Optimal Currency Values

[phillip1882]

for the purposes of this discussion, we'll assume a fiat currency, where you can put any whole number value on a bill.

let's say there's a government proposal to have 1 billion dollars in circulation, and the government has tasked you with setting the denomination values.

on your own initative, you want there to be the minimal amount of currency, while giving everyone the maximum ability to trade with it.

for the purpose of this problem, you can assume 1 milion people.

what currency values do you choose?

how much of each currency value should there be?

 

 

 

my own aproach would be the following

1, 3, 5, 9, 15, 25, 41, 67, 109, 177.

the idea is that as long as each side in the trade has roughly phi of the numbers in the sequence, any value can be achieved.

as for how many of each currency, i would do the following.

 

30,041,024  3
18,566,374  5
11,474,650  9
7,091,724  15
4,382,926  25
2,708,797  41
1,674,128  67
1,034,668 109
639,460  177

 

with 1 getting the rest.

 

 

[ErlyRisa]

Without looking at the spoiler the answer is dependant on what people value the most.

 

eg. The price of a carrot. Vs. 24 Carrot Gold.

The denomination for alot of carrot exchanges is very low if that's what the populous trades in, if they would rather eat gold though, then the denomination would be higher.

 

Accounting for both transactions being of equal rates of exchange means that there is an answer. ie. Just as many people exchange carrots as gold.

 

So then lets say Gold exchanges are typically $100 per transaction, and carrot is $1 per transaction.

The answer is easy (minimising volume of currency while keeping exchange rates high) ...but if some-one invents a carrot that no longer needs to be bought fresh and say CostCo starts to sell carrots by the barrel - 100 carrots for $100 then the need for loose change drops.

The problem is that through an apathy of the populous to eat fresh, and the technological advancement that CostCo provides...exchange rates drop and we would only need $100 bills.

 

Because exchange is what drives an economy: CostCo has now slaughtered the fresh food market by being competitive -- providing more with less overheads, but because CostCo needs more exchanges once they have obliterated the competition, they begin to try selling 200 carrots for $200. They also try to make the populous eat their carrots faster, and hence begin advertising that the more carrots you eat the better you will see. The populous now gets fatter as a byproduct of CostCO wanting to be profitable, and now the populous watches more adverts about carrots and being able to see the adverts better to the point that they are too tired too go shopping annually for 200 carrots they start to shop for 1000 carrots at a time. The populous now goes shopping even less while being proud of the fact that they can see the advertisements from CostCo better.

 

CostCo(Dumbie) the governement(Lawyer) and advertiser(Pschologist/Lawyer) (That live off of the people digging the Carrots out of the ground for $0.1ea. and would rather eat Gold than to be caught with a carrot in their mouth (of course said Carrot cultivator is only paid by the 10 carrot load ie. $1 per transaction)), end up selling not so high quality carrots: The populous is getting fat and just tear the carrots out of the ground...so now the Upper echelon of society only employ those that are thin and don't buy Carrots annually because they were imprisoned for stealing 3 Carrots from CostCo farm lot B. These prisoners have been eating carrot soup in prison with added laxatives, and have been taught that Carrot soup is the Food of the Gods (Lawyer bunch), so once they leave prison they actually learn to make special carrot soup themselves straight from the farm, negating the need to pay these people, and keeping them thin (the special ingredient - laxative is supplied for every 24th carrot they dig). Now there are 3 tiers in soceity, those that transact in 24 Carrot gold, those that transact bi-annually and consume as much as possible, and the ex-cons that are supplying quality carrots while CostCo no longer has to pay $0.1 per carrot, rather it only costs them fools gold in farming capability.

 

The 24 Carrot gold investors now start learning alot more about the environment (b/c they have so much spare time on thier hands, and they don't see as well as the major part of the populous, and hence don't waste thier time watching adverts). The ones eating gold realise they would like to live longer for some strange reason (They all go to Gold Members, utilising ex-con's daughters as waitresses or dancers - b/c the average part of the population is too fat anyway). So they learn biology and the so forth, too extend their lives. It turns out once they have learnt the phlisophy of science that inorder to have conclusive proof you need to run experiments. At first they start too experiment on lowly Rabbits...but because the entire human population is addicted too carrots, Rabbits are in short supply: Now they switch over too experimenting on the Fattened part of the population...Those that have the least amount of external variables can be place into unwitting experiments the best, they do nothing all day but eat carrot and watch advertisements...maybe it would be possible too demonstrate that if we split the Fat portion of society into two groups and factionalise them we could run the experiment.

 

Some experiments on the table:

Can I convince a person to live for less or more time, just by utilising the advertisements?

Can I convince a person to do something for me, that is very specific? (Loose weight and become a dancer at Gold Members)

Can I convince the factions too war against each other in the hope that they get too Visit Gold Members just once in their lifetime?

Can I rear a survival of the fittest scenario in which I enjoy more of the Blue eyed dancers at Gold Members?

 

An accountants family at CostCo has a daughter that used to work for Gold Members, but was fired for not using a clean carrot during her dance routine, she now has distain for the world and starts to talk about the state. She starts simply by talking alot, but soon learns that if you use a carving knife you can turn carrots into a printing press, she names it the HeinieGold Print press and starts printing discident material and selling it for $0.1ea.

 

DO YOU SEE THE PROBLEM: There is NO 10 cent coin - only $100 dollar bills now.

In other words the HeinieGold Print press never gets made, because the value of her work would never reach $100 per transaction: Which is the base amount now...and the only people that can exchange are those that are in power.

 

...But Babs is determined (The Accountants daughter)

 

She used to service an ex-con lucky enough to get Free nights at Gold Members, b/c he was very thin and very fast at picking quality carrots. This ex-con taught Babs how to make Carrot soup, and it occurs to Babs that she can help the fat people simply by promoting Carrot soup.

 

The fat people get thin, end of story: Everyone works at Gold Members for free - and we have eternal youth and everlasting life too boot.

 

OR DO WE?

 

Laxatives turn out to be priceless.

 

Now CostCo gets word the populous is paying ex-cons for special Carrot soup: The governement outlaws Carrot soup, but it's too late, CostCo knows the mind of the consumer and starts selling Laxatives (Special Carrot soup Spice) at 24pills for $24. All of a sudden loose change is in over supply, and people start putting away money in Jars. Soon a thin scientifically apt x fatty learns how to make Laxatives by utilising all that spare change he/she has saved, and starts a business selling 100pills for $24. Everyone gets thinner and thiner and smarter and smarter, to the point that Laxative production is done by the common man, and is unsellable:

Now people still buy Carrots from CostCo, but also have laxatives, and therefore the Value of a daughter working at Gold Members drops, so much so that those that were trading in Gold no longer find being just one of the average part of the populous interesting because the value of it isn't there. (The Gold Traders existence is based on the fact that they are in power and different too the plebs) Gold Traders try to take back the extravagance of their lifestyle by promoting other things: It occurs to one of the gold Traders that Bannanas grow on trees, so he develops a powerpoint presentation for a meeting at CostCo. The meeting goes well and Bannanas are all the craze. Now the populous gets fat again: but at a lower rate, b/c they still eat Carrot soup on special occasions (The Annual CostCo sale).

 

The person that invented backyard Laxative production is heralded by the media for being the first too create Laxatives.

 

Now the populous also want to be like the Laxative inventor, and start to play with Bannanas.

Finally after 10yrs of research and funding a monkey figures out how to peal a Bannana.

In the next couple of years, thier is a Carrot famine b/c everyone wants Bannanas , so crime goes up, and one specific style of crime is leaving bannana peels at CostCo and inadvertantly slipping on one, and suing the company for damages. Now more lawyers are needed again (The Gold traders)...but this time the lawyers are willing to work for Bannanas.

 

LOL I could keep going with this...I was thinking Coconuts - but thier are too many variables now.

 

On the whole the answer is in the Total annual wage amount for the Fat people.

If the exchange rates are slow than wage amounts drop, so exchanges get closer to integer amounts, which becomes a self perpetuating decline in exchanges. (less change) The higher the wages are kept, the more choppy the exchanges become ...eg. using Pyschology too promote cheapness of an item based on numerology (29.99 type stuff) , hence more change.

 

Switching over too full digital money means all the exchanges turn into time based alotments. ie It is more perceived by the Gold Traders that THIER time is money: They don't care about the price, and they Don't waste their time at CostCo, they just want to make sure that Gold Members has valued dancers that are worth their time to be their. Gold Members would end up switching over to a system where we would be trading in time absolutes: ie. The carrot would be priced according to it's enjoyability like lobster rather than its sustenance capability.

 

It's a scary time we may be leaving for the future generations...because the dancing girl will not be valued according too carrots, the dancing girl may have todo more extravagant things that have perceived value by those that are always strapped for time and find that thiers is more precious than others.

 

ie. The mentality that Royalty lived with (worth of the Jester) is now common place. (Internet Based advertising taking on the same format as TV based advertising, the laxative is the internet itself, 3D printing is the new Banana, The real life based nude dancing place is dropping in value b/c the internet is laden with it for free - the only thing worth my time now is bestiality or something illegal/extravagant , either via the internet or to have performed/witness the extravagant state myself)

 

I would rather be playin with the 3D printer: but I now from the very inception of the common place of this device that peeling bananas at a restaurant is more profitable than wasting my time doing Autocad drawing for people that are not going to pay me in the same/similar time allotments that the Lawyer gets away with, just because I wanted to sit at the restaurant with a plate of bananas. So the best thing todo is too start selling my body: I enjoy it, and its a fair exchange of my time vs. your time.

Edited January 25, 2015 by ErlyRisa

[Racoon]

The obvious question is how do you back the currency??

 

 

None othe Math equations mean a damn thing if you can't back it up with something.. ie Silver, Gold, or Deer/Beaver Skins..,

 

 

It all depends on where you are at.   In the Gold Rush era of 1849-1860 there were many forms to pay off a debt.  

Edited January 25, 2015 by Racoon

[CraigD]

This is essentially a numeration problem, and a fun one. :thumbs_up

 

I’ve no done any rigorous proof or exhaustive brute force calculation, but sketching get this answer:

 

The solution is optimal when each denomination is the same multiple of the next lowest denomination, starting with 1 (for example: 1, 10, 100, 1000 … 100000000 (10⁸) and when the multiple is the smallest integer greater than 1 (that is, 2). So the denomination should be 1, 2, 4 … 536870912 (2²⁹).

 

The probem is simpler if we assumption that rather than $1000000000 in circulation, there is 2³⁰ = 1073741824.

 

If there’s only a single person, then number of “coins” of all denominations needed is only 30, one of each denomination. If there are the given 1000000 people, the largest denomination needed is 512, and 1000000 coins of each denomination are needed, for a total of 10000000 coins.

 

Larger denomination multipliers require larger numbers of coins. For a multiplier of 10, for example, 27000000 coins would be needed.

[Racoon]

OK Craig... You solved the math of it... But how do you supply the actual Metals and Coinage of it??

The Blacksmith work of it, and keep it in line with whichever King demandeth??

[ErlyRisa]

Wait...is it number of coins or number of denominations?

 

I understand the aim is to have as little cash as possible; to save on having to have too provide through the mint.

Those that are trading in high volume absolutes eg. Gold are not a part of the equation.

Those that are trading in base absolutes (carrots) are the ones that trade with the intermediary system called coins and notes.

True that the Gold Trader on the occasion utilises a Carrot trader for a Taxi ride, or a Tailor for a nice suit. But if the main commodity is carrots or in the modern world may one day be oxygen (life) then the price of a carrot is based on how many of the carrot exchanges are done per time frame. ie. More Carrots exchanged the more of a price drop there is and the lower the tax rate per exchange, (Tax: The Gold Exchanger taking/skimming off of the average portion of the populous that are happy with carrots - and are promised everlasting life or a retirement villa in Florida via those Tax dollars so that the carrot munchers can continue trading in carrots through to old age, and maybe behave like rabbits producing more of the little carrot munchers). which in effect the Gold Trader wants a higher population so that the value of exchanges is low enough for his meager exchanges to take precedent in time (The more carrot traders the Gold Merchant is working with, the higher the value of his gold).

ie. The Gold Trader stays in power simply by adjusting what is necessary, so that his state is always in power over the lowly carrot traders.

 

Say there was somesort of wierd economic model where everyone born to the earth was completely satisfied being nothing more than a rabbit and ate nothing but carrots: Gold is not valued. Then we may proceed todo math...sort of: Rabbits nibble at carrots, and some smart arse may start taxing the rabbits per nibble (or bites).

 

Say typical carrot consumption is done in four bites. Those that do it faster in 2 bites would have spare time on their hands, and come up with a method to dig for more carrots even faster. Or they may do more of the Rabbit Warren type stuff instead (fluffy bunny bedroom past-time). There is always going tobe some-one that will utilise that typical loop that people get into and use that to its advantage. Fairness isn't the issue its a survival of the fittest thing - the 2 bite per carrot person is bored and therefore thinks. The 2 bite per carrot person will also try to promote eating and savouring carrots in 8 bites, and taxing the 8th bite as it's method of reward, therefore having its carrots pre-bitten and not having too have to chew the carrot itself. The smallest possible denomination is 1 bite, while its the samrt rabbit that procured the state of exchanging in 8 bite alotments per carrot...because there would be alot of 7bite and multiples of 7 exchanges, there may end up being a need for floating the point of exchanges...and this is based on how large the rabbit population is and how often they exchange amongst themselves without sacrificing the eighth bite. Some rabbits may do 3 bites or 6 bites leaving bites to be taxed in 2s and 1s.

 

Sooo to keep the least amount of carrot nibbles in population is also based on the typical dietary intake of the rabbit. If a rabbit gets full at 2 and half carrots then it used 6bites as a typical, or 12 bites as a savoury rabbit. The dietary intake is the same...the denomination is different, based on a smart arse teaching the Rabbits too savour thier carrots.

 

Therefore the smaller the denominations...the more transactions that are procurred and the longer it takes to digest your carrot.

 

If you had an automated carrot cutter that sliced your carrots into bite sized portions, then you would switch over too exchanging the value of water or dirt to grow the carrot.

 

Denominations and the practicallity of what fits into a bunnies wallet.

A whole carrot is better than bites or nibbles. But what is the bite of a carrot being exchanged for?

If bunny bedtime is charged by the nibble then carrying a whole carrot maybe unnecessary.

If inflation sets in and the female bunnies want bigger longer lasting carrots, then you would have to carry larger denominations. eg. In my case I need 8 carrots in order to get around on the town for one night.

[CraigD]

OK Craig... You solved the math of it... But how do you supply the actual Metals and Coinage of it??

I wouldn’t claim to have solved it, but think I’m on the right track.

 

We should leave it to Phillip to say for sure, as he created the problem, but I think this is purely a math puzzle using money to make it more readable, not a question about practical economics – hence, it’s in the Math, not the Economics, forum.

 

Note that my optimum scheme of denominations $1, 2, 4, 8, 16, 32, 64, 128, 256, 512 is very impractical. It calls for there to be only 1000000 coins of each denomination. This means that, at any given time, there may be several people with no $1 coins, and only few people with 2 or more $1 coins. Before a person with no $1 coins can pay another person with none $1, they must find, a person with 2 or more, and exchange a $2 coin for 2 $1 ones. If we imagine ever body in this world to be in a typical city of 1000000, this might take hours, and require talking to thousands of people, or employing many agents to do so. Describing how this could be done is a fun math puzzle, too. :)

 

Wait...is it number of coins or number of denominations?

Again, it’s Phillips problem to state authoritatively, but I interpreted his “you want there to be the minimal amount of currency, while giving everyone the maximum ability to trade with it” to mean you want the minimum total number of coins that allows an exchange of any amount, from $1 to $1000000000, to be possible.

 

The problem is trivial if you just want to minimize the number of denomination of coins: you only need one denomination, $1. The total number of coins, then, is the maximum, 1000000000, 100000 times more than the optimum solution I gave.

[Buffy]

None of the analysis so far takes into account those massive piles on coin trays that you guys seem to like to build.

 

My rather limited perusal of such piles indicates they're heavily weighted toward the smallest denominations, thus are most frequently "out of circulation" creating a shortage thereof.

 

Strange fact: did you know that the $100 bill makes up 80% of the currency in circulation (by amount, not count).

 

My theory would seem to be validated by this data on circulation of US money: (which is very out of date, 1997, but I'm too lazy to find more recent stats):

 

 

 

Source: Peter Y. Chou, wisdomportal.com

 

 

Yep. Pennies.

 

 

The easiest way for your children to learn about money is for you not to have any, :phones:

Buffy

[phillip1882]

though i created the problem, i'm uncertain of the answer. i have a few ideas, but in general you need more 1's than the next currency up, and more of that currency than the next highest one, and so on, to ensure change can be made with any currency.

for example, let's assume that the powers of 2 are the correct denomination. even only limiting yourself to a maimum of 512, you can't really assign 1,000,000 of each currency. you have to assume there will be imbalances in the market. not everyone will have 1 of each currency. the most productive members will have the most currency, and the least productive will have the fewest.

[ErlyRisa]

Donot Read waste of brain cells:

 

Does Bitcoin (I have never touched it) use multiplier place holder coins?

 

eg. 1 Carrot TIMES a ZERO Carrot = 10 Carrot value.

 

of course this doesn't work b/c we would all want alot of Zero Carrots.

 

But in Binary if you agree to exchanging in sets of coins then denominations would be placeholder values rather than the value itself.

 

eg. 2nd bit value = 2 carrots , 3rd bit value = 4 carrots, 4th bit value = 8 carrots. You now only have 4 denominations and can do hex.

but an agreement has to be made that you have to trade in nibbles.

 

Or in decimal...

 

You have to trade 2 coins in very transaction. meaning the largest trade is $99 and there would be 10 denominations. (0-9) and the order that the coinage is handed over is recorded, eg. 3 and 8 = $38, 8 and 3 = $83

 

Yeah I know: I'm deluding myself. $100 note is the placeholder.

 

but in somesort of advanced techno world where cash welds itself together, eg. a 30 note and a 08 = a 38 note , and if you want to pull the 08 out of the 30 then unwelding of the note would be possible.

ie. In this system there would be denominations of only 0-9 and the welding of notes would be recorded in every transaction. (ie all notes in your wallet would have a paperclip holding them together in pairs, denoting thier decimal value upto 99 , then pairs can be welded again into fours to denote what notes you have accrued, eg. $67 = $60pair + $07pair)

eg. 5267 dollar bill is accrued by working for:

 

1of 07

1of 60

1 of 200

1 of 5000

 

the $200 dollar bill would have been welded from 99+1 x 2 transactions (2 paper clips)

the $5000 dollar bill would have been welded from 99+1 x 50 transactions. (50 paper clips)

 

This is a Total of 54 transactions -> 52 of which were done on a weekly basis ($100 dollar wage - 2 notes), and the first 2 of which are a xmas bonus ($67)

 

The problem is shopping with a $5267 dollar bill. If you bought something for say $3 , Then tender would have to be $5264: The change would need a minimum of 53 transactions if the till is only made of notes from below the $100 dollar range. (a typical shopping experience would include alot of paperclips)

 

The solution for the till operator would be to be able to switch welding. (Going to the bank for bigger denominations - for headache customers that always pay with large denominations)

 

Being able to unweld a large denomination without using a bank would be very handy:

eg. $5000 bill can be turned into denominations necessary to fill the till.

 

You could end up selling paperclips as a commodity too cash register owners - eg. $5000 could be split by going too a paperclip dispenser that charges $01 per paper clip...you buy 50 paperclips to turn your $5000 into 49 $100 notes and 1 $50 note. The note automagically dissolves into the lower denominations as soon as you start placing the paperclips onto it.

 

Of course there is never a "maximum" placeholder note ($100 - is actually 99+1 pair $1000 is 999+1 pair), much like 16decimal in hex is 16thnibble + 1stnibble....but as numbers get larger we switch to floating point representation, but in reality the floating point representation is always converted too tinyint's for tangible tender.

Edited January 26, 2015 by ErlyRisa