Wannan takarda, "Farashin da Kudin Bitcoin" na Marthinsen da Gordon, ta magance wata matsala mai mahimmanci a cikin tattalin arzikin kriptokurenci: dangantakar da ke tsakanin farashin kasuwar Bitcoin da kudin samar da shi (hako). Yayin da wani sanannen labari ke nuna cewa kudin hako yana aiki a matsayin tushen farashi, nazarce-nazarce na gwaji na tattalin arziki (misali, Kristofek, 2020; Fantazzini & Kolodin, 2020) sun nuna akasin haka—kudin hako yana bin sauye-sauyen farashi. Wannan binciken yana da nufin samar da ka'idar tattalin arziki da ta ɓace don bayyana wannan dalilin da aka gani, tare da wucewa daga alaƙa zuwa kafa sarkar dalili mai ma'ana daga farashi zuwa kudi.
Samfuran kuɗi na gargajiya kamar Ka'idar Yawan Kuɗi (QTM) ko Daidaiton Ƙarfin Siyayya (PPP) ba su da tasiri sosai ga nazarin Bitcoin. Wannan saboda Bitcoin a halin yanzu ba ya aiki da kyau a matsayin ma'auni ko hanyar musayar kuɗi (Baur et al., 2018). Yawancin kayayyaki da ayyuka ana farashin su da kuɗin ƙasa, inda Bitcoin ke aiki fiye da zama kadari mai hasashe fiye da kuɗin yau da kullun.
Wani sanannen imani amma ba a tabbatar da shi sosai ba ya nuna cewa kudin ƙirƙirar Bitcoin (hako) yana ba da matakin goyon baya na asali ga farashinsa. Dalilin shine cewa idan farashin ya faɗi ƙasa da kudin samarwa, hako ba zai yi riba ba, masu hako za su daina aiki, kuma tsaron hanyar sadarwar Bitcoin (kula da littafin jama'a) zai kasance cikin haɗari (Garcia et al., 2014). Wani imani mai alaƙa shine cewa farashin dole ne ya tashi tare da ƙaruwar kudin samarwa.
Binciken tattalin arziki na baya-bayan nan ya karyata ka'idar tushen kudi, yana nuna cewa sauye-sauyen kudin hako suna zama martani mai jinkiri ga sauye-sauyen farashin Bitcoin. Duk da haka, waɗannan samfuran ƙididdiga, yayin da suke gano hanyar alaƙa, sun kasa bayyana dalilin—tsarin tattalin arziki na asali da ke tafiyar da wannan hali. Wannan takarda tana neman cike wannan gibin na bayani.
Babban hujja shine cewa farashin Bitcoin ana ƙayyade shi a cikin kasuwa mai hasashe na duniya ta hanyar dalilai kamar ra'ayin masu zuba jari, labaran ƙa'ida, yanayin tattalin arzikin duniya, da labaran amfani—galibi ba su da zaman kansu daga kudin hako na yanzu. Farashin da ke tashi yana ƙara yuwuwar samun kudin shiga ga masu hako, yana haifar da ƙarfafawa ga su su zuba jari a cikin ƙarin kayan aiki mafi kyau (ƙara ƙimar hash) don yin gasa don ladan lada. Wannan zuba jari yana haifar da haɓakar kudin haɓaka na hako (musamman wutar lantarki da kayan aiki), yana haifar da kudade su bi farashi.
Tsari: Ana iya wakilta samfurin dalili mai sauƙi azaman zane mai jagora mara zagaye (DAG):
Girgiza na Waje (misali, labaran ƙa'ida masu kyau) → ↑ Farashin Kasuwar Bitcoin → ↑ Yiwuwar Ribar Hako da ake tsammani → ↑ Shigar Sabbin Masu Hako & Zuba Jari a cikin ASICs → ↑ Jimlar Ƙimar Hash na Hanyar Sadarwa → ↑ Wahalar Hako (daidaitawar ƙa'ida) → ↑ Kudin Haɓaka na Samarwa (Wutar Lantarki + Rage ƙima).
Misalin Lamari (Gudu na Bijimi 2020-2021): Farashin Bitcoin ya tashi daga kusan $5,000 a cikin Maris 2020 zuwa sama da $60,000 nan da Maris 2021. Wannan hauhawar farashin ya riga ya kasance gaban babban jujjuyawar zuba jari na hako. Kamfanoni kamar Marathon Digital da Riot Blockchain sun ba da odar sabbin na'urorin hako daruruwan biliyoyin daloli. Jimlar ƙimar hash na hanyar sadarwar Bitcoin ta duniya da wahalar hako sun tashi zuwa kololuwa bayan watanni bayan farashin ya fara, yana nuna jinkirin amsa na kudin hako (capex da opex) ga alamun farashi.
Ana iya tsara dangantakar. Ribar mai hako ($\pi$) a kowane lokaci shine:
$\pi = \frac{R}{D \cdot H} \cdot H_m \cdot P - C_e \cdot H_m - C_h$
Inda:
$R$ = Ladan toshe (BTC)
$D$ = Wahalar Hanyar Sadarwa
$H$ = Jimlar Ƙimar Hash na Hanyar Sadarwa
$H_m$ = Ƙimar Hash na Mai Hako
$P$ = Farashin Bitcoin (USD/BTC)
$C_e$ = Kudin Makamashi a kowane raka'a na Ƙimar Hash
$C_h$ = Kudaddun Kayan Aiki (an daidaita su)
A cikin ma'auni mai gasa, ribar da ake tsammani tana karkata zuwa sifili. Saita $\pi = 0$ da warware don farashin daidaitawa $P_{be}$ ya nuna dogaronsa akan yanayin hanyar sadarwa ($D, H$) waɗanda su kansu ayyuka ne na farashin da suka gabata:
$P_{be} = \frac{D \cdot H}{R} \cdot (C_e + \frac{C_h}{H_m})$
Tun da $D$ da $H$ suna daidaitawa sama don amsa mafi girma $P$ tare da jinkiri (saboda lokutan saye da isar da kayan aiki), $P_{be}$ aiki ne na $P$ mai jinkiri, ba mai ƙayyade $P$ na yanzu ba.
Babban Fahimta:
Marthinsen da Gordon sun ba da gyara mai mahimmanci, ko da yake an jinkirta, ga wani tatsuniya na kasuwa da ya yaɗu. Ka'idar "kudin-a-matsayin-tushe" ba kawai ba daidai ba ce ta gwaji; a zahiri ta koma baya. Hako Bitcoin wani masana'antar da aka samo ne wanda tattalin arzikinsa ke ƙayyade shi ta farashin kasuwar kadarin, ba akasin haka ba. Yin amfani da kudin hako a matsayin ma'auni na ƙima na asali yana kama da kimanta Tesla ta kudin wutar lantarki na masana'antarsa—yana rikitar da shigarwar aiki tare da mai tafiyar da buƙatar hasashe.
Tsarin Ma'ana:
Ma'anar takardar tana da kyau kuma ta yi daidai da ƙananan tattalin arziki: alamun farashi suna tafiyar da rabon albarkatu. Babban farashin Bitcoin yana ƙara samfurin kudin shiga na ƙarfin hash, yana jan hankalin jari da aiki (a wannan yanayin, ASICs da wutar lantarki) har sai kudin haɓaka na samarwa ya tashi don saduwa da sabon ma'auni. Daidaitawar wahala na kwanaki 14 shine babban tsarin ƙa'ida wanda ke fassara ƙaruwar ƙimar hash da farashi ke tafiyar da shi zuwa manyan kudade masu dorewa.
Ƙarfi & Kurakurai:
Ƙarfi: Takardar ta sami nasarar samar da hanyar haɗin ka'idar da ta ɓace don binciken tattalin arziki na baya. Ƙarfinta yana cikin amfani da ka'idar samarwa ta gargajiya ga sabon kadari na dijital. Yana karyata wata hanya mai haɗari da wasu masu zuba jari ke amfani da ita yadda ya kamata.
Kurakurai: Nazarin, ko da yake daidai ne akan hanya, yana da ɗan sauƙi. Ba ya nuna yuwuwar dangantakar ma'auni na rauni na dogon lokaci. A cikin yanayin faɗuwar farashi na tsawon lokaci, raguwar masu hako na iya rage ƙimar hash na hanyar sadarwa da wahala, rage kudin haɓaka ga waɗanda suka tsira, yana iya haifar da ƙananan iyaka. Bugu da ƙari, bai haɗa rawar kuɗin ma'amala gaba ɗaya ba, wanda zai iya zama mafi mahimmanci na kudin shiga na mai hako bayan rabin, yana iya canza yanayin.
Fahimta Mai Aiki:
Ƙarshen wannan takarda yana goyan bayan babban bincike a cikin farashin kadari. Kamar yadda aka lura a cikin babban aikin kan kumfa na hasashe na Brunnermeier & Oehmke (2013), farashin kadari a kasuwanni tare da imani daban-daban da kuma amfani da lefa na iya rabu da duk wani "kudi" na asali na tsawon lokaci. Bitcoin, tare da ƙayyadaddun wadata da masu tafiyar da buƙatar hasashe kawai, babban misali ne na wannan al'amari.