Can We Stabilize the Price of a Cryptocurrency?: Understanding the Design of Bitcoin and Its Potential to Compete with Central Bank Money

Abstract

This paper discusses the potential and limitations of Bitcoin as a digital currency. Bitcoin as a digital asset has been extensively discussed from the viewpoints of engineering and security design. But there are few economic analyses of Bitcoin as a currency. Bitcoin was designed as a payments vehicle and as a store of value (or speculation). It has no use bar as money or currency. Despite recent enthusiasm for Bitcoin, it seems very unlikely that currencies provided by central banks are at risk of being replaced, primarily because of the market price instability of Bitcoin (i.e. the exchange rate against the major currencies). We diagnose the instability of market price of Bitcoin as being a symptom of the lack of flexibility in the Bitcoin supply schedule ‐ a predetermined algorithm in which the proof of work is the major driving force. This paper explores the problem of instability from the viewpoint of economics and suggests a new monetary policy rule (i.e. monetary policy without a central bank) for stabilizing the values of Bitcoin and other cryptocurrencies.

Full text

Discussion Paper Series A No.617
Can We Stabilize the Price of a Cryptocurrency?:
Understanding the Design of Bitcoin and Its Potential to
Compete with Central Bank Money
Mitsuru Iwamura
(Graduate School of Commerce, Waseda University)
Yukinobu Kitamura
(Institute of Economic Research, Hitotsubashi University)
Tsutomu Matsumoto
(Faculty of Environment and Information Science,
Yokohama National University)
and
Kenji Saito
(Keio Research Institute at SFC, Keio University)
November, 2014
Institute of Economic Research
Hitotsubashi University
Kunitachi, Tokyo, 186-8603 Japan

1


CanwestabilizethepriceofaCryptocurrency?:
UnderstandingthedesignofBitcoinanditspotentialto
competewithCentralBankmoney

MitsuruIwamura,YukinobuKitamura, 
TsutomuMatsumotoandKenjiSaito
October25,2014

Abstract
ThispaperdiscussesthepotentialandlimitationsofBitcoinasadigital
currency.Bitcoinasadigitalassethasbeenextensivelydiscussedfrom
the viewpoints of engineering and security design. But there are few
economicanalysesofBitcoinasacurrency.  Bitcoinwasdesignedasa
paymentsvehicleandasastoreofvalue(orspeculation).Ithasnouse
bar as money or currency.  Despite recent enthusiasmfor Bitcoin, it
seems very unlikely that currencies provided by central banks are at
riskofbeingreplaced,primarilybecauseofthemarketpriceinstability
ofBitcoin(i.e.theexchangerateagainstthemajorcurrencies).  We
diagnosetheinstabilityofmarketpriceofBitcoinasbeingasymptom
ofthelackofflexibilityintheBitcoinsupplyschedule‐apredetermined
algorithminwhichtheproofofworkisthemajordrivingforce. This
paper explores the problem of instability from the viewpoint of
economics and suggests a new monetary policy rule (i.e. monetary
policywithoutacentralbank)forstabilizingthevaluesofBitcoin and
othercryptocurrencies.
Keywords:Bitcoin,Cryptocurrency,Currencycompetition,FriedrichA.Hayek,Proofofwork. 
JELclassification:B31,E42,E51

MitsuruIwamuraisaprofessorattheGraduateSchoolofCommerce, Waseda University
(Address: 1‐6‐1 Nishi Waseda, Shinjuku‐ku, Tokyo 169‐8050, Japan) Yukinobu Kitamura is a
professor at the Institute of Economic Research, Hitotsubashi University(Address:2‐1Naka,
Kunitachi‐shi, Tokyo 186‐8603, Japan), Tsutomu Matsumoto is a professor at the Faculty of
Environment and Information Sciences, Yokohama National University (Address: 79‐7
Tokiwadai, Hodogaya‐ku, Yokohama, Kanagawa, 240‐8501, Japan) and KenjiSaito is a visiting
seniorresearcheratKeioResearchInstituteatSFC,KeioUniversity (Address: 5322 Endo,
Fujisawa‐shi,Kanagawa,252‐0882,Japan).Addresscorrespondencetokitamura@ier.hit‐u.ac.jp


2

1. Bitcoinasavirtualregistrysystem

Circulation of Bitcoin 1 as digital asset is guaranteed by
authenticationprocessbetweentraders.Thisprocessconsistsof both
anasymmetrickeycryptosystemandbycompetitionbetween
coin‐releasing‘miners’whovalidatetransactionstopreventdouble
spendsbytraders.Itisimportanttorecognizethatitisoperationally
feasiblefortraderstoauthorizetransactionsbymeansofadigital
signature,basedonaasymmetrickeycryptosystem.Itisbyfarmore
difficulttovalidatetransactionsofBitcoin,orotherdigitalassets,whilst
preventing double spending of assets. For paper money and checks
anti‐counterfeittechnology,suchashologramsandsignatures,prevents
forgery.  Butthestateofdigitalassetsneverdeterioratesanditisnota
simpletasktoidentifyagenuinetransactionfromaforgedone.
Many electronic securities and electronic money systems employ
eitheracentralized(anodewithhubfunction)tradingsystemoranIC
cardsystemwithsecretkeythatpreventssuchdoubledspending. The
formersystemrequiresacentralizedadministrationwithareasonable
governancestructure.  ThelattersystemrequiresanICcardoperation. 
These systems may transfer incidents of regulation and other
institutionalriskstotheownersofdigitalassets.  
  In Bitcoin the validation of transactions (preventing double
spending) is made possible by sharing the virtual registry bookthat
containsallinformationontransactionsandownershipofBitcoin. 
Thevirtualregistrybookisalwaysopentoeveryparticipant,so any
doublespendiseasilyidentified.  Bitcoingivestheimpressionthatitis
asetofindependentgold‐likecoinageassetswithitsco‐option of
‘mining’and‘coin’ phrases.  ButBitcoinmorecloselyresemblesareal
estateregisterorrecordinwhichthenewownerofeachlotofreal
estate is recorded whenever a new transaction is taken place. This
virtualrealestateregisterrecordcontains21millionlots(i.e.21million

1 Inthispaper,werefertoBitcoinaseitherasoftwarepackagethatcanbuyandsellBitcoinor
anoperationalsystemunderwhichminersarevoluntarilyinvolved.  It does not necessarily
reflecttheoriginalideaofSatoshiNakamoto(2008).

3

BTCs)beforesub‐dividing2. ToissueBitcoin is toattachan IDnumber
to each BTC lot, a settlement BTC is to replace an ID number bynew
number3. 
  As of July 20, 2014, 13.04 million BTCs have been issued in the
marketwithIDnumbers(about62%of21millionBTCs).Roughly
every ten minutes, 25 BTCs are being issued with new IDs.  This
procedure of new issue is implemented as a reward for the first
person/grouptovalidatetransactionswithoutdoublespendsthathave
beencollectedinablock.Thisisacompetitionofvalidationvia
computation,withtheaimofsolvingaspecificmathematicalproblem4.
Thiscomputationisdescribedasmining,andthosewhoconduct
mining are miners. The speed of new issue of Bitcoin on the register
recordis set tobe halvedin every fouryears. Atthe beginning of the
Bitcoin system in January 2009, the reward was 50 BTCs per ten
minutes, it was halved to 25 BTCs per ten minutes on November 25,
2012.Itremainsthesamerewardpertenminutestillnow5.Itwillbe
halvedto12.5BTCspertenminutesinaroundNovember2016,and
this halving process will continue until 2140 when new issue ofBTC
willbeterminated.  TotalcirculationofBTCwillbefixedat21million
BTCs.
  Thereare differencesbetween areal estate registrysystem andthe
Bitcoinsystem.  InJapan,forinstance,therealestateregistrysystemis
maintainedandadministered solelyby the LegalAffairs Bureau.The
real estate register record is kept exclusively by the Legal Affairs
Bureauandthepublicisonlyallowedtoreadtherecord.Incontrast,
thevirtualregistrybookthatcontainsallinformationonBitcoin
transactions and ownership is maintained individually among
participants.  This decentralized nature of virtual registry

2 TheminimumunitofBTCisnot1BTC,butitcanbedividedinto1/108unitsofBTC. 
3 Infact,settlementismadeover(multiple)partoflotsthatcanonlybeidentifiedasquantities.
Butwebelievethat thismetaphor by a realestate register record captures an essence of BTC
trading.
4 WewilldiscussthisproblemindetailinSection2.
5 Four years after January 2009 must be January 2013. The actualeventseemstohappen
quickerthantheoriginalstatement.Thisisduetotheprogramthatsetsarewardtobehalvedin
every210thousandBTCblockextensions,i.e.aminingrewardishalvednotbycalendar,butby
theblockextensionnumbers.Insection2,themeaningofblockextensionisfullyexplained.   

4

book‐keeping activity may create some inconsistencies among
participants.IntheBitcoinprotocol,whenanidenticalBitcoinsegment
is used twice for different payments –leading to a Bitcoin segment
having two branches (double spends) ‐ the majority decision rule is
used to determine which payment is genuine. The advantage of
majoritydecisionruleistosolveadeadlocksituationinwhich two
partiesdisagreewitheachother.However,asEyalandSirer(2013)
argue, the majority decision is not enough to protect against selfish
miningpoolsthatcommandlessthan1/4oftheresources,giventhe
delayedfinalityconfirmationstructure6.
  To be more precise, the Bitcoin protocol authenticates a genuine
Bitcoinregistrybookinwhichablock‐chain,afterbranching,extends
the longest7.  This decision rule works due to the delayed finality
confirmationstructure.Wewilldiscussthisinthenextsection.
  Thebook‐keepingmethodofownershiptransactionisnot restricted
toatypeofrealestateregistrysysteminwhichthe ownershipofeach
segmentisrecorded.   Depositaccountdatainabankingsystemkeeps
transactionandbalancerecordsforindividuals;inBitcoinphrasing,this
isequivalenttothenumberofsegmentsthedepositaccountholderhas
previouslyusedandcancurrentlyuse.Theadvantageofthismethod
isthatitallowsthemanagementofalargenumberof segments with a
relatively small number of accounts8. The reason why the Bitcoin
protocol employs the real estate‐like registry system, rather than the
bank deposit‐like account system is probably because Mr. Nakamoto
andhiscollaboratorsthinkthatitissuitablefordecentralized
processing.  
  TheBitcoinprotocolusesahashvalueofabeneficiary’spublickeyas
itsIDnumber.Ahashvalueisasortofdigestoforiginaldata,whichis

6 Eyaland Sirer (2013) illustrates that Bitcoin’sminingalgorithmisnotincentivecompatible,
and that the Bitcoin ecosystem is open to manipulation, and potential takeover, by miners
seekingtomaximizetheirrewards(p.15).
7 According to Nakamoto (2009), the system is supposed to authenticate the longest
block‐chain,inpractice,however,thechainwhose“totaldifficulty”isthegreatestprevails. 
8 Forexample,incaseoftentrillionyendepositsby1000millionpeople,itcanbepossibleto
keeptheownershiprecordsofeachyen,itmayrequireaverylargecomputationaland
maintenancecosts.Designofsuchasystemisfarmorecomplexthanabankaccounttypeof
recordkeeping.

5

obtained after a designated calculation process by some specific
algorithm(we will comebackto thislater).  Byusing a hashvalue as
anIDnumber,togetherwith  apublickeyitself,theBitcoinprotocolis
abletomaintainanonymitywithaswellastrustworthinessoftrade. 
The Bitcoin protocol recommends owners utilize asymmetric key
cryptography9.

2. Miners’important,exhaustingrole

The essence of the Bitcoin protocol is its structure that guarantees
theuniquenessofthesegmentinformation‘registrybook’.This
confirmation process broadly corresponds to one provided by the
centralized payment system in the case of traditional banking. The
Bitcoin protocol validates all transactions by means of open
competition among profit seeking miners as described above.  This
wholeprocessisreferredtoasconfirmationintheBitcoinprotocol.  
The winner of the open competition provides the hash value as a
stamp on the registry book, marking a validation of the trades in the
specific block. At the same time this winner receives newly created
Bitcoin,andisrecordedastheownerofsuchintheregistrybook.This
processiscalledmining.  Inthispaperwedistinguishtheconfirmation
processin which all mining activitiesare involvedfrom thevalidation
processinwhichthewinnerofcompetitionprovidesthehashvalueasa
stampontheregistrybook.

  Miners play an important role in the validation of Bitcoin
transactionsthatguaranteestheuniquenessoftheregistrybook.  We
callthemminersbecausetheyarenotatrustedthirdpartythat is
assignedtopreventdoublespendevents,butarevoluntaryparticipants
seeking for a reward from the open competition of validation.  Only
thewinnerreceivesBitcoininreward,allotherminersreceivenothing

9 Seehttps://bitcoin.org/en/protect‐your‐privacy. 

6

andmustpaytheirminingcosts.Thisisperhapsacruelsystemfrom
theviewpointofminers.
  This competition of validation is open every (about) ten minutes. 
Tradescollectedbyaminerbeforesuchtenminuteintervalsform a
block.  Afterthevalidation,anewblockisaddedtotheexistingblocks
– a process called extending a block chain. Newly created Bitcoin
received as a reward for validation can be used for payment after
reasonablylongblockchainsareextended(i.e.longenoughto prevent
disputesoverdoublespends)10.TheBitcoinprotocolemploysadelayed
finality confirmation structure in which Bitcoin cannot be used
immediately after a transaction from the other party, even after
validationoftransactionis made. This structure is quite differentfrom
thecentralizedpaymentsystememployedbythebankingsector. 
TheBitcoin protocolsets avariable difficultyof computationfactor,
to be solved by the miners in approximately ten minutes. When the
miners’computationspeedbecomesfaster(i.e.lessthantenminutes),a
parameterthatdeterminesadifficultyofcomputationisresettomakea
blockchainintervalapproximatelytenminutes11.
  This delayed finality confirmation structure is regarded as a
weaknessoftheBitcoinsystemfromalternativecryptocurrency
creators’pointofview.However,therecertainlyexistsatrade‐off
between approaching real‐time finality and increasing risk in
alterationsofvalidatedtransactions. 
  Letusclarifythevalidationprocessin the Bitcoinprotocol.This isa
block chain extension process after confirming finality in all past
transactions: 
(1) Thehashvalue12h0intheimmediatelypreviousblock,

10 Bitcoinstransferredbetweenuserscanconventionallybeusedafter6block‐chainextensions
(about one hour later) Generated bitcoins and transaction fees as a rewardfor a block‐chain
extension(wewilldiscussthislater)canonly  beusedafter100block‐chainextensions(about
17hourslater).
11 This parameter adjustment is based on the algorithm for the Bitcoin protocol.  The
algorithm examines thespe ed ofnew block is created in every 2016 block extensions (ifone
blockiscreatedintenminutes,2016blocksareequivalenttotwoweeks)andmakesparameter
adjustment.
12 According to Wikipedia, a hash function is any function that canbeusedtomapdataof
arbitrary size to data of fixed size, with slight differences in input data producing very big

7

(2) Thehashvalueqincludedinalltransactionsinthecurrentblock, 
(3) Searchforavaluerthatsatisfiescertainconditions,and
(4) Newhashvalueh1isgeneratedfromthreeinputs(h0,q,r).Thisnew
hash value h1 is used as a validation stamp on the virtual registry
book(seeFigure1forillustration).

IntheBitcoinprotocol,h0and qare exogenously given (these figures
dependonthepasthistoryoftrades),andminershavetosearch rto
satisfythe conditionh1≦t(target).Thisexercise iscalled theproof of
work. This concept of proof of work comes from Dwork and Naor
(1992).  Theyprovideacomputational techniquefor combattingjunk
mailandcontrollingaccesstoasharedresource.Theirmain
contributionis requiring a usertocompute amoderatelyhard,butnot
intractable, function in order to gain access to the resource, thus
preventingfrivoloususe.IntheBitcoinsystem,thisconceptisused to
giveconfirmationofthetransactionsviatheminingcompetition. In
exchange the winner of the competition receives a reward. This
incentivemechanismisthe most innovativepart oftheBitcoinsystem
anditworkswell.

3. ProofofWorkorProofofWaste?

  Let us clarify the meaning of the problem the Bitcoin protocol
imposesontheminers.Theproblemis“tosearchxtosatisfythe
conditionh1≦t(targetin256bit)wherethehashvalueh1is
generatedfrom(h0,q,x).Putsolutionxasr.”  Ifwedonotimposeany
restrictiononr(thatis,t=2256‐1), any number would satisfy the
problem.Ifwesetttobesmall,aprobabilityoffindingrinthehash

differences in output data. The values returned by a hash function are called hash values. A
cryptographichashfunctionisahashfunctionwhichisconsidered practically impossible to
invert,that is,to recreatethe input data fromits hashvalue alone. Ahash algorithmturns an
arbitrarily‐largeamountofdataintoafixed‐lengthhash.Thesamehashwillalwaysresultfrom
thesamedata,butmodifying thedatabyevenonebitwill completelychange thehash.Bitcoin
uses the SHA‐256 hash algorithm to generate verifiably "random" numbers in a way that
requiresapredictableamountofCPUeffort. 

8

function would drop sharply13 .Ifthedifficulty(asmeasuredby
parametern)ofthisproblemgoesbeyondacertainpoint,anystandard
personalcomputercannotfindasolutionwithinacertainperiod of
time(tenminutesinthiscase).
  This implementation differs from the original design by Nakamoto
(2008). The original design states that “to search a hash valueh1
obtainedform(h0,q,x)whosefirstnbitiszero.Putsolutionxasr.”  In
this design, a difficulty parameter nfortheproofofworkcanbe
adjusted,butallowsonlyforadiscretechange.Thecurrentdesign is
superiorandencompassestheoriginaldesign14.
  Theoriginal design of Nakamoto isintuitive, a description of which
follows.  Note, in this paper, we use tandninterchangeablysince
t=2256‐n‐1.

  The difficulty parameter n becomes a very useful operational
instrument. 
(1) Ifnisreasonablysmallerthan256,searchvaluer,given h0andq,
canexistalmostinfinitely.
(2) Ifngrowsgraduallylargerfromzero,aprobabilitytofindaserch
valuerbecomesverysmallandultimatelyclosertozero.
Byadjustingthedifficultyparametern, together with exogenous
technological change and miner entry and exit, the speed of a block
formation can be controlled.  Parameters torn enable the speed of
blockformationtostaymoreorlessconstantattenminutes.
  Asisclearfromtheabovediscussion,achoiceofparametertornin
the proof of work depends on computational power technological
changeandthenumbersofminers
15. The impact of technological

13Ifr is any arbitrary number in 256bit and the hash function used in this protocol can
generate an ideally uniform random diffusion, the probability would be about 1/2256‐log2t. 
Actualprotocolisabitmorecomplex,riscallednoncein32bitvalue,qwouldchangewhena
miner obtains bitcoins as a reward, the hash function (SHA‐256) could generatean identical
outputfromdifferentinputswithaverysmallprobability,actualprobabilitywouldbealittlebit
smallerthan1/2256‐log2t. 
14 Theoriginaldesignof Nakamotoallowsselecta realnumbert such that log2t generates an
integer.InthecurrentBitcoinprotocolallowstoselectanyrealnumberforadifficulty
parameter.  
15 Duetothecharacteristicsofhashfunctionintheproofofworkproblem,anumberoftrades

9

changeisintuitive:ifthecomputationalpowerdoubles,difficultyofthe
problem must double: n must shift to n+1.  Theimpactofnumberof
minersisbasicallysimilar,butmoreimportantinpracticeasitismore
likely the number of miners will double than would computational
power. 
Letusfurtherelaborateupontheissuesrelatedtotheproofofwork.
Theessenceofthisissueisthattowemayassumeaminer’sprobability
offindingasolutiontosomearbitrarilylargenumberofcalculationsis
independent even if there are reasonable numbers of miners.  Letus
assumeaminer’srareeventoffindingsomerthatsatisfiestherequired
conditionswithinatenminuteintervalissettoprobability(provided
allminershavethesamecomputationalpower),andMminers
participate in the mining competition, the probability of no miner
findingrwithinanintervalisgivenas(1‐)M,theprobabilityofaminer
finding r within an interval is 1‐(1‐)M.Wealsoassumethata
probability of such a rare independenteventfollowsthePoisson
distribution.  Thenanaveragewaitingtimeforsucharareeventisan
inverseoftheprobabilityofevent,
 
 (1)
Transformingeq.(1), 
＝
∑


 
∑



(2)
iisthenumberofminerswhoexperienceevents(i=0,1,2,…),

isavery
smallnumbercomparedwithM,thesecondterminthedenominator
canbeignored,thenwecansimplifyeq.(2)assuch,
≒ 
 (3)

inablockdoesnotmatterwithnort.  If trades use some divisions or mergers of bitcoin
segmentswithinablock,thevalidationprocesscouldbeabitmore complex although
calculationburdendoesnotincreasemuch.Itistruethattransactionfeesarepaidtotheminers
with such additional calculations are involved.  A share of transaction fees in the miners’
rewardsisverysmall(seehttps://en.bitcoin.it/wiki/Transaction_fees).

10

Furthermore,letusassumetheaveragecomputationalpowerofminer
withinanintervalissetconstantK.Byconstructionofthehashfunction,
Kmustbereasonablysmallcomparedwith2256‐n, 
≒ 
 (4)
PutK/2256=k,eq.(4)becomes
≒2
/ (5)

Thatistosay,theaveragetimeofablockvalidation(theaverage
waitingtimefortheminertofindr)
(1) increasesasdifficultynfortheproofofworkatthespeedof2n.
(2)decreasesininverseproportiontothenumberofminersMand 
(3)decreasesininverseproportiontothecomputationalpower.

ThesearethebasicdeterminantsofBitcoinproductivity. 

The difficulty parameter nfortheproofofworkwas32inJanuary
2009,raised to 40in December 2009,raisedto 62inDecember 2013,
and is 64 as of June 2014.  These changes cannot be explained by
increases in computational technological change, but must reflect the
factthatmanynewminersenteredinminingcompetitionbytheendof
2013andtheyalmoststoppedafter2014.     

  Theseobservationshintatthenatureofproofofworkasthecore
conceptoftheBitcoinsystem.Asshownabove,difficultyparameternis
nothingtodowiththequalityofvalidationofablock.That’swhyncan
beraisedandreducedflexiblywithoutaffectingavalidationprocess.
Thatis,theproofofworkisnotanissueinmaintainingthequalityof
Bitcoin,butisthecosttomaintainasteadyspeedofnewissues of
Bitcoin(atthemoment,itis25BTCsperabouttenminutes).Inorderto
evaluatethenatureofproofofwork,thisrolemustbeexamined.  The
role is properly carried out, it would be considered reasonable.
Otherwiseitwouldnotbetheproofofwork,butitwouldbetheproof

11

ofwastebecauseitwouldbeamechanismtoproviderewardsforthe
miningcompetitionwithexcessivelylargecomputationalcost.  

  ItisessentialtheBitcoinsystemprovidesanincentiveforthosewho
contributetothemaintenanceofthesystem.Incaseofstandard
electronicmoney, anissuer ofelectronic money receivesparticipation
feesdirectly fromthe retailshops; theyare paidnot by theelectronic
moneytheyissue,butbycentralbanknotes.Central banks themselves
paymaintenancecosts andreceiveservice rewards inthemoney they
issue.

  IncaseofBitcoin,theminerwhocontributestothemaintenance of
the system receives Bitcoin as his reward, and so it resembles to the
centralbank system.A differencebetween theBitcoin systemand the
centralbanksystemliesinthefactthattheformergivesarewardtoa
miner who happens to win the mining competition while the latter
receivesareward constantly.  Ifthereisa singleminerin theBitcoin
system,rcanbeanyarbitrary256bitvalue(ncanbezero).  Insucha
case,thecompetitionmechanismthat guaranteesavalidityofproof of
workdoesnotworkandwerequiresomealternative.Ifanalternative
works, it could be sufficient to prevent double spends. This situation
canbedescribedasthemintmodelofcryptocurrency.

 ThemintmodeldiffersfromtheBitcoinmodelinasensethatthe
former model uses a finality confirmation structure with legal
enforcement,whilethelattermodelusesafinalityconfirmation
structure via mining competition. Note again that the winner ofthe
competition is the only competitor to be rewarded with Bitcoin.The
probability of winning a reward must be based on the proportional
computationalpowerof anindividualminertothetotalcomputational
powerofallminingparticipants:allminersmayexpecttoreceive

12

rewardsproportional totheir computationalpowerafterareasonable
numberofminingcompetitions16.

  Thenwemustaskourselves,cantheproofofworkcontributetothe
stability of Bitcoin value? Nakamoto(2008) states “once a
predeterminednumberofcoinshaveenteredcirculation,the incentive
cantransitionentirelytotransactionfeesandbecompletelyinflation
free”(p.4).
  Answerisno.AsFigure2amplyillustrates,thevaluesofBitcoinas
measuredinU.S.dollarfluctuatewildlycomparedwiththoseofother
foreigncurrencies.Thereasonforthishighvolatilityisapparent. 
Demand for Bitcoin, regardless of the motivation for holding (i.e.
paymentorspeculation),increasesasitspricedecreasesandvice‐versa. 
As Figure 3 shows, the demand curve of Bitcoin, therefore, would be
downwardsloping17 whilesupplycurveofBitcoinatanypointoftime
wouldbevertical.Alldemandshocks(suchasE
*orE
**) must be
absorbedinpriceadjustments(suchasP*orP**).
  WenoteBitcoinpricingdiffersfromthepricingmechanismunderthe
goldstandardintwoaspects.First,thesupplyofgoldasnatural
resourcemustbeadjustedtothemarginalcost(i.e.theminerwouldset
its production so as to make the market value of gold equal to the
marginalcostofgoldmining).Secondly,goldcanbeusedforindustrial
andjewelrypurposesaswellasamoney.  Ifthepriceofgoldcoingoes
up,thegoldusedforindustrialandjewelryuseswouldbeconvertedto
thegoldcoinsandviceversa.
  Goldcoins should consequentlybe expected tomanifest anupward
slopingsupplycurve(see Figure4).Inthiscase,asshowninFigure4,
demand shocks can be absorbed in both prices and quantities.
ComparedwithBitcoin,thepriceofgoldcoinswouldbeconsequently

16 Ofcourse,weneedtoconsiderhowfairminingcompetitionis.Butifthelooserwithlower
computationalpowerwouldhavenochancetowinthecompetition,he/shewouldexitfromthe
competitionafterseveraltrials.Inthe longrun,allcompetitionparticipantsmusthavemoreor
lessthesimilarcomputationalpowers.  
17IfpeopletakeintoaccountofBitcoinpricesandallnewsuptothepreviousperiodsand
expectthecurrentpriceproperly,thentheyformtheirdemandcurvefairlyclose tohorizontal
(i.e.flat).Wedonotdiscusssuchacasehere. 

13

lessvolatileduetothissupplyelasticity18.ThepricevolatilityofBitcoin
mayreflectarathernaïveunderstandingbythedesignersoftheBitcoin
systemthatthemonetaryvalueofBitcoinwouldbestabilizedwith a
fixedmoneysupplyrule. 

4. DualInstability

  Let us consider the miner’s behavior from a broad cost/benefit
analytic perspective.  Miners voluntarily participate in the mining
competition,andinvestintheircomputationalpower,andwouldexitif
miningcostsexceeditsbenefits.Inprinciple,thissituationofentryand
exit is common to all industries.  The only difference from standard
industries is that supply of Bitcoin is independent from miners’ entry
andexit.
To elaborate upon this point, we divide the miners’ computational
powersintoMunits.Mvariesaccordingtominers’entryandexit.But
therewardforthewinnerofminingcompetitionisfixedasaboutZper
hour(atthemoment,25BTCspertenminutes,Zwouldbeabout150)
regardlessofentryandexitofminers
19 .AssumingtheBitcoin
protocolsetsnproperly,Zwouldbefixedforacertainperiodoftime.
ThisfactisreflectedintheverticalsupplycurveofFigure3.
 Expectedreward/benefitperunitperhourisZ/M. Ifthemarket
value of Bitcoin is given as P, the market value of expected reward is
PZ/M.  Ifthe miningcostis lowerthan PZ/M,thenthe minersobtain

18 Of course, the price stability of gold coin under the gold standard may not be attributable
solelytothesupplycurveadjustmentmechanism.  Astothegoldpricestabilityinthelate19th
centurytotheearly20thcentury,Keynes(1924)argues“forwhengoldwasrelativelyabundant
andflowedtowardsthem,itwasabsorbed bytheirallowing theirratioof goldreservestorise
slightly;and when it wasrelativelyscarce,the factthat theyhadnointentionofeverutilising
theirgoldreservesforanypracticalpurpose,permittedmostofthemtoviewwithequanimitya
moderateweakeningoftheirproportion.AgreatpartoftheflowofSouthAfricangoldbetween
the end of the Boer War and 1914 wasable to find its way into thecentralgoldreservesof
European and other countries with the minimum effect onprices” (pp.166‐167). The supply
shocksof goldandsilverdiscoverysometimecausevolatility ofthegold andsilvercoins.From
1550to1620,thepricesinWesternEuropeasmeasuredinthesilvercoinsincreased2.5times
(annualinflationrateisabout1.5%)asaresultofnewflowof silver from the American
continent.Thisiscalledthepricerevolutionperiod.
19 We put “about” because the Bitcoin protocol set a time intervalofablock10minuteson
averagebyadjustingdifficultyparametern.  

14

net benefit/return, and vice versa.Letusreflecttheseaspects in the
pastoneyearorso.

(1)If the market valueof expectedreward PZ/Mexceeds the average
costofaddingoneunit(itisgivenexogenouslybyatechnological
change),newentrywouldincrease.  ButasMincreasesaccordingly,
theexpectedreward/returnperunit(averageproductivity)woulddrop.
Eventually new entry would cease. This situation is a kind of
equilibriumand remainsuntilnews onthe Bitcoin pricearrives. Good
news,orBitcoinpriceincreases,inducesnewentrywhichcontinuesup
tothepointwhereMequilibratesbetweenthemarginalcostandthe
marketprice.Theproblemhappenswhenbadnewsarrives.

(2)AssumebadnewsarriveswhentheBitcoinsystemequilibrates.If
badnewsreducestheBitcoinmarketprice,theminers’netreturn
would be negative.  If the miners’ computational power can be
reallocatedtotheotherpurposes,migrationfromBitcoinminingwould
happen gradually.  Accordingly, depending on the size of the M
decrease,the expected returnper unitwould recover.  This situation
could happen when the mining is conducted in a spare time of
mainframe computer.  This can describedasthepastoralrealityof
earlyBitcoinmining. 

(3)Butthecurrentrealityisnotpastoralatall.  AsFigure2illustrates,
theBitcoinpriceshotupafterNovember201320.Thisfactrenderedthe
mining business very profitable. As a result, many entrepreneurs
entered into the Bitcoin mining competition equipped with super
powerfulcomputerswithdesignatedICchips21.  Thecurrentsituation

20 The Bitcoin market price was about ten dollars in the early 2013. It shot up above 1000
dollars in the end of November 2013. It is hard to tellthe exact reason for this.  We cannot
exclude a possibility of the bubble because the Bitcoin system tends to create babble as the
supply curve stands vertically. If Bitcoin was used to transfercapitalfromCyprusincaseof
financial crisis 2012‐13, the price hike of Bitcoin can be explained reasonably by this event.
Suppose,ifoneBitcoinistendollars,100milliondollartransfersfromCyprusrequire10million
BTCs.  ThatwouldexhaustalmostallBitcoinsinthemarket.   
21 Thismovementisconsistentwithchangeindifficultyparametern.Aseq.(5)indicates,an
increaseinn(fromnton+1)isequivalenttodoublethenumberofminersunitsM. 

15

resemblesaheavyequipmentindustryinwhichitiseasytoenter,butit
difficulttoexitbecauseoflargesunkcosts.

(4) Suppose that the Bitcoin price drops a by substantial, but not a
deadly,margin.  Tobemoreprecise,itfallstosomepricelowerthan
the average cost per unit but above the average variable cost. The
minerswouldcontinueminingbecauseitisrationaltokeepoperations
as long as return/revenue exceeds variable cost (i.e. total cost minus
fixed cost); the eventual operational loss would be smaller than that
incurredbyimmediatestoppage.AccordingtosomereportsonBitcoin
mining,manylarge‐scaleminerswhoenteredaftertheBitcoinboomin
late2013continuerunningtheiroperationsevenwithnegativereturns.
Theymaynotactivelyanticipatethereturnofabove‐1000
dollar/Bitcoin days, but they might simply assume that eventual
operationallosswouldbeminimizedbycontinuedoperation.

(5) Miners may also migrate to another mine in which they can
continuemining,  should computational powers be convertibletothe
newmine22.Aswementionedbefore,iftheminersmigratetotheother
mines,thesizeofMdecreases,andtheexpectedreturnperunitwould
recover.  Bythismechanism Bitcoinminingcansurvive evenundera
very volatile Bitcoin price.  Ontheotherhand,miners’computing
equipmentmayreachtheendofitsusefullife,andminersmighthaveto
stopminingbeforetheyrecoveralltheirsunkcosts.

(6)Bitcoinminingmightendanotherway.IftheBitcoinpricedrops
sharply below the average variable cost, all miners would exit from
mining.Manyminers enteredtheBitcoin mining competitionafterthe
Bitcoinboominthelate2013.Theircomputationalpowerwouldbe
expected to be broadly similar23.Ifthatisthecase,theminers’exit

22 Manyalternativecryptocurrencies to Bitcoin emergerecently.Iftheoperationalprotocolis
closertothatofBitcoin,itwouldbemucheasiertoconverttheirminingoperationintothenew
cryptocurrency. There already existsaservicetoinformrelative mining profitability among
alternativecryptocurrenciessothattheminerscanmovearoundtheprofitablemines. 
23 MostofcalculationintheBitcoinminingisallocatedtosearchforthevaluertosolvethe

16

strategywouldnotbeagradualone,butcouldbesudden.IftheBitcoin
pricedropsbelowathreshold,theBitcoinsystemasawholemay
collapseortheBitcoinusersarelimitedtoaverysmallnumberofinner
memberswithwhichBitcoinisexchangedataverysmallscale.Onceall
minersleavetheBitcoinmining,noonewouldbeengagedintheproof
ofwork.Avalidationofablockwouldbedelayedorstopped,and in
consequenceBitcoin ceasestobe a useablecurrency. Thistypeof risk
doesn’t’existingoldmining24.

  From the above observations, it is clear that the Bitcoin system
intrinsically manifests dual instability. The first instabilitystemsfrom
an inflexible supply curve of Bitcoin, which amplifies Bitcoin price
volatility;theminers’revenue/rewardfullyabsorbsanypricechanges. 
There is no price stabilization mechanism.  The second instability
comesfromriskstothesustainabilityofmining.DuringaBitcoinprice
boomminersengageinminingactivitywhichguaranteesthesupplyof
Bitcoin.ButduringaBitcoinpricedepression,nosmoothwaytoinduce
exitsfrom miningexists25. Thecurrent situationof theBitcoin system
canbeinterpretedasafreezingequilibriumwithdualinstability.

5. SceneaftertheGoldRush

The dual instability could be accelerated by miners’ strategic
behavior.RememberthattheBitcoinsystemsharesthevirtualregistry
book among all participants, and that everyone can monitor what all
others do.  It is not a big problem when new miners enter mining
activity as a result of the Bitcoin boom. Strategic behavior becomes a
problemwhennoadditionalprofitcanbefoundaftertheminers’rush.

problem.ThiscalculationismadebytheBitcoinminingdedicatedICchips(ASIC). 
ComputationalpowerisproportionaltothenumbersofASIC.  Wesupposetheproductivityof
minersintermsofcomputationalpowerperunitismoreorlessequal.
24 ThisfactindicatesthatBitcoinisnotnecessarilyacheappaymenttool.Wehavetorealize
thatBitcoinhasanexternality.WewillcomebacktothisinSection7.
25 Oncethepricefallsintothelevelthat is lowerthantheaveragecostperunitbutabovethe
averagevariablecost,onesolutionfortheminersistoselltheircomputerstotheotherminers. 
ButthisactionmightinduceasharpdropinthepriceofBitcoinminingdedicatedICchip.That,
inturn,makesexitmoredifficult.Thiscouldbetheworstscenariofortheminers.

17

Anexampleisvoluntaryandcollectiveminingpoolformation.Figure5
illustrates how the mining pool occupies the Bitcoin mining business. 
Twolargepoolinggroups(i.e.GHash.IOandDiscusFish)occupyalmost
50%ofitsshares26. 
  Howcan a miningpool be createdeasily in theBitcoin system? The
virtualregistrybookissharedcommonly,soeveryIDnumbercanbe
tracedby allparticipants, enablingminers to form a collectivemining
pool.  Oncethepooliscreated,itiseasyforthepool administrator to
monitor the behavior of all members in the pool27. It becomes very
difficulttoobservefromtheoutsidewhatminingstrategythepooluses. 
Asymmetricinformationbetweentheinsiderandtheoutsiderofthe
pool is generated via a virtual registrybookandsomespecialID
replacementsystem.
  In the long run, any reward/return from mining competition is
probabilisticandrealizedreturnswouldconvergetoexpectedreturns.
Butintheshortrun,fromtheindividualminer’sviewpointtheriskof
lowreturnisnon‐negligible.  Itisquiterationaltoformaminingpool
to reduce the risk of return volatility without changing the expected
return.Poolmemberminerstypicallyagreetoallocatereturnsin
proportiontotheircontributedcomputationalpower.
  Letus clarifythe rationale forthe miningpool. If thesearch itemis
rare,theminerscandividetheirsearchareabyspacesothattheminers
can avoid inefficiently searching the same space. But Bitcoin can be
consideredas2256‐ncoinsbeingrandomlydistributedoveralargespace
of2256lots.Fromtheviewpointofreducingthewaitingtimebetween
rareeventstohappen,theminingpooldoesnothelp.Butpoolscan
reducetheriskofanindividualminer’sreturn.
  The Bitcoin mining competition is repeated every ten minutes
(equivalent to 144 races with equal odds repeated daily).  If the

26 Eyal and Sirer (2014) points out that pools over 25% can cheat the system with selfish
mining and earn more than theirfair share, over 33% presents risk of unilaterally successful
selfish mining, large pools risk double spends with low confirmations, and over 50% is an
unmitigateddisasterandthatsuchmajorityminersaretoxic.  
27 AsRonandShamir(2013)shows,fromcertaincharacteristicsoftransactions,IDnumbersin
theBitcoinsystemcanbetracedbackwardlyandidentifiedtheownersofBitcoin.  

18

miners’riskinmeasurednotineachcompetitionbutinaday,itwould
bereducedto1/12(i.e.thesquarerootof144).Ontheotherhand,if
100minersformaminingpool,theirriskcanbereducedto1/10ofthe
applicablestandarddeviation.Takingintoaccountpooladministration
cost,actualpoolformationmaygobeyondtherationaleforthemining
poolofriskdiversification.  
  Whydowecareabouttheminingpool?Itcanbeasourceofstrategic
andopportunisticbehavior,whichmayinturndamagethecredibilityof
the Bitcoin system.  Firstly, theminersinthepoolcanforcelosses
upontheminersoutsidethepoolandencouragethemtoexitmining28.
Second,ifmultiplenumbersofsizablepoolsexist,eachpoolcanrotate
their mining in proportion to the computational power.  In so doing,
each pool can raise their mining efficiency29. As Figure 5 illustrates,
small numbers of mining pools accumulate computational power. 
That said, we cannot find any evidence of strategic behavior ofthe
minersinthepool,asindicatedbyEyalandSirer(2013)30.
  ThecurrentsituationofBitcoinminingremainsusofthesceneafter
thegold rush inCalifornia.The minersenteredafter theBitcoinboom
lookexactlylikethe49ers31:mostofthemmadelittleorlostmoney.
  It is true that mass migrations during the gold rush period to
Californialaiddownthefoundationsofeconomicprosperityinlater
years.ThesamecanbesaidofBitcoin,whichattractssubstantialpublic
attention.Ifwetakeadvantageofthisopportunitywecanfoster an
improvedBitcointhatcancompetewithcentralbankmoney.

6. MonetaryPolicywithoutaCentralBank


28 SeeEyalandSirer(2013).
29 Suppose two mining pools are oligopoly, economic efficiency canberaisedbyonepool
miningwhiletheotherresting.Thistypeofcollusioncankeepdifficultyparameterntoremain
loworraisehighastheywish.
30 We do not know exactly that such strategic behaviorhas not been taken place or that the
actionsaretakenbuttheyarenotknowntothepublic. 
31 Thisname is giventothe gold prospectorswhoarrivedinnorthernCaliforniaaround 1849
duringtheCaliforniagoldrush.

19

CryptocurrencieslikeBitcoindonotdepend on acentralbank.With
some amendments to its design, we can use this cryptocurrency (we
callthiscurrency, an extensiontoBitcoin,ImprovedBitcoin orIBC)to
implementsomeequivalentpolicyeffectsasacentralbankconducting
monetarypolicy.It isindeedmonetarypolicywithoutthecentralbank. 
To do so, we need to conquer the dual instability issues discussed in
Section4.  

6‐1.CurrencyBoardsasinspiration
  Asimpleandstraightforwardcurrencysupplyruleisthat‐giventhe
marketvalue/priceofIBCvis‐à‐visU.S.dollarorEuroasabenchmark‐
ifthemarketvalueofIBCincreases,thesystemwouldissueIBCsuntil
themarketvaluereturnstothebenchmarklevel.Thisrulecanbe
describedasthepeggingruleofexchangerates,orthecurrencyboard
system. 
  To be more concrete, suppose the market value/price of IBC isP
dollar at the moment. A reward for the proof of work, V is set torise
whenthemarketvaluePisabovethebenchmarkvalueandarewardV
issettobezerowhenPisbelowthebenchmark.Alternativelysome
difficulty parameter n, adjusting the speed of proof of work is to be
changed.  Inthiscase,withoutchangingV,thequantityofnewissueof
`IBCperhourZisadjusted32.Whichruleisbetter?Intheory,bothrules
affectthemarketvalueofIBCequally.  Theabovediscussioncan be
considereda starting pointto considerthe marketvalue stability ofa
cryptocurrency.IntheBitcointypeofcryptocurrency,withoutacentral
authority,thepolicyframeworkformarket value stabilizationmustbe
rule‐ratherthandiscretion‐based.
  Thismethodhasaseriousdefect:toreducethenewissueofIBCto
zeroisnotequivalenttoabsorbingexcessIBCincirculation.  Figure6
illustrates the kinked supply curveofIBC,withcurrentpointE as a
refraction point (for simplicity, let us assume supply and demand
equilibrates at E).  A positive demand shock to IBC (increase in IBC

32 HereZ=V/θwhereθistheaveragewaitingtime.

20

demand)can beabsorbed byshifting thesupply curvefrom Lto L*.A
negativedemandshocktoIBC(decrease in IBC demand) cannot be
absorbedbecausethesupplycurveisverticalinthiscase.Consequently
themarketvalueofIBCdropstoP**. 

  Thesupplyofcentralbanknotescaneasilyexpandandcontract.For
a positive demand shock to bank notes (shifting from
consumption/investment to money: i.e. it is a deflationary shock), the
centralbankincreasesmoneysupplybybuyingsecuritiesandforeign
currencies.  For a negative demand shock to bank notes, the central
bankabsorbsmoneyincirculationbysellingsecuritiesandotherassets.
IncaseofIBC,thelatteroperationisnotincludedinitsprotocol.Thatis
to say, the cryptocurrency protocolusuallyincludesthecurrency
supply rule, but does not have a currency absorption or write‐off
protocol.Canwereducethisirreversibility? 

6‐2.Built‐inRevaluationRuleforExchangeRate
  It is the irreversibility of cryptocurrency supply that concerns us
most, perhaps because of our obsession of understanding currency
supplyintermsofnumbers.Ifwetrytocontrolcurrencyquantitiesin
terms of real purchasing power, it may not be so difficult to absorb
surplus currencies in circulation. It is possible to include aninflation
rate in the supply rule to amend irreversibility of currency.  If our
basicideaisclosertoacurrencyboard,thisamendmentisanamended
currencyboardwiththebuildinrevaluationruleforexchangerates.
  Ourproposed amendment uses the market value of IBC, P,vis‐à‐vis
the benchmark price as policy indicator to control our policy
instruments,V,Z and n.Theamendmentuses the marketvaluePwith
inflation rate α, i.e. P*exp(ατ) as policy indicator to control policy
instruments,V andn (τis timeperiods sincethe starting point).With
this rule, we can virtually absorb excessive currency or purchasing
powerincirculationduetocurrencydemandshocksorpolicymistakes.
Thatis,wemaynotbeabletoeliminatecurrencyincirculationbutwe
canreduceitsrealvaluebyallowinginflation.

21

  Howcanwedetermineinflationrateα?  Itisclearthatahigherαis
more effective at absorbing demand shocks. Figure 7 illustratesthis
situation.Horizontalaxisis convertedquantity, ratherthan(currency)
quantity.  Convertedquantity measuresthe real purchasing power of
IBCintermsofbenchmarkcurrency.Withhigherα,realpurchasing
poweratthemomentshiftsfromLtoL
** and equilibrium point also
shifts from E to E**.  As a result, if a demand shock shifts D curve to
D**curve,thesupplysideabsorbthisshockandstabilizesthemarket
value/priceaccordingly.   
  However,it isnotnecessarilytruethathigherαisbetter. Higherα
impliesthatmonetaryvalue depreciatesquickly.Withhigherα,people
wouldavoidholding IBCperse.If theIBCsystem maintains adelayed
finalityconfirmationstructureliketheBitcoinsystem,participants
mustholdIBCintheirwalletfor a while after receiving IBC as their
rewardforminingorinexchangeforthetransactionofgoodsand
services.  ItwouldbepainfulforIBCholderstoseesuchdepreciation
duringtheirhoardingperiod.
  Inordertomakeourbuilt‐inrevaluationrulepracticallyworkable,it
maybe betterto separate theIBC operationrule fromthe benchmark
price vis‐à‐vis the U.S. dollar. To do so, we need to investigate an
intrinsicvalueforIBC.   

6‐3.MonetaryPolicywithoutaCentralBank
 ThefirsttaskistoconstructanIBCsupplyrulethatcanabsorb a
positivedemandshock.FromourdiscussioninSections6‐1and6‐2,if
theIBCsystemcanadjustsupplyproportionaltocomputationalpower,
themarketvalue/priceofIBCwouldriseandnewminerswould
participatein IBCmining. Forthe long run33 we can constructan IBC
supplyschedulesimilartoFigure6. 
RecallinSection3weobtainthefollowingresult,  ≒ 2/.The
current Bitcoin system adjusts difficulty parameter n to stabilize an
averagewaitingtimeθasthenumberofminersMincrease.Whatwill

33 HerethedemandandsupplyadjustmentpresumesnewentryoftheIBCminers. 

22

happen if nisnotadjustedtoanincreaseinM?Fromeq.(5),θ will
shrinkinverselyproportionaltoM.Ifarewardfortheproofof work V
isfixedforacertainperiod, new IBCissueperhour(Z=V/θ)would go
upordowndependingonM.  Ifθbecomestoosmall,ncouldberaised
(i.e. n+1 would double θ)oralternativelyVcouldbedoubled.In
allowingforthedurationofablockformationθtoshortenasM
increases, a duration of finality confirmation would also be shorten.
That has merit, but, at the same time, the risk of admitting double
spends increases.  Recall that the new issue policy Z=V/θ depends
solelyonM34.
  NowtheIBCsystemhasacquiredabuilt‐inrevaluationmechanism35. 
Itisthefirststeptowardsmonetarypolicywithoutacentralbank.The
monetaryvalueofIBCwithsucharulewillbefarmorestableover
time:anupwardchangeinpriceinducesnewentryofminersuptothe
pointwherethemarginal costbecomesequaltothe rewardmeasured
inthepriceofIBC. 

  As discussed in Section 6‐1, the IBC system can accommodate a
positivedemandshock(i.e.anupwardchangeofpriceoradeflationary
shock).Thissystemcannotreact properly toanegativedemandshock
(i.e.adownwardchangeofpriceoraninflationaryshock).Isthereany
remedyforthis?  

6‐4.ImplicitInflationTargetinCryptocurrency
TheansweristosetastructurethatmakestheIBCminingcost
(determinesthe market value/priceof IBC)gradually decreasingover
time.Tobemoreprecise,arewardVforablockformationincreasesat
a designated growth rate of β. Together with a technological change

34 This is somewhat related to the labor theory of value, initiallysuggestedbyAdamSmith,
DavidRicardo,andKarlMarx.ThevalueofIBCisdirectlylinkedwiththeminingwork.  Thatis
tosay, the real economic activity islinkedwithmonetary economy.This is also relatedto the
ideaofthegoldstandardinwhichthegoldisconvertiblewiththepapermoneyatthefixedrate.
Thegoldistherealanchor. 
35 Allowingfortheseamendments,theIBCprotocolhastobecompletelychanged.Forexample,
duetothealterationofsupplyrule,totalamountofIBCsupplyshouldbeinfinite.  Durationofa
blockformationcanbevariable. 

23

rateγ36,theIBCminingcostperhourdecreasesattherateofβγ;market
participantsexpect inflation at exp(βγ)perhourandtherealvalueof
IBC would drop.  As long as a negative demand shock reduces IBC
demand within the range of IBC value depreciation, we can avoid
unexpectedIBCinflationshocks. 
  From Figure 7, the point L**istherealIBCpurchasingpower
discounted by expected inflation. L‐L** is depreciation of purchasing
power.IfanegativedemandshockfallsintherangebetweenDandD**,
suchashockcanbeabsorbedperfectly.Takingintoaccountofinflation
expectationintheIBCvaluation,aninflationaryshockviamonetary
policycanbeoffset.   
  We note this rule is closely related to the inflation targeting policy
implementedbymanycentralbanks.  Inflationtargetingiseffectivein
softening an unexpected inflectionally shock37. Thecurrentrulehas
thesameeffect.Wemaycallthisruleanimplicitinflationtarget for
cryptocurrency.Thisrule,however,isdifferentfrominflationtargeting
bythecentralbanks,inthattheirinflationtargetdependsheavily on
expectationsformationbythepublic,andcredibilityofthecentralbank
ingeneralandthegovernorinparticular.Bothdonotnecessarily have
strong linkages with the real economy, as a result, their effects are
sometimesvague and usuallycontroversial. Ourrule, on thecontrary,
dependsonaneconomic principle, i.e.thecoststructureof themining
thatisrealeconomicactivity.   

7. FriedrichA.Hayek’sCurrencyCompetition

WehaveanalyzedtheBitcoinsystemingeneralandtheroleof
miningastheproofofwork. We’veproposed analternativetoBitcoin,
Improved Bitcoin (IBC) that is supposed to overcome the inherent
instabilityofBitcoin.ButcanIBCcompetewithmajorcurrenciesissued

36 Astechnologicalchange increases in k (k=K/2256; K=computationalpower),IBC supply per
hour will increase through shortening θ. We assume the technological change rate γis
exogenouslygiven. 
37 Fordetaileddiscussions,seeIwamuraandWatanabe(2006).  


24

bymajorcentralbanks?Wenoteatleastfourproblemswithsuch
cryptocurrencies.

First, cryptocurrencies are more expensive to produce, and the
productioncostsarehardtoretrieve.  Banknotesissuedbythecentral
banks require some printing and material costs. These costs are
negligiblecomparedwiththeface(nominal)value.  
Second,banknotesarereversiblebetweennewissuesand
absorptionbecausethecentral bank basicallybuysandsells securities
with bank notes.  A cryptocurrency cannot be absorbed, but if
equippedwithabuilt‐invaluestabilizationmechanism,thisshortfallof
irreversibilitycanbesoftened(butnoteliminated)inpractice. 
Third, Bitcoin‐type cryptocurrencies use a delayed finality
confirmationstructuretoavoiddoublespending.Consequentlyit
typicallytakeshourstouseobtainedmoney.  Banknotescanbeused
immediatelyasobtained. 
Fourth, Bitcoin type cryptocurrencies face security risks, suchas
DenialofServiceattacks,morewidelythanbanknotes.

  Thethirdandfourthpointsarerelativeproblems,andalsointrinsic
to Bitcoin‐type currencies.  They are not general problems with
cryptocurrency.Thethirdpointconsidersaproblemdirectlycompared
withbank notesfor directtransactions. Consideringtransactions with
Bitcoin‐type currency may occur over a remote distance, finality
confirmation may be quicker and much cheaper with a Bitcoin‐type
currencythanthatthroughabank.  Thefourthpointiscloselyrelated
totheprotocoldesignofaBitcoin‐typecurrency,andisnotageneral
cryptocurrency issue.  The instability associated with mining pools
due to strategic behaviors between and within pools can be reduced
substantially if the valuation system is improved in line with our
suggestions. 

Thefirstandsecondpointsarefundamentalshortfallsof
cryptocurrency. As currently described, cryptocurrency values are

25

based on associated production costs.  This mechanism is similar to
commoditymoney,notablygoldandsilvercoins.  Historicallygoldand
silvercoinshavebeenreplacedbycredit(orfiat)moneybasically
becauseoftheabove‐mentionedfirstandsecondpoints.
  AsVanceandStone(2014)reports,theproductioncostofBitcoinare
the mainly variable costs of equipment and electricity. In general
Bitcoinminingappearstobealoss‐makingbutstableindustry(i.e.no
net entry). Under these circumstances, the Bitcoin reward per hour
reflectsthemarginalcostofmining.Forexample,ifthemarketvalueof
BitcoinisUSD$600,  then the Bitcoinsystemis maintainedbyissuing
25*600 =$15000 dollarsper tenminutes (i.e. 90 thousand dollarper
hour, 2.16 million dollar per day).  This is not a small amount.The
Bitcoinsystem isoftendescribedasinexpensivebecausemaintenance
costsarenotchargedtotheBitcoinusers,butaregeneratedasreward
tomining.  Inshort,Bitcoinisbasedonasystemthattakesadvantage
ofanexternality.Itisnotacheapsystematall.

  Thiscapitalization‐by‐externality willbe liquidatedsometime inthe
future.  A collapse in Bitcoin value might happen in the near future.
Whopaysthisbill?
  Ourproposed amendedsupply schedule,i.e. thebuilt‐inrevaluation
mechanism and the implicit inflation target has an implication beside
the value stabilization of IBC. These rules would prevent excessive
currencydemandduetotheexternality.  Thesameistrueofgoldand
silvercoins: itis trulywaste of limited resources if such arekept ina
safeorincomputersafterexpendingalargeproductionorminingcost.
Thencanwesaybanknotesaresuperiortocryptocurrencies?Notwith
anycertainty. 

  Directproduction costsof banknotes arenot high.  Butwe cannot
ignoretheimplicitcostsgenerated dependence of monetary value on
policy decisions by governments or central banks. The central bank
alwayshasanoptiontoengageinanunexpectedpolicychange. Many
economists agree that perfectly expected inflation is welfare neutral. 

26

But under the name of a bold policy initiative, monetary policymay
generate welfare losses due to unexpected inflationary and/or
deflationarypressures. 
  Reversibilityofbanknotes‐betweennewissuesandabsorption‐is
basedontheexchangebetweenbanknotesandgovernmentbondsat
somepointintime.Thisisnothingtobeproudof.  Ifthecredibilityof
governmentbondsisshaken,thatofbanknoteswouldbealsoshaken. 
Onthecontrary,ifgovernmentbondsdominatethecapitalmarket,the
centralbank,simply monetizing it,hastoworryaboutever‐expanding
its balance sheet 38 .Reversibilityofbanknoteshasmerit,and
inescapablecosts. 

  Shall we prefer bank notes or a cryptocurrency? There is no
unconditional answer. Bitcoin‐type cryptocurrencies, with some
amendments,canbereasonablycompetitivewithcentralbanknotesin
terms of value/price stability. Currency competition in a senseof
FridrichA.Hayekisdesirable.Suchcompetitionmustbeencouraged,
notonlybetweencentralbanknotesandacryptocurrency,butalso
betweencentralbanknotesandamongdifferentcryptocurrencies. 
  Indeed, currency competitions among cryptocurrencies are already
takingplace.Somehundredsofcryptocurrencies already exist,
followingthesensationalsuccessofBitcoin.  Ifthiswasthe‘bigbang’
of currency competition among cryptocurrencies, a better designed
cryptocurrency(suchasanIBC)mayemergeandbecomestrong
contendertothecentralbanknotes.
Howaboutcentralbanknotes?Centralbankersarekeenon
international cooperation, but not so keen currency competition. The
currentgenerationofcentralbankersinU.S.,EuropeandJapanindicate
tomarketsthattheycaremoreforbusinessthanforpricestability.   It
isincreasinglyacceptedthatpricestabilitymaynotbetheonlygoalof
central bankers. Excessive international cooperation may obstruct

38 Fiscaltheoryofthepricelevel(FTPL)discussestheseissues.SeeIwamuraandWatanabe
(2002)forafulldiscussion. 


27

capital’sexit;ifinvestorsworryaboutthefutureoftheyen,thenthe
prospectsoftheEuroordollararenotsodifferentunderthecurrent
setof circumstances.  Some investorshaveconsequently shiftedtheir
capital to Bitcoin, in which thepriceisveryvolatileandnocredible
authorityguaranteesitsvalue.  
  Centralbankersshouldnotindulgeinponderinghowtogiveminor
shocks to markets, given limited usages of money, but they should
investigate why people are so attracted to Bitcoin and what features
canbeusedinmonetarypolicy. 
  The key differentiation of Bitcoin from central bank notes and
existingdigitalcashtypeelectronicmoneyisaframeworkinwhichall
vintage information of each segment of Bitcoin are recorded39. Not
manypeopleareawareofthisusefulfeatureofBitcoin.  Ifthisfeature
isintroducedintobanknote‐likeelectronicmoney,eachatomofbank
note‐likeelectronicmoneywithitsvintageinformationcanreflecttime
value, i.e. each note is priced differently according to the time passed
sinceits issuance.  In otherwords,we can provideinterestwith each
note. This system implies that owners of bank note‐like electronic
money can receive interest or pay some penalty, depending on
economic conditions. In the current central banking system, these
benefitsaretransferredtothegovernmentasseigniorage.Notethatthe
monetaryinterestrate,asmeasuredaunitofmoneytoday,ishow
muchthesameamountisanticipatedtobeworthoneyearfromnow.It
isdifferentfromnominalinterestratethatisareturnfrominvestment
ofzerointerestbearingmoney40.
  If the legal system permits, these bank note‐like electronic moneys
can provide a substantial business opportunity. Strangely, the current
generationofcentralbankersdonotpayalotofattentiontothe

39  In practice, when Bitcoin is issued, all vintage information is recorded. After some
transactions, divisions and merges are repeated so that original vintage information can no
longercarryover.  Adesignofelectronicmoneythat can keepallvintageinformationcannot
beusedintheBitcoinsystemasitisnow.Wesupposethereisawaytomaintainallvintage
informationevenafterrepeatedtransactions.Itisanimportantresearchquestion.
40 SilvioGesell(1918)advocatedthe ideaofstamped money.Hisideaisusedinsomeregional
moneysnow.Alas,mostofthesemoneysemployonlyintheregionofnegativeinterestrate(i.e.
penaltycharge). It is alsoworthwhilepointingout that Keynes (1936) spares hisChapter 23,
Section6todiscussandevaluateGesell’sideaofstampedmoneypositively.

28

associatedopportunities:toexpandtheflexibilityofmonetarypolicyby
convertingfrompapermoneytobank note‐likeelectronic money with
vintageinformation.With this framework,centralbanksare nolonger
vulnerableto Keynes’ (1936)liquidity trap,byavoidance ofthe  zero
lowerboundinterestrate41.

8. Conclusion

  Why Bitcoin did not exist until recently? Decentralized money
provision, and similar economic systems with P2P technology, were
proposedwellbeforeBitcoin.Butthesetrialsfailedtogrowlike
Bitcoin. Perhaps early challengers may take the nature of moneyand
autonomyofeconomicactivitytooseriously.
The major drivers behind Bitcoin’s success are (1) a naïve
understandingofcurrency,(2)theemploymentofan
easy‐to‐understand asymmetric key cryptosystem for validation of
transactions and a virtual register system, and (3) the creation of a
participatory system with a P2P network maintained by the elliptic
curvedigitalsignaturealgorithmandahashfunction.  Thisframework
hasattractedmanyprogrammersandcollaboratorstoimproveuser
softwareandthat,inturn,attractmanyusersofBitcoin.  
  In addition, the originator of Bitcoin ‐ Satoshi Nakamoto ‐ and his
collaborators demonstrated they can create a currency without a
centralbankviaproofofwork,andthatthereexistsdemandforsucha
currency.  

  AunexpectedfeatureofBitcoinisthat,contrarytotheoriginalbelief
of Satoshi Nakamoto that he can create currency without inflation by
meansofcontrollingandpreannouncingtotalsupplyofBitcoin,the
marketvalue/priceofBitcoinfluctuatesup(deflationorthevalue of
Bitcoingoesup)anddown(inflationorthevalueofBitcoingoesdown).

41 It is possible to add vintage information to the current paper money by printing the issue
date.Itwouldbefartroublesometohandleeachnotedifferently.  Ifincaseofdigitalcurrency,
thatproblemcanbesolvedeasily.  

29

We hope that Satoshi Nakamoto’s important contributions can nullify
his misunderstandings.  We are grateful to Satoshi for his imperfect
Bitcoininnovation.  There remainsmuchroomforimprovement,and
fordiscussionofourfuturemonetarysystem. 




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Figure1FlowChartoftheProofofWork

Figure2MarketPriceofBitcoininUSDasofOctober25,2014
Source: blockchain.info.

Figure3.SupplyandDemandofBitcoin:CaseofaVerticalSupplyCurve
D**
D D*
P*
P**
P
L
S
E
E*
E**
O
Value
Quantity

Figure4.SupplyandDemandoftheGoldCoin:CaseofUpwardSloping
SupplyCurve
D**
D D*
P*
P**
P
S
E
E**
E*
O
Value
Quantity

Figure5.ShareofMiningPoolasofOctober25,2014.
Source: blockchain.info

Figure6.SupplyandDemandofImprovedBitcoin:CaseofKinkedSupply
Curve
D**
DD*
P**
P
L
S
L*
EE*
E**
O
Value
Quantity

Figure7.SupplyandDemandofImprovedBitcoin:CaseofAmended
SupplyCurve
D**
D D*
P
L
S
L*
EE*E**
L**
O
Value
Converted Quantity