Some dilemma regarding investments and social welfare in an all bitcoin economy

[jerye]

1. Assume perfect competition (reasonable assumption for analysis before we move on to other market models, this is the status quo in bitcoins; no regulation, free market entry, etc), no firm invests (I) today unless tomorrows revenue (R) is higher than the investment.

2. Higher I in a prior period results in higher R in the next. At any I < R, firms make a profit the next period, new entrants can enter and invest some (I + small amount) such that R > I + e > I.

3. In perfect competition, I = R because both firms (or any number of n firms) will invest up to a point just below I > R.

4. Limit currency to 1 (divisible infinitely).

5. Population n and amount of total goods and services x are growing. Note that investment is not needed for either of this to grow. Someone might find a new mineral, new population = new labour, etc.

6. Because 4 and 5, then 1/n and 1/x is decreasing. Population n has to spend 1/x on goods each period.

7. Assume perfect information and n buys all x goods produced by firms.

8. Because I = R, firms investing gets a smaller and smaller balance sheet as the time period increases infinitely.

9. Knowing that, and playing the game from 1 to 8, firms hold onto their money instead of investing.

10. 9 is especially apparent if  one firm is starts out the game endowed with a significant proportion of the currency. E.g. If any one firm holds 0.9 currency (arbitrary value), there would be no way any competitor can invest and come out on top because the sum of money = 1.^*

Hence, no investment, which is needed to improve social welfare. In a one economy world with limited currency, money can't expand to attract investments so they obtain more in the next period because everyone knows in the next period, the quantity of money is the same while more n people and more x goods chase the same portion of 1.

^* Note that the current distribution of Bitcoin is also skewed with a smaller proportion holding a significant amount. Read: http://eprint.iacr.org/2012/584.pdf

No math/econ expert by any means and would love to hear your thoughts on this.

Edit:

Simple example:

There ever exists only 2 types of investments.

1) I<R. More people make this investment and crowding decreases the return until I=R and people stop investing. This is what is happening with asic investments right now.

2) I>R. Keeping the money makes more sense then investing. So these investments are never made.

The problem with a capped currency is almost all investments fall into category 2 and therefore a bitcoin only world would stifle investment.

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[Foxpup]

You're forgetting the obvious: investing is risky. No investment is guaranteed to give a positive return. In a perfect market, the price of an investment is equal to the expected return multiplied by the expected probability that it will actually deliver that return. Companies (and individuals) will invest if they believe (possibly with good reason) that a particular investment is less risky (or would give a greater return) than what the rest of the market believes.

Take Bitcoin for example. I, personally, believe Bitcoin is grossly undervalued. It has the low value that it has because most of the market believes that it is very risky, and unlikely to generate good returns. I, on the other hand, do not think it's as risky as people say it is, and that it has the potential to generate fantastic returns. So I invest in it. All other investments are bought for ultimately the same reason.

[jerye]

You're forgetting the obvious: investing is risky. No investment is guaranteed to give a positive return. In a perfect market, the price of an investment is equal to the expected return multiplied by the expected probability that it will actually deliver that return. Companies (and individuals) will invest if they believe (possibly with good reason) that a particular investment is less risky (or would give a greater return) than what the rest of the market believes.

Take Bitcoin for example. I, personally, believe Bitcoin is grossly undervalued. It has the low value that it has because most of the market believes that is very risky, and unlikely to generate good returns. I, on the other hand, do not think it's as risky as people say it is, and that it has the potential to generate fantastic returns. So I invest in it. All other investments are bought for ultimately the same reason.

Lets include investment risk in the model. Combine this risk with the fact that money will not expand the next period and you get an even stronger case for the 0.9 currency individual to NOT invest in improving goods for the next period. Why would he? The most he can get is a smaller part of that 0.1 currency left and even that is uncertain (risky).

I myself believe that Bitcoins are undervalued and so I have them. In my model above however, we use a currency (may or may not be bitcoins) as money which facilitates transactions, not as an investment tool/commodity.

[Etlase2]

9. Knowing that, and playing the game from 1 to 8, firms hold onto their money instead of investing.

This won't happen because if it does, bitcoin doesn't work. So we must distract and conflate away the issue such as foxpup has attempted to do, and throw in homerisms about how bitcoin is undervalued to encourage people to ignore the irrationality of the system.

[Foxpup]

7. Assume perfect information and n buys all x goods produced by firms.

Whoops, I missed this. This is the fatal flaw in the model. In any real economy, not all participants have access to the same information. People with access to good information can profit at the expense of those who don't, by buying undervalued investments and selling overvalued ones. I don't see how that's "conflating away the issue" or "irrational", that's just common sense. (It also allows one to put an exact price on the act of acquiring good information, but that's another story.)

[Etlase2]

This is the fatal flaw in the model. In any real economy, not all participants have access to the same information. People with access to good information can profit at the expense of those who don't, by buying undervalued investments and selling overvalued ones.

The point, my dear Watson, is that either way you are more profitable by doing nothing.

[Foxpup]

This is the fatal flaw in the model. In any real economy, not all participants have access to the same information. People with access to good information can profit at the expense of those who don't, by buying undervalued investments and selling overvalued ones.

The point, my dear Watson, is that either way you are more profitable by doing nothing.

No I'm not. If I have information that nobody else has, I am more profitable using that information to make better investment decisions than everybody else. Everyone else is losing money by lacking this information, so it is more profitable for them to try to acquire this information, assuming it is not too expensive (the cost of information is the main reason (and if you assume everyone acts rationally, the only reason) for the market being a game of imperfect information in the first place). Either way, it is most certainly not profitable to do nothing.

This model also neglects the changing value of money. Suppose a company invests in more efficient manufacturing technology, and can produce twice as many goods as a result. Since the money supply is constant, the same amount of money is now buying twice as many goods, or in other words, each unit of currency is worth twice as much in terms of goods. So even if the company has not gained any money in nominal terms by its investment, in real terms, it has doubled its wealth (along with the wealth of everyone else using the currency).

[jerye]

This is the fatal flaw in the model. In any real economy, not all participants have access to the same information. People with access to good information can profit at the expense of those who don't, by buying undervalued investments and selling overvalued ones.

The point, my dear Watson, is that either way you are more profitable by doing nothing.

No I'm not. If I have information that nobody else has, I am more profitable using that information to make better investment decisions than everybody else. Everyone else is losing money by lacking this information, so it is more profitable for them to try to acquire this information, assuming it is not too expensive (the cost of information is the main reason (and if you assume everyone acts rationally, the only reason) for the market being a game of imperfect information in the first place). Either way, it is most certainly not profitable to do nothing.

This model also neglects the changing value of money. Suppose a company invests in more efficient manufacturing technology, and can produce twice as many goods as a result. Since the money supply is constant, the same amount of money is now buying twice as many goods, or in other words, each unit of currency is worth twice as much in terms of goods. So even if the company has not gained any money in nominal terms by its investment, in real terms, it has doubled its wealth (along with the wealth of everyone else using the currency).

Perfect information and perfect competition are unlikely to economic situations though is a benchmark case necessary to analyse before moving forward into imperfect markets.

I invest x today which buys one output so tomorrow I can get double the output for which the value is y. If y < x (we both agree in nominal terms we have less money), then it is certainly better I not invest x in the first place because y = 2 output and x > y, thus x > 2 output.

Consider 2 periods t=0 and t=T. Any any real positive value at time T will hold for time t=0 irregardless of the nominal value, wouldn't you say so? If I invested 10 at t=0 and get 8 at t=T and at t=T, 8 buys me 8 goods, wouldn't that 10, I spent at t=0, if saved and spent at t=T buy me 8 goods + more?

[Foxpup]

I invest x today which buys one output so tomorrow I can get double the output for which the value is y. If y < x...

Hold it. If y is twice the value of x, then, by definition, y is not less than x (assuming positive values of x and y).

...(we both agree in nominal terms we have less money), then it is certainly better I not invest x in the first place because y = 2 output and x > y, thus x > 2 output.

Impossible. x is 1 output, remember? How, then, can it be greater than 2 output? Oh, right, because you assumed that y < x when the opposite is the case.

Consider 2 periods t=0 and t=T.

Those aren't 2 periods. Those are just three ways of writing the number zero. 0 is zero, t is zero, and T is zero.

Any any real positive value at time T will hold for time t=0 irregardless of the nominal value, wouldn't you say so? If I invested 10 at t=0 and get 8 at t=T and at t=T, 8 buys me 8 goods, wouldn't that 10, I spent at t=0, if saved and spent at t=T buy me 8 goods + more?

Uh, yeah. "Saving" 10 for a zero period of time is better than "investing" 10 and instantly receiving 8. Not exactly what I would call a good investment, though. Or a good savings, plan, for that matter. "Saving" and "investing" is generally something that you do for a non-zero period of time (at least, that's the way I do it). What was this supposed to prove, exactly?

[jerye]

I invest x today which buys one output so tomorrow I can get double the output for which the value is y. If y < x...

Hold it. If y is twice the value of x, then, by definition, y is not less than x (assuming positive values of x and y).

...(we both agree in nominal terms we have less money), then it is certainly better I not invest x in the first place because y = 2 output and x > y, thus x > 2 output.

Impossible. x is 1 output, remember? How, then, can it be greater than 2 output? Oh, right, because you assumed that y < x when the opposite is the case.

Consider 2 periods t=0 and t=T.

Those aren't 2 periods. Those are just three ways of writing the number zero. 0 is zero, t is zero, and T is zero.

Any any real positive value at time T will hold for time t=0 irregardless of the nominal value, wouldn't you say so? If I invested 10 at t=0 and get 8 at t=T and at t=T, 8 buys me 8 goods, wouldn't that 10, I spent at t=0, if saved and spent at t=T buy me 8 goods + more?

Uh, yeah. "Saving" 10 for a zero period of time is better than "investing" 10 and instantly receiving 8. Not exactly what I would call a good investment, though. Or a good savings, plan, for that matter. "Saving" and "investing" is generally something that you do for a non-zero period of time (at least, that's the way I do it). What was this supposed to prove, exactly?

Sorry, you seem to be misinterpreting a lot of these. Firstly it doesn't matter how you label 2 consecutive periods. It can be period 1 and period 2, today and tomorrow, period 0 and period 1, period t and period T, 2011 and 2012, etc. Its just a reference to 2 time periods.

For the first part:

y comes from investing x in the prior period. We both agree that the nominal value of what we have now decreases, thus the x that we had in period 1, in nominal terms would be worth more than y period 2, hence x > y. Suppose instead of using x to buy 1 good in period 1, we invest that and get y in the next period and y = 2 goods, then instead of investing x in period 1 we save it and bring it forward to period 2, because x > y (we both agree on this, the nominal value we get from investing anything is a lower nominal value next period, why? because of the limited supply of money) and y = 2 , then it follows that x > y = 2, i.e. we would be better off not investing.

Secondly,

No one said I'm investing 10 and "instantly" getting 8. I don't really get where you come across me saying non-zero period of time. Using 2 time periods again, period 1 and period 2. Both time periods can have a start and end (i.e. Jan 2011 and Dec 2011, Jan 2012 and Dec 2012, 2 time periods). At the start of period 1, we have the choice of investing 10 or saving 10. If we choose to invest, the return we get is at the beginning of period 2, the return of which is 8 (once again, we both agree the nominal value of what we are holding drops if we invest). If we choose to invest, we get 8 in period 2 which we can use to buy 8 goods. BUT what if we decided to just put the 10 into our pocket at the beginning of period 1 instead of investing it? THEN at the beginning of period 2, we most certainly still have 10 of which in period 2 can buy us 8 goods + more. This proves we are better off putting the 10 in our pocket instead of investing.

[Impaler]

Your describing how deflation reduces the incentive to invest.  The systemic effect of reduced investment is that #5 growing future goods in fact do not grow.  But this leads to a catch-22, once their is no growth the conditions fro growth exist again, and once their is growth it's very existence is self defeating.  The result is a fluctuation stop-start serious of growth spurts and growth stoppages or outright contractions which we call the 'business cycle'.

Freicoin developers are well aware of this shortcoming in BTC and have implemented a solution thought up over a hundred years ago by German/Argentine monetary theorist Silvio Gesell.  Coins simply lose face value at a modest rate of 5% a year. This changes the math of #1 to I - Demurrage < R which cascades to allow a real growth rate equal to demurrage rates.

[jerye]

Your describing how deflation reduces the incentive to invest.  The systemic effect of reduced investment is that #5 growing future goods in fact do not grow.  But this leads to a catch-22, once their is no growth the conditions fro growth exist again, and once their is growth it's very existence is self defeating.  The result is a fluctuation stop-start serious of growth spurts and growth stoppages or outright contractions which we call the 'business cycle'.

Freicoin developers are well aware of this shortcoming in BTC and have implemented a solution thought up over a hundred years ago by German/Argentine monetary theorist Silvio Gesell.  Coins simply lose face value at a modest rate of 5% a year. This changes the math of #1 to I - Demurrage < R which cascades to allow a real growth rate equal to demurrage rates.

I recently came across Freicoin and demurrage. Extremely interesting concepts. Couple of question though;

1. Why would any reasonable merchant/seller/firm accept currency for their goods and services if it is common knowledge? Wouldn't they rather have currency that stays the same in face value or even goes up in face value?

2.  Is the supply of Freicoin limited as well? Can't seem to find this on the wiki/site.

[Foxpup]

Sorry, you seem to be misinterpreting a lot of these. Firstly it doesn't matter how you label 2 consecutive periods. It can be period 1 and period 2, today and tomorrow, period 0 and period 1, period t and period T, 2011 and 2012, etc. Its just a reference to 2 time periods.

It does matter when you label them the exact same thing. If t=0 and t=T, they're all zero. t=0 means t is zero. It doesn't mean anything else. t=T means T is the same thing as t, which is also zero.

For the first part:

y comes from investing x in the prior period. We both agree that the nominal value of what we have now decreases, thus the x that we had in period 1, in nominal terms would be worth more than y period 2, hence x > y. Suppose instead of using x to buy 1 good in period 1, we invest that and get y in the next period and y = 2 goods, then instead of investing x in period 1 we save it and bring it forward to period 2, because x > y (we both agree on this, the nominal value we get from investing anything is a lower nominal value next period, why? because of the limited supply of money) and y = 2 , then it follows that x > y = 2, i.e. we would be better off not investing.

But you can't use x to refer both to "what you invest" and "what you would have if you didn't invest", if x increases in value if you invest and does not increase in value if you don't. They're two different quantities.

Secondly,

No one said I'm investing 10 and "instantly" getting 8. I don't really get where you come across me saying non-zero period of time. Using 2 time periods again, period 1 and period 2. Both time periods can have a start and end (i.e. Jan 2011 and Dec 2011, Jan 2012 and Dec 2012, 2 time periods). At the start of period 1, we have the choice of investing 10 or saving 10. If we choose to invest, the return we get is at the beginning of period 2, the return of which is 8 (once again, we both agree the nominal value of what we are holding drops if we invest). If we choose to invest, we get 8 in period 2 which we can use to buy 8 goods. BUT what if we decided to just put the 10 into our pocket at the beginning of period 1 instead of investing it? THEN at the beginning of period 2, we most certainly still have 10 of which in period 2 can buy us 8 goods + more. This proves we are better off putting the 10 in our pocket instead of investing.

Not if the real value of the currency increases. In that case, the 8 you get by investing can be used to buy 16 goods (because the currency increased in value as a result of the investment), as opposed to the 10 you get by not investing which can only buy 10 goods (because, by not investing, the currency did not increase in value). 16 goods are better than 10, last time I checked.

[Impaler]

1. Why would any reasonable merchant/seller/firm accept currency for their goods and services if it is common knowledge? Wouldn't they rather have currency that stays the same in face value or even goes up in face value?

Ideally demurrage currency is stable in the sense that prices do not gradually rise so demurrage is the only thing causing money to lose value (the value loss is entirely by nominal loss rather then inflation loss), as most economies typically have inflation of 2-5% this is no worse for the merchant then the current monetary paradigm.  Second their would still be bank deposits that pay interest of a few percent which manifests as subtracting from demurrage, so a short term deposit might be net 3% demurrage and a savings account just 2% and most people will naturally use these accounts when they want to save.  Third most businesses have a high turn over of their cash so transaction fees have a much larger impact on them then dose demurrage, our implementation will pay miners from demurrage thus keeping transaction fees to a minimum.  Third demurrage lowers interest rates meaning loans can be very near zero (in practice their would be a risk premium which is legitimate), and merchants can thus finance their business by a low interest loan and will naturally need to acquire FRC to repay it with.  The merchant also dose not suffer from increased cost of overhead burden, if things like salary and rent are payed for in denominated in deflating currency then all these costs are constantly growing.  Lastly the potential customer no longer has a death-grip on the coins, in fact they want to spend them so the merchant isn't forced to constantly undercut and race-ahead of the current deflation by offering an even lower price such that the customer is finally induced to buy (their are BTC merchants adopting that strategy right now), when merchants do this they are forced to hold coins themselves waiting on deflation so they can sell them for enough to cover their costs.  This slows down commerce and drives yet more deflation as coins are removed from circulation and velocity drops.

2.  Is the supply of Freicoin limited as well? Can't seem to find this on the wiki/site.

Yes the current protocol is for a stable 100 million coin base, but we reach it quickly in just 3 years because we have no need to stretch it out for eternity as BTC dose and we really want to know what happens when a coin base stops growing, it's literally never been done before.  Now we have some some theories on what will happen if demand continues to grow after that point, one possibility is that velocity of money goes up to accommodate the higher level of goods being exchanged, but it might also happen that we see deflation emerging, though we expect it would never be as high a deflation rate as seen in BTC.  Possible solutions range from simply forking to create more coins, or my personal preference creating a futures-market like mechanism inside the protocol that manages money supply in a distributed fashion, much like how difficulty is controlled now.  As users buy futures with present coins they indicate the predicted future value of coins and volume is increased or decreased in a compensatory manor.

[jerye]

It does matter when you label them the exact same thing. If t=0 and t=T, they're all zero. t=0 means t is zero. It doesn't mean anything else. t=T means T is the same thing as t, which is also zero.

This is how I meant it to be:

https://i.imgur.com/FmpcmeO.png

But you can't use x to refer both to "what you invest" and "what you would have if you didn't invest", if x increases in value if you invest and does not increase in value if you don't. They're two different quantities.

I have 10 in my pocket now. Let 10 = x. If I invest 10, I invest x. If I didn't invest the 10, how much would I have? 10, which is x.

What I invest = 10
What would I have if I didn't invest? the 10 in my pocket.

Is 10 = 10 not the same quantity? Is there something wrong with this assumption? Sorry I'm not getting where you're coming from.

Not if the real value of the currency increases. In that case, the 8 you get by investing can be used to buy 16 goods (because the currency increased in value as a result of the investment), as opposed to the 10 you get by not investing which can only buy 10 goods (because, by not investing, the currency did not increase in value). 16 goods are better than 10, last time I checked.

Even if you didn't invest, population grows (unreasonable to assume we can stop this), your 10 is now worth more in real terms of distribution of income. In this case, the 8 I used to hire 16 singers in the next period to sing to me, is most certainly less than the number I can hire if I kept the 10.

Appreciate the comments

[Foxpup]

I have 10 in my pocket now. Let 10 = x. If I invest 10, I invest x. If I didn't invest the 10, how much would I have? 10, which is x.

What I invest = 10
What would I have if I didn't invest? the 10 in my pocket.

Is 10 = 10 not the same quantity? Is there something wrong with this assumption? Sorry I'm not getting where you're coming from.

Wrong. If you invest 10 in something that increases the value of the currency (ie, something that makes goods cheaper, such as a more efficient manufacturing process), then that 10 (in nominal terms) is suddenly worth more than 10 in real terms, eg, if the value of the currency doubles, it is worth 20 in real terms. Let us postulate two alternate universes, Alternate Universe A, in which your investment increased the value of the currency, and Alternate Universe B, in which you didn't make that investment, and so the currency did not increase in value. $10 from Alternate Universe A are certainly not the same as $10 from Alternate Universe B if dollars from A are worth more than dollars from B. I honestly can't help you if can't figure that out.

[Impaler]

A single investment can not possibly have such an effect as to cause a shift in the total value of money, that's only the result of the cumulative effect of all investment the overwhelming majority of which are outside any one investors control (unless your now in favor of communism).  From the perspective of the individual investor the value of money is the same if you make or do not make the investment, it is thus a classic tragedy of the commons ware the individual incentive is to do the 'wrong' thing from the wider group perspective.

[Foxpup]

A single investment can not possibly have such an effect as to cause a shift in the total value of money, that's only the result of the cumulative effect of all investment the overwhelming majority of which are outside any one investors control (unless your now in favor of communism).  From the perspective of the individual investor the value of money is the same if you make or do not make the investment, it is thus a classic tragedy of the commons ware the individual incentive is to do the 'wrong' thing from the wider group perspective.

The increase in the value of money happens not because investors are deliberately trying to bring about that effect, but simply as a natural consequence of them trying to increase their own wealth by investing (the invisible hand strikes again). Companies invest in means of increasing their own production, to sell more goods. As best as I can tell, what jerye is trying to prove is that because the same supply of money is buying the same supply of goods, there is no increase in value to be had anywhere, and therefore investing is pointless. But increasing the supply of goods while the supply of money remains the same increases the value of money (because each unit of currency can buy more goods), and that's why investing can produce a net increase in value (not that it always does; I initially got sidetracked by that point).

[Impaler]

Foxpup:  Way to completely miss the point and state the obvious, I never said investments don't increase the volume of good.  IT DOSE.  My point that you completely failed to respond too is that the individual investor is not large enough to change the volume of goods or the value of money by anything but a trivial amount.  For the individual the state of the rest of the economy is independent of his actions, if deflation is going to happen regardless of what you do then you act accordingly and only invest if your future revenue exceed the investment in NOMINAL units.  You do not invest $10 to get back $6 of money that has doubled in value (for a effect $12 of spending power), you would just have been better off holding the original $10 which would double to the equivalent of $20.

[jerye]

bump