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GoodDollar: A Distributed Basic Income
Overview
Background
The GoodDollar Basic Income Economy
Value Adoption and Network Effect
Monetary Tools and Controls
Smart Contracts
Distribution & Impact
Governance
Conclusion
Appendix
Special Thanks
References
Legal Disclaimer
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Appendix
Mathematical Equations
Equation 1: Reserve Ratio Equation
Let:
P
P
P
- the price of one 1G$ in Supported Currency;
R
R
R
- the amount of Supported Currency in the reserve;
S
S
S
- total G$ coins in circulation.
Then
r
r
r
- the reserve ratio - is defined as:
r
=
R
P
⋅
S
r=\frac{R}{P \cdot S}
r
=
P
⋅
S
R
At launch,
r
=
1
r=1
r
=
1
and overtime, will computationally decline at a daily rate in accordance with the
Expansion Rate
. In Equation 1, given
R
R
R
and
r
r
r
the system has two degrees of freedom,
P
P
P
and
S
S
S
that will be calculated as described below.
Equation 2: Buy/Sell Function & Current Price(
Bancor Formula
for Automated Market Making)
Current Price function:
C
u
r
r
e
n
t
P
r
i
c
e
=
R
e
s
e
r
v
e
B
a
l
a
n
c
e
S
m
a
r
t
T
o
k
e
n
′
s
T
o
t
a
l
S
u
p
p
l
y
⋅
R
e
s
e
r
v
e
R
a
t
i
o
Current Price = \frac{Reserve~Balance}{Smart~Token's~Total~Supply~ \cdot ~Reserve~Ratio}
C
u
rre
n
tP
r
i
ce
=
S
ma
r
t
T
o
k
e
n
′
s
T
o
t
a
l
S
u
ppl
y
⋅
R
eser
v
e
R
a
t
i
o
R
eser
v
e
B
a
l
an
ce
Buy function:
T
o
k
e
n
s
I
s
s
u
e
d
=
S
u
p
p
l
y
⋅
(
(
1
+
C
o
n
n
e
c
t
e
d
T
o
k
e
n
s
P
a
i
d
B
a
l
a
n
c
e
)
C
W
−
1
)
Tokens~Issued = Supply \cdot ((1+\frac{Connected ~Tokens~Paid}{Balance}) ^ {CW} -1)
T
o
k
e
n
s
I
ss
u
e
d
=
S
u
ppl
y
⋅
((
1
+
B
a
l
an
ce
C
o
nn
ec
t
e
d
T
o
k
e
n
s
P
ai
d
)
C
W
−
1
)
Sell function:
C
o
n
n
e
c
t
e
d
T
o
k
e
n
s
P
a
i
d
O
u
t
=
B
a
l
a
n
c
e
⋅
(
(
1
+
T
o
k
e
n
s
D
e
s
t
r
o
y
e
d
S
u
p
p
l
y
)
C
W
−
1
)
Connected~Tokens~Paid~Out = Balance \cdot (\sqrt[CW]{(1+\frac{Tokens~Destroyed}{Supply})} -1)
C
o
nn
ec
t
e
d
T
o
k
e
n
s
P
ai
d
O
u
t
=
B
a
l
an
ce
⋅
(
C
W
(
1
+
S
u
ppl
y
T
o
k
e
n
s
Des
t
roye
d
)
−
1
)
Equation 3:
Expansion Rate
Formula
q
=
r
t
r
t
−
1
q=\frac{r_t}{r_{t-1}}
q
=
r
t
−
1
r
t
Equation 4: Mint G$ from Declining Reserve Ratio - Once a day the reserve ratio is reduced while all other parameters are unchanged.
The GoodReserve contract mints an amount of G$ to satisfy Equation 1
P
=
R
r
⋅
S
P=\frac{R}{r \cdot S}
P
=
r
⋅
S
R
. If P and R do not change and the daily change in r=𝚫r and the corresponding change in S is 𝚫S, then
r
s
=
(
r
+
Δ
r
)
(
S
+
Δ
S
)
r s=(r+\Delta r)(S+\Delta S)
rs
=
(
r
+
Δ
r
)
(
S
+
Δ
S
)
and from here we can see that:
Δ
S
=
S
⋅
−
Δ
r
r
+
Δ
r
=
S
⋅
r
t
−
1
−
r
t
r
t
\Delta S=S \cdot \frac{-\Delta r}{r+\Delta r}=S \cdot \frac{r_{t-1}-r_{t}}{r_{t}}
Δ
S
=
S
⋅
r
+
Δ
r
−
Δ
r
=
S
⋅
r
t
r
t
−
1
−
r
t
From Equation 2 we get
q
=
r
t
r
t
−
1
q=\frac{r_t}{r_{t-1}}
q
=
r
t
−
1
r
t
and thus:
S
r
t
−
1
−
r
t
r
t
=
S
1
−
q
q
S \frac{r_{t-1}-r_{t}}{r_{t}}=S \frac{1-q}{q}
S
r
t
r
t
−
1
−
r
t
=
S
q
1
−
q
Equation 5: Mint G$ from Deposit Formula - The number of new tokens based on the daily interest deposited in the Reserve.
Z - Value deposited into the reserve
E - Newly minted tokens
The formula does not change the price or reserve ratio:
E
=
R
+
Z
R
r
−
P
⋅
S
P
E = \frac {\frac{R + Z}{Rr} - P \cdot S}{P}
E
=
P
R
r
R
+
Z
−
P
⋅
S
Monetary Example
This is an illustrative example, with simple rounded numbers, aimed at trackability:
10 Supporters have staked a total value of US$10 million in supported crypto to a third-party protocol
Protocol annual interest rate of 10%
Daily interest of US$2,736
G$ Price = US $1
GoodReserve = US $1,000,000
Supply of G$ = 1,250,000
G$ Market Capitalization = US$ 1,250,000
G$ Reserve Ratio = 80%
Daily Expansion Rate = 1%
Every day G$ minting occurs from two methods: From the deposit of interest to the GoodReserve and from the decline in reserve ratio.
1.
Minting derived from deposite of daily interest to the GoodReserve
1.
Deposit of US$2,736 to GoodReserve
2.
Calculated as follows:
1.
S
⋅
P
=
R
R
r
S \cdot P=\frac{R}{Rr}
S
⋅
P
=
R
r
R
2.
(1,250,000 +X)*1=(1,000,000 + 2736)/0.8
3.
1,250,000 + X = 1,002,736/0.8
4.
1,250,000 + X = 1,253,420
5.
X = 3,420
3.
3,420 G$ are minted
4.
2,736 G$ are allocated back to the 10 supporters
5.
684 G$ are distributed as basic income
2.
Mint from Reserve Ratio Decline
1.
Lower the Reserve Ratio from 80% to 79%
2.
Calculated as follows:
1.
S
⋅
P
=
R
R
r
S \cdot P=\frac{R}{Rr}
S
⋅
P
=
R
r
R
2.
(1,253,420+X)*1= 1,002,736/0.79
3.
1,253,420 + X = 1,269,286
4.
X = 15,866
3.
15,866 G$ are distributed as UBI
In total, on that day 16,550 G$ were distributed as basic income to Claimers.
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1yr ago
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Contents
Mathematical Equations
Monetary Example