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Bitcoin price and its marginal cost of production: support for a fundamental value

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This study back-tests a marginal cost of production model proposed to value the digital currency Bitcoin. Results from both conventional regression and vector autoregression (VAR) models show that the marginal cost of production plays an important role in explaining Bitcoin prices, challenging recent allegations that Bitcoins are essentially worthless. Even with markets pricing Bitcoin in the thousands of dollars each, the valuation model seems robust. The data show that a price bubble that began in the Fall of 2017 resolved itself in early 2018, converging with the marginal cost model. This suggests that while bubbles may appear in the Bitcoin market, prices will tend to this bound and not collapse to zero.
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Applied Economics Letters
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Bitcoin price and its marginal cost of production:
support for a fundamental value
Adam S. Hayes
To cite this article: Adam S. Hayes (2018): Bitcoin price and its marginal cost
of production: support for a fundamental value, Applied Economics Letters, DOI:
10.1080/13504851.2018.1488040
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ARTICLE
Bitcoin price and its marginal cost of production: support for a fundamental value
Adam S. Hayes
Department of Sociology, University of Wisconsin-Madison, Madison, WI, USA; MSc Program in Digital Currencies, University of
Nicosia, Nicosia, Cyprus
ABSTRACT
This study back-tests a marginal cost of production model proposed to value the digital currency
Bitcoin. Results from both conventional regression and vector autoregression (VAR) models show
that the marginal cost of production plays an important role in explaining Bitcoin prices,
challenging recent allegations that Bitcoins are essentially worthless. Even with markets pricing
Bitcoin in the thousands of dollars each, the valuation model seems robust. The data show that a
price bubble that began in the Fall of 2017 resolved itself in early 2018, converging with the
marginal cost model. This suggests that while bubbles may appear in the Bitcoin market, prices
will tend to this bound and not collapse to zero.
KEYWORDS
Bitcoin; cost of production;
valuation model; bubbles;
cryptocurrency; model
testing
JEL CLASSIFICATION
D40; E47; G12; C52
I. Introduction
The price of Bitcoin increased from $250 in June
of 2015 to more than $19,000 by December of
2017, where it commanded a market capitalization
in excess of $325 billion before stabilizing around
the $10,000 level.
1
Presently, Bitcoin sees many
hundreds of millions of dollarsworth of transac-
tions cross its system on a daily basis; and yet, the
cryptocurrency functions entirely as its own
decentralized computer network, without any cen-
tral bank, government, or regulatory body to back
it. This has led some to conclude that the price of
the cryptocurrency is a massive speculative bub-
ble, with some researchers claiming that there is
no fundamental underpinning to its value (e.g.
Hanley 2013; Yermack 2013). Cheah and Fry
(2015), among others, echo recent comments
made by Jamie Dimon, the CEO of investment
bank JPMorgan Chase, in asserting that the funda-
mental value of Bitcoin is indeed zero, and that
the entire pursuit is a fools errand, or worse a
fraud.
2
Even the Wall Street Journal has opined
that Bitcoin is probably worth zero.
3
Nonetheless,
the popularity of the cryptocurrency continues to
rise, and its price remains far from nil. Against
this backdrop, it is of growing concern to evaluate
the basis for value of Bitcoin.
Challenging the views of Mr. Dimon and the
grim hypotheses of some sceptical researchers,
Hayes (2016) suggests that Bitcoin does indeed
have a quantifiable intrinsic value and formalizes
a pricing model based on its marginal cost of
production:
4
mining,or the process of creating
new Bitcoins through concerted computational
effort requires the consumption of electric power,
which incurs a real monetary cost for mining par-
ticipants, and thus the value of Bitcoin is the embo-
died costs of production (on the margin).
This study seeks to test the validity of this cost of
production theory of value by back-testing the pri-
cing model against the observed market price, going
back nearly 5 years. A simple ordinary least squares
(OLS) regression indicates that the model price
explains approximately 81% of the observed market
price and a striking 97% of the observed changes in
marketprices.Followingthisup,aGrangerteston
the postestimation results of a subsequent vector
autoregression (VAR) model is carried out, which
strongly rejects the null hypothesis that the pricing
model does not causethe market price. The
CONTACT Adam S. Hayes ahayes8@wisc.edu Department of Sociology, University of Wisconsin-Madison, Madison, WI, USA
1
For consistency, Bitcoin with a capital Brefers to the general system, network and protocol, while Bitcoin with a small brefers to the digital currency itself
or units thereof.
2
https://www.bloomberg.com/news/articles/201709-12/jpmorgan-s-ceo-says-he-d-fire-traders-who-bet-on-fraud-bitcoin.
3
https://www.wsj.com/articles/bitcoins-wild-ride-shows-the-truth-it-is-probably-worth-zero-1,505,760,623.
4
Or at least, an expected lower bound to its market price.
APPLIED ECONOMICS LETTERS
https://doi.org/10.1080/13504851.2018.1488040
© 2018 Informa UK Limited, trading as Taylor & Francis Group
Granger test is used here not asset causality, but to
support the notion that the modelled price and the
observed price match up to a statistically significant
degree over time.
II. The cost of production model
The process and technical elaboration of Bitcoin pro-
duction (mining) is described at length elsewhere
(e.g.Kroll,Davey,andFelten2013; Sapirshtein,
Sompolinsky, and Zohar 2016; Nakamoto 2008).
Suffice it to say that mining involves a competition
among producers; with a novel feature that the rate of
new unit formation is fixed so that increased demand
cannot induce a greater supply, and so this elasticity is
manifest instead through increased difficulty in the
production process itself, increasing the system-wide
marginal cost of production.
The primary ongoing cost for Bitcoin produc-
tion is that of electricity, measured in dollars per
kilowatt hour (kWh). Of course, different regions
of the world will consume electricity at their local
rates (which may vary by customer type, power
generation source, and time of day) and in their
local currencies, but for the sake of convenience it
is a good working assumption that the average
rate of electricity worldwide accounting for both
residential and commercial rates is approximately
USD $0.135 per kWh.
5
Following Hayes (2016), the (marginal) cost of
production per day, Eday per unit of mining
power can be expressed as follows:
Eday¼ρ=1000ðÞ$=kWh WperGH=shrday

(1)
where E
day
is the dollar cost per day for a producer, ρ
is the hashpower (computational power) employed by
a miner, $/kWh is the dollar price per kilowatt hour,
and W per GH/s is the energy efficiency of the hard-
ware, and hrs
day
is the number of hours in a day.
In order to calculate the expected number of Bitcoins
the same miner can produce daily, the following equa-
tion is used to calculate the daily (marginal) product:
BTC=day¼ βρ sechr
δ232

hrday (2)
where BTC/day* is the expected level of daily
Bitcoin production when mining Bitcoin, βis the
block reward (expressed in units of BTC/block), ρ
is the hashing power employed by a miner, and δ
is the difficulty (expressed in units of GH/block)
The constant sec
hr
is the number of seconds in an
hour and hr
day
is the number of hours in a day.
Presently, the block reward is 12.5 BTC per block.
According to microeconomic theory, under
conditions of competition, the marginal product
should equate with its marginal cost, which should
also equal its selling price. Because of this theore-
tical equivalence, and since cost per day is
expressed in terms of $/day and production in
BTC/day, the $/BTC price level is revealed as the
ratio of (cost/day) divided by (BTC/day). This
objective price of production, P*, serves as a logi-
cal lower bound for the market price, below which
a producer would operate at a marginal loss and
presumably remove themselves from the network.
P* is expressed in dollars per Bitcoin, given the
difficulty and cost of production:
P¼ Eday
BTC=day(3)
III. Testing the model empirically
I back-test the above model usinghistorical observed
price data and compare that to what the model
would have predicted. Observed market price and
difficulty data were collected using the website
blockchain.info, a reliable and transparent source
of Bitcoin market and protocol data, at the dates of
difficulty changes in the network (approximately
once every 2 weeks) to consistently measure market
price given a particular value of mining difficulty,
from 29 June 2013 through 27 April 2018.
The model requires as an input the average
energy efficiency of the mining network. This
information was extracted from Bitcoin mining
hardware manufacturer websites and checked
against a dedicated wiki page that catalogues the
efficiency of current mining hardware (https://en.
bitcoin.it/wiki/Mining_hardware_comparison).
These data were then collected for each date of
difficulty change, scraped from the web using the
5
https://en.wikipedia.org/wiki/Electricity_pricing.
2A. S. HAYES
internet archiveswayback machine (https://web.
archive.org/web/20,170,215,000,000*/https://en.bit
coin.it/wiki/Mining_hardware_comparison). As
stated above, for simplicity, I hold electricity
costs constant at 13.5 cents per kWh. Table A1
describes these data points along with estimated
model price for each difficulty change date.
Conventional regression analysis
As a first pass, I compared the ratio of observed price
to modelled price over time, from June 2013 through
April 2018. As shown in Figure 1, since June 2013,
the market price has tended to fluctuate about the
price estimated by the model. In the chart, a y-axis
value of 1.00 indicates that the market price and
model price are identical. The values >1.00 indicate
a premium in the market relative to the model and
<1.00 a relative discount. Over the long-run
(~5 years), the average ratio is 1.05, σ= 0.33, which
is striking in its accuracy. This suggests that the
market for Bitcoin has been quite efficient from a
production standpoint, if not volatile, contradicting
assertions that this market is consistently inefficient
(e.g. Urquhart 2016). There is evidence of increased
volatility from approximately September 2017
through January 2018, indicating that the market
had deviated substantially from the model, but did
eventually converge once again. This spike indicates
the emergence and reconciliation of a price bubble;
however, the presence of such bubbles does not
indicate a zero value, only that prolonged departures
from the modelled price can exist, but which ulti-
mately resolves to the marginal cost of production.
This initial result is suggestive, and so a more
rigorous analysis was undertaken to test the fitof
the pricing model against observed historical data.
The valuation model output and observed prices
appear in Figure 2, with what amounts to two time
series for comparison. A conventional OLS regres-
sion was first carried out to obtain a proxy for model
fit and to judge how much of the market price is
described by the model; which produces R
2
= 0.813,
telling us that 81% of the observed market price can
be explained by the marginal cost of production
model over the sample period. Next, I conduct a
second OLS regression on the log transformations
of each time series, yieldingan R
2
= 0.969, suggesting
that nearly all of the marginal change in market price
can be explained by the change in marginal cost.
VAR Granger analysis
Next, in order to compare these two time series
directly to each other in a methodologically rigorous
way, I estimate a multivariate VAR with two lags each
on the log transformation of market price and implied
model price.
6
The purpose of the VAR is primarily to
test the postestimation results using a Granger test
(Geweke 1982).Typicallyusedtosuggesttemporal
causality, I instead use this test here to evaluate the
0.500
1.000
1.500
2.000
2.500
3.000 Ratio of Bitcoin Market Price to Model Price
Figure 1. Ratio of Bitcoin price observed in the market to the expected price produced by the model using historical data (source:
www.blockchain.info). 1.00 would indicate that the two prices are identical, anything over 1.00 indicates a premium in the market
and below a discount. The average for the study period is 1.05, σ= 0.33, indicating that over the long-term, the market price seems
to fluctuate around the modelled price with striking consistency.
6
Testing for autocorrelation suggests that two is the appropriate number of lags.
APPLIED ECONOMICS LETTERS 3
post-hoc predictive power of the cost of production
pricing model. The test considers two null hypotheses:
H
0
1: The market price does not causethe model
price; and
H
0
2: Themodelpricedoesnot causethe market
price.
As shown in Table 1,H
0
1 cannot be rejected, which
is to be expected: the model is supposed to describe
the market and not the other way around. H
0
2, how-
ever, is strongly rejected, and the alternative hypoth-
esis that the model price implies the market price is
given a large degree of support (p< 0.001). This key
finding lends credibility that the marginal cost of
production of Bitcoin describes its price and disputes
those who claim that Bitcoin is worthless.
IV. Discussion and conclusion
The marginal cost of production has been proposed as
a model to value Bitcoin (Hayes 2016). In this paper,
the cost of production model was back-tested using
historical data showing that the market price of
Bitcoin tends to fluctuate around the model price,
and with the model price explaining the market
price in a statistically significant manner.
This finding is striking given the volume of recent
media accounts and research projects that have sup-
posed no fundamental value at all for Bitcoin (e.g.
Cheah and Fry 2015). Moreover, it suggests that
attempts to find a causal link between the long-run
price of Bitcoin and various exogeneous factors may
be misguided (e.g. Ciaian et al. 2016; Kristoufek and
Scalas 2015; Polasik et al. 2015), as well as attempts to
value Bitcoin as if it were a traditional financial asset
(e.g. Cretarola, Figà-Talamanca, and Patacca 2017).
These findings are also indicative that the Bitcoin
market is susceptible to price bubbles, as has been
suspected. However, despite a significant deviation
in price to the upside from the Fall of 2017 through
early 2018, the cost or production model has
remained resilient as the market price did ultimately
converge with the model. This novel pricing method
leadsustoexpectthatduringperiodsofexcess
demand(e.g.apricebubble),eitherthemarketprice
will fall and/or the mining difficulty will increase to
Table 1. Granger test on VAR postestimation equations.
Granger causality Wald tests
HO χ
2
df Prob > χ
2
1: Market price does not Granger
cause the model price
4.579 2 0.101
2: Model price does not Granger
cause the market price
13.301 2 0.001
HO l cannot be rejected, which is to be expected: the model is supposed to
describe the market and not the other way around. H02 however, is strongly
rejected, and the alternative hypothesis that the model price implies the
market price is given a large degree of support (p< 0.001). This key finding
lends credibility that the marginal cost of production of bit coin describes its
price and disputes those who claim that bit coin is worthless.
Figure 2. Historical Bitcoin market price vs. ex-post implied model price, June 2013April 2018.
4A. S. HAYES
resolvethediscrepancy.Inthecaseofthelate2017
bubblejustdescribed,itdoesappearthatboth
mechanisms were at play: the price fell and the mining
difficulty rose simultaneously. Bubbles in the Bitcoin
market have been explored in-depth elsewhere (e.g.
Garcia et al. 2014; Cheah and Fry 2015;Lietal.2018;
Hafner 2018). Cheung, Roca, and Su (2015)aswellas
Su et al. (2018) use the Phillips, Shi, and Yu (2013,
2015)) method of bubble detection, confirming that
multiple short-lived bubbles have characterized
Bitcoin prices, with four explosive bubblessince
2011 inclusive of the late-2017 period already
described (see also: Corbet, Lucey, and Yarovya
2017). The current study adds to this literature sug-
gesting that while bubbles can andindeedhave
existed in the Bitcoin market, the resolution of such a
bubble will not be a collapse towards zero, but rather
towards its marginal cost of production. Future ana-
lysis of Bitcoin bubbles given this prediction can be
explored further following the method elaborated by
Pavlidis, Paya, and Peel (2017)sincetherecentintro-
duction of Bitcoin futures markets in December 2017.
This type of analysis, however, will require a lengthier
time series than what is presently available.
It is important to note that the above analyses apply
primarilytoBitcoinanddoesnotnecessarilyextendto
other cryptocurrencies such as Ethereum or Litecoin;
although a similar study may indeed support the cost
of production thesis there as well. Still, with Bitcoin
dominating the digital currency market, both in scale
and scope, it is a worthwhile pursuit to understand
why this unique asset has value.
Disclosure statement
No potential conflict of interest was reported by the author.
ORCID
Adam S. Hayes http://orcid.org/0000-0001-5481-8906
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Appendix
Table A1.
Date Difficulty (observed) Market price (observed) Energy efficiency (J/GH) Implied model price Ratio mkt price/model price
06/29/13 21,335,329 77.87 500 68.73 1.133
08/03/13 37,392,766 94.95 400 96.36 0.985
09/04/13 86,933,018 119.10 225 126.01 0.945
10/16/13 267,731,249 164.08 100 172.48 0.951
10/25/13 390,928,788 195.05 90 226.67 0.861
11/05/13 510,929,738 333.93 90 296.25 1.127
12/21/13 1,180,923,195 683.69 90 684.72 0.998
01/24/14 2,193,847,870 792.02 60 848.03 0.934
02/05/14 2,621,404,453 682.21 45 759.97 0.898
02/16/14 3,129,573,175 580.01 25 504.05 1.151
02/28/14 3,815,723,799 614.46 25 614.57 1.000
03/13/14 4,250,217,920 595.75 25 684.55 0.870
03/24/14 5,006,860,589 495.02 15 483.85 1.023
04/05/14 6,119,726,089 449.62 10 394.26 1.140
04/17/14 6,978,842,560 468.89 10 449.61 1.043
04/29/14 8,000,872,136 434.67 9 463.91 0.937
05/12/14 8,853,416,309 457.65 9 513.34 0.892
05/24/14 10,455,720,138 598.07 9 606.24 0.987
06/05/14 11,756,551,917 616.04 8 605.93 1.017
06/18/14 13,462,580,115 584.68 7 607.12 0.963
06/29/14 16,818,461,371 623.82 6 650.11 0.960
07/12/14 17,336,316,979 616.36 5.5 614.29 1.003
07/25/14 18,736,441,558 581.91 5 603.54 0.964
08/08/14 19,729,645,941 534.26 4 508.43 1.051
08/19/14 23,844,670,039 501.86 3.3 506.94 0.990
08/31/14 27,428,630,902 474.96 3 530.12 0.896
09/13/14 29,829,733,124 426.66 2.25 432.40 0.987
09/25/14 34,661,425,924 360.23 1.75 390.78 0.922
10/09/14 35,002,482,026 375.10 1.75 394.63 0.951
10/23/14 35,985,640,265 338.82 1.5 347.75 0.974
11/05/14 39,603,666,252 370.64 1.5 382.72 0.968
11/18/14 40,300,030,328 366.80 1.5 389.45 0.942
12/02/14 40,007,470,217 352.88 1.5 386.62 0.913
12/17/14 39,457,671,307 319.05 1.25 317.76 1.004
12/30/14 40,640,955,017 288.21 1.1 288.01 1.001
01/12/15 43,971,662,056 221.97 1 283.29 0.784
01/27/15 41,272,837,895 226.81 0.85 226.01 1.004
02/09/15 44,455,415,962 231.28 0.85 243.44 0.950
02/22/15 46,684,376,317 252.45 0.85 255.65 0.987
03/08/15 47,427,554,951 276.01 0.85 259.72 1.063
03/22/15 46,717,549,645 248.65 0.85 255.83 0.972
04/05/15 49,446,390,688 233.50 0.8 254.84 0.916
04/19/15 47,610,564,513 228.89 0.8 245.38 0.933
05/03/15 47,643,398,018 238.70 0.8 245.55 0.972
05/17/15 48,807,487,245 237.34 0.8 251.55 0.944
05/31/15 47,589,591,154 228.49 0.8 245.27 0.932
06/14/15 49,692,386,355 244.30 0.8 256.11 0.954
06/28/15 49,402,014,931 261.20 0.8 254.62 1.026
07/11/15 51,076,366,303 278.70 0.8 263.25 1.059
07/25/15 52,278,304,846 280.99 0.8 269.44 1.043
08/08/15 52,699,842,409 249.33 0.75 254.64 0.979
08/22/15 54,256,630,328 222.53 0.65 227.20 0.979
09/04/15 56,957,648,455 235.00 0.65 238.52 0.985
(Continued)
6A. S. HAYES
Table A1. (Continued).
Date Difficulty (observed) Market price (observed) Energy efficiency (J/GH) Implied model price Ratio mkt price/model price
09/17/15 59,335,351,234 231.26 0.65 248.47 0.931
10/01/15 60,813,224,039 241.15 0.65 254.66 0.947
10/15/15 60,883,825,480 270.82 0.65 254.96 1.062
10/29/15 62,253,982,450 348.63 0.65 260.69 1.337
11/11/15 65,848,255,180 324.50 0.65 275.75 1.177
11/24/15 72,722,780,643 346.90 0.65 304.53 1.139
12/06/15 79,102,380,900 396.00 0.65 331.25 1.195
12/18/15 93,448,670,796 461.00 0.65 391.33 1.178
12/31/15 103,880,340,815 432.00 0.65 435.01 0.993
01/13/16 113,354,299,801 432.00 0.6 438.17 0.986
01/26/16 120,033,340,651 405.00 0.5 386.65 1.047
02/07/16 144,116,447,847 377.35 0.4 371.39 1.016
02/19/16 163,491,654,909 397.83 0.4 421.31 0.944
03/04/16 158,427,203,767 401.64 0.4 408.26 0.984
03/18/16 165,496,835,118 411.96 0.4 426.48 0.966
04/01/16 166,851,513,283 420.71 0.4 429.97 0.978
04/14/16 178,678,307,672 430.07 0.4 460.45 0.934
04/28/16 178,659,257,773 456.00 0.4 460.40 0.990
05/11/16 194,254,820,283 455.00 0.35 438.02 1.039
05/24/16 199,312,067,531 448.00 0.35 449.42 0.997
6/8/16 196,061,423,940 550.00 0.25 631.56 0.871
6/21/16 209,453,158,595 587.00 0.25 674.70 0.870
7/4/16 213,398,925,331 600.00 0.25 687.41 0.873
7/18/16 213,492,501,108 673.00 0.25 687.71 0.979
8/2/16 201,893,210,853 565.00 0.25 650.34 0.869
8/15/16 217,375,482,757 581.00 0.25 700.22 0.830
8/29/16 220,755,908,330 579.00 0.25 711.10 0.814
9/12/16 225,832,872,179 611.00 0.25 727.46 0.840
9/25/16 241,227,200,230 608.00 0.25 777.05 0.782
10/08/2016 258,522,748,405 616.00 0.25 832.76 0.740
10/22/2016 253,618,246,641 653.00 0.25 816.96 0.799
11/05/2016 254,620,187,304 712.00 0.25 820.19 0.868
11/18/16 281,800,917,193 750.00 0.25 907.74 0.826
12/02/16 286,765,766,821 764.00 0.25 923.74 0.827
12/15/16 310,153,855,703 782.00 0.25 999.08 0.783
12/28/16 317,688,400,354 955.00 0.25 1,023.35 0.933
01/10/17 336,899,932,796 902.00 0.25 1,085.23 0.831
01/22/17 392,963,262,344 923.00 0.25 1,265.82 0.729
02/05/17 422,170,566,884 1,018.00 0.25 1,359.91 0.749
02/18/17 440,779,902,287 1,061.00 0.25 1,419.85 0.747
03/03/17 460,769,358,091 1,272.00 0.25 1,484.24 0.857
03/17/17 475,705,205,062 1,131.00 0.25 1,532.35 0.738
03/30/17 499,635,929,817 1,037.00 0.25 1,609.44 0.644
04/13/17 520,808,749,422 1,193.00 0.25 1,677.64 0.711
04/27/17 521,974,519,554 1,314.00 0.25 1,681.40 0.781
05/10/17 559,970,892,891 1,821.00 0.25 1,803.79 1.010
05/23/17 595,921,917,085 2,379.00 0.25 1,919.60 1.239
06/04/17 678,760,110,083 2,698.00 0.25 2,186.44 1.234
06/17/17 711,697,198,174 2,507.00 0.25 2,292.54 1.094
07/02/17 708,659,466,230 2,561.00 0.25 2,282.75 1.122
07/17/17 804,525,194,568 2,059.00 0.25 2,591.56 0.795
07/27/17 860,221,984,436 2,570.00 0.25 2,770.97 0.927
08/09/17 923,233,068,449 3,424.00 0.25 2,973.94 1.151
08/24/17 888,171,856,257 4,363.00 0.25 2,861.00 1.525
09/06/17 922,724,699,726 4,311.00 0.25 2,972.30 1.450
09/18/17 1,103,400,932,964 3,943.00 0.25 3,554.30 1.109
10/02/17 1,123,863,285,133 4,293.00 0.25 3,620.22 1.186
10/15/17 1,196,792,694,099 5,711.00 0.25 3,855.14 1.481
10/26/17 1,452,839,779,146 5,773.00 0.25 4,679.92 1.234
11/10/17 1,364,422,081,125 6,363.00 0.25 4,395.11 1.448
11/24/17 1,347,001,430,559 8,707.00 0.25 4,339.00 2.007
12/07/17 1,590,896,927,258 11,000.00 0.25 5,124.64 2.146
12/18/17 1,873,105,475,221 17,373.00 0.25 6,033.70 2.879
01/01/18 1,931,136,454,487 15,000.00 0.22 5,474.15 2.740
01/13/18 2,227,847,638,503 13,850.00 0.22 6,315.23 2.193
01/25/18 2,603,077,300,218 11,000.00 0.22 7,378.89 1.491
02/06/18 2,860,000,000,000 8,100.00 0.2 7,370.16 1.099
02/20/18 3,007,383,866,429 10,500.00 0.2 7,749.97 1.355
03/05/18 3,290,605,988,754 10,750.00 0.2 8,479.83 1.268
03/19/18 3,462,542,391,191 9,000.00 0.2 8,922.90 1.009
04/01/18 3,511,060,552,899 7,000.00 0.18 8,143.14 0.860
04/14/18 3,839,316,899,029 8,350.00 0.18 8,904.46 0.938
04/27/18 4,022,059,196,164 9,330.00 0.18 9,328.29 1.000
This table consists of historical data observed for Bitcoin mining difficulty and price as well as estimated average network energy efficiency. Modelled prices also appear
along with the ratio of market price to modelled price. Energy prices for the model held constant at $0.135 per kWh. Data source: www.blockchain.info
APPLIED ECONOMICS LETTERS 7
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