red system it expands its balance sheet by helicoptering green money on the contingency that everyone also takes an equal amount of red money with it. Red money just represents private debt, but the only creditor in this society is the central bank.

Or am I missing something about this model?

Hmm, I see that was Benoit's question, and he came around to your view that they belong to no one, but I don't see an explanation of why. So I reread your post, and I still don't see why. In your post, a fixed stock of red paper is introduced. It doesn't say where it comes from, it just appears. You can't have a credit without a debit somewhere else.

Neil: in Samuelson's model, we can imagine a fixed number of shells just lying on the ground. People pick them up, and start trading with them. They aren't issued by any central bank. They are valuable assets, but aren't anyone's liability. Or, imagine that the shells are initially intrinsically valuable, because people like wearing them, but then fashions change, and they lose their utility as jewelry, but continue to be valued in samuelson's model.

Now imagine a negative version of that story, like antimatter. The shells are garbage, that bring the owner sadness, but you are not allowed to throw them on anyone else's land, because it will make them sad. And again suppose fashions change, but the shells retain their negative value.

"Each period the old give some of their consumption goods to the young, in exchange for the young agreeing to accept red bits of paper in exchange"

Give? Why? A model that legally prohibits destruction or disdposal of red money will also *legally enforce the transfer of red bits from the old to the young*. You can't simply wish it away - that would be like having a system of simulatenous equations that has no solution. You can write it down, but that itself does not make the solution 'exist' , even in theory.

So it IS a model of debt. :)

Ritwik: in a green money world, I give you apples, and you give me green bits of paper. You cannot take my apples without my consent; I cannot take your green paper without your consent. Neither of us is allowed to create green paper.

The red money world is exactly symmetric to the green money world.

In a red money world, I give you apples, and you take my red bits of paper. You cannot take my apples without my consent; I cannot give you my red paper without your consent. Neither of us is allowed to destroy red paper.

When I hold green money, it is not truly a liability of the central bank, aside from in an accounting sense. If I hold shells, there is no issuing bank, so the shells cannot be the liability of any bank. Instead, the green money/shells that are my asset can be consider a liability of the community that is willing to accept that money. If I counterfeit money or find more shells, I make all other users of the currency a little poorer.
So to extend this thinking to red money: my red money liability is an asset of society at large. Because I must get rid of the red money by the time I die, other people have a claim on part of my output. If somehow a ton of red money is dumped on my head, the group of everyone else will be better off because I will need to produce a lot more for other people's benefit than I would have otherwise.

louis: yep, there's a perfect symmetry there.

Nick,

"Neither of us is allowed to destroy red paper"

Ok, so I will just let the red paper be. What does it mean to say that I am not allowed to have red paper when i die? The sovereign will jail my mortal remains?

"It is against the law to discard or destroy the red bits of paper you own. You are born owning no red bits of paper, and it is against the law to own red bits of paper at your death (nasty things will happen in the afterlife). You can only give red bits of paper to someone else with their consent"

This is a system of simultaneous condistions with no solution. It is not even *theoretically* possible. That you can write something down does not prove its logical existence or truth. Again, ref my analogy with a system of 3 simultaneous equations with no solution.

And just to clarify - at all times I am talking about *logical* validity or existence, nothing even remotely approaching empirics or the historical record.

Ritwik: it is perfectly logically possible to imagine a world where there is a tabu against dying in debt to society, or even just a tabu against owning red paper when you die. There are tabus against suicide, for example, or dying without receiving the last rites.

@Ritwik:

> Ok, so I will just let the red paper be. What does it mean to say that I am not allowed to have red paper when i die? The sovereign will jail my mortal remains?

This is merely a useful way of incorporating a no-default condition into the economic model. If all debts are good, then we don't yet need to worry about risk premia.

Real life is of course not so cooperative, but that's why real life is more complicated than a back-of-napkin model. The differences raise questions about which aspects of simple economic models are applicable to a real economy, but these questions should be after we examine just what the simple model is saying.

I have a couple gripes with this, mainly that I think it's silly to say that this is not debt. I wrote it before some of these comments so let me add the addendum that taboos against suicide and last rites don't prevent anyone from committing suicide or not receiving last rites. And these actions don't carry a large material reward for going through with. But I think my post gets at the heart of the issue.

http://realfreeradical.com/2015/01/22/et-tu-nick-rowe/

Not sure how you handle legal challenges in a red money economy.

With a bi-directional monetary exchange economy a legal body can compare the value of the two goods exchanged (green money for goods) and make some ruling on the quality / quantity of each to determine if fraud has occurred - hence the set of scales often associated with the legal system.

With a red money system (buyer receives both goods and red money) it would seem that the seller is under no obligation to speak for the legitimacy / quality of either the red money or the good.

I sell you a defective car and you accept a bunch of fake red money along with the defective car. Have I committed fraud if they are equally worthless?

Frank: it's symmetric: let's ask 'I sell you a defective car and you give me a bunch of fake green money in exchange for the defective car. Have I committed fraud if they are equally worthless?'

Nick,

If I sell you a defective car (without telling you it is defective) and you give me fake green money (without telling me it is fake) then yes, both parties have committed fraud - and both can be fined by the legal system. There are legal cases of the sort where both parties in a transaction have been found guilty of fraud and faced criminal prosecution for it. Civil cases (party versus party) can become criminal cases (party / parties versus state).

It seems that in a green money marketplace, each party carries a portion of the proof that a transaction has taken place. In a red money marketplace, only the buyer holds that proof - and therein lies the asymmetry.

Does the buyer of goods have an asymmetric advantage in a legal proceeding because he holds both the good that is purchased and the means of exchange (red money)? The old saying "possession is nine tenths of the law" comes to mind.

Sorry if this rambles a bit. Just trying to get my head around all of the implications of negative money.

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