A Chemical Analysis of Hybrid Economic Systems—Tokens and Money
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Connection between Chemical Reactions and Market Transactions
2.2. Chemical Model
- : X and Y enter the reactions/market in exactly the same quantity.
- and : The presence of the tokens in the reactions is superfluous.
- : In the RM2s context, this means that product Y can be bought with tokens only. This strategy can be used to reward loyal customers instead of introducing vouchers.
- and : Tokens are fully integrated and play an active role in the pricing of the products.
- : By starting with more of product X than Y, one may end up with a surplus of tokens at the end of the reactions that will have to be transferred and accounted for in the subsequent reaction mechanism.
- : One might run out of tokens in this step of the sequence of reaction mechanisms simply because selling product X will not generate enough tokens to buy all of the Y products. This is not an issue in RM2, but might become one in RM2s, where selling Y is restricted to token involvement.
- One can also imagine supplementing the reaction mechanisms with a way to buy X only with tokens at later stages.
2.3. Kinetic Study
2.4. Stability Analysis
2.5. Coefficient Adjustments According to the Supply and Demand Laws
3. Results
3.1. The Kinetic Study
3.2. The Stability Analysis
3.3. Coefficient Adjustments
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
DT | Digital technology |
ICO | Initial Coin Offering |
Reaction rate | |
RM1 | Reaction mechanism 1 |
RM2 | Reaction mechanism 2 |
RM2s | Reaction mechanism 2 short |
ODE | Ordinary differential equation |
Tr(J) | Trace of Jacobian |
Det(J) | Determinant of Jacobian |
S(J) | |
P | Price |
D | Demand |
S | Supply |
Appendix A. Integrated Rate Law
Appendix B. Experimental Assumptions
[X] (M) | [A] (M) | Rate (M/s) | Significance |
---|---|---|---|
units of product are sold for units of currency | |||
and the transaction speed in 10 units/s | |||
2 × | doubling the produce concentration does not | ||
affect the transaction speed | |||
2 × | 2 × | doubling the currency concentration | |
doubles the transaction speed |
[X] (M) | [A] (M) | Rate (M/s) | Significance |
---|---|---|---|
units of product are sold for units of currency | |||
and the transaction speed in 10 units/s | |||
2 × | 2 × | doubling the produce concentration | |
doubles the transaction speed | |||
2 × | doubling the currency concentration | ||
does not affect the transaction speed |
Appendix C. Scaling Factors
Appendix D. General and Special ODE Solutions
Nr. | Mec. | Fix. | Var. | Sol. |
---|---|---|---|---|
1 | X | Y, A | ||
2 | RM1 | Y | X, A | |
3 | - | X, Y, A | solutions exist only for known powers of a | |
4 | X, Y | A, B | no sol. | |
5 | X, A | Y, B | many sol. | |
6 | X, B | Y, A | ||
7 | RM2s | Y, A | X, B | |
8 | Y, B | X, A | ||
9 | A, B | X, Y | ||
10 | X | Y, A, B | no sol. | |
11 | Y | X, A, B | no sol. | |
12 | A | X, Y, B | no sol. (for and ) | |
many sol. (for ) | ||||
13 | B | X, Y, A | no sol. (for ) | |
14 | - | X, Y, A, B | no sol. | |
15 | X, Y | A, B | no sol. | |
16 | RM2 | X, A | Y, B | |
17 | X, B | Y, A | ||
18 | Y, A | X, B | ||
19 | Y, B | X, A | solutions exist only for known powers of a | |
20 | A, B | X, Y | ||
21 | X | Y, A, B | solutions exist only for known powers of a | |
22 | Y | X, A, B | solutions exist only for known powers of a | |
23 | A | X, Y, B | ||
24 | B | X, Y, A | no sol. (for ) | |
25 | - | X, Y, A, B | no sol. |
Mec. | Fix. | Var. | Sol. | Cond. | Comments |
---|---|---|---|---|---|
X | Y, A | (+, −) | |||
RM1 | Y | X, A | (i, i), (i, i) | ||
- | X, Y, A | (+, +, −) | |||
X, A | Y, B | many sol. | - | consistent, dependent | |
X, B | Y, A | (i, i), (i, i) | |||
Y, B | X, A | (+, −) | |||
RM2s | X | Y, A, B | - | inconsistent, independent | |
Y | X, A, B | - | inconsistent, independent | ||
A | X, Y, B | many sol. | consistent, dependent | ||
- | inconsistent, independent | ||||
B | X, Y, A | - | inconsistent, independent | ||
X, B | Y, A | (i, i), (i, i) | |||
Y, B | X, A | (i, i), (i, i) | |||
(+/−, −), (+/−, −) | |||||
RM2 | X | Y, A, B | (−, i, i), (−, i, i) | ||
Y | X, A, B | (−, i, i), (−, i, i) | |||
A | X, Y, B | (+, +, +) | |||
B | X, Y, A | - | inconsistent, independent |
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Chem. Elem. | Possible Interpretations |
---|---|
Z | Total amount of produce coming from a single supplier (e.g., vegetables), Total amount of produced goods, e.g., clothing, furniture |
X | Products not usually desired by most customers: imperfect products, e.g., tomatoes, used/not new goods, e.g., out-of-fashion clothing, second-hand furniture, recycled paper goods, e.g., notebooks |
Y | Niche or impactful products: organically sourced produce, traditional products (e.g., clothing) supporting local businesses, environmentally friendly building materials, renewable energy sources, low-power electronics |
A | Conventional currency |
B | Token(s) received for actions such as: consuming imperfect fruits and vegetables, buying second-hand goods, donating food and goods to the community, taking part in clean-up projects in nature, volunteering activities that benefit the community, minimising one’s CO footprint |
T | Market transactions |
Cases | Reaction Rates in RM1—Equations (2) and (3) | Reaction Rates in RM2s—Equations (6)–(8) |
---|---|---|
Mec. | ODE System | Scaled ODE System |
---|---|---|
RM1 | ||
RM2s | ||
RM2 | ||
Mec. | Fix. | Var. | Sol. | Cond. | Tr(J), Det(J), S(J) | Node |
---|---|---|---|---|---|---|
X, Y | A, B | (0, 0) | 0, 0, 0 | stable | ||
RM2s | Y, A | X, B | (+,+) | −, +, + | stable | |
A, B | X, Y | (+,+) | −, +, + | stable | ||
X, Y | A, B | (0, 0) | 0, 0, 0 | stable | ||
RM2 | Y, A | X, B | (+,+) | −, +, + | stable | |
X, A | Y, B | (+,+) | −, +, + | stable | ||
A, B | X, Y | (+,+) | −, +, + | stable | ||
A | X, Y, B | (+,+,+) | +, −, + | saddle |
Product | Status | Difference | New Coefficient |
---|---|---|---|
X | surplus | ||
X | deficit | ||
Y | surplus | ||
Y | deficit |
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Pardi, A.-L.; Paolucci, M. A Chemical Analysis of Hybrid Economic Systems—Tokens and Money. Mathematics 2021, 9, 2607. https://doi.org/10.3390/math9202607
Pardi A-L, Paolucci M. A Chemical Analysis of Hybrid Economic Systems—Tokens and Money. Mathematics. 2021; 9(20):2607. https://doi.org/10.3390/math9202607
Chicago/Turabian StylePardi, Anabele-Linda, and Mario Paolucci. 2021. "A Chemical Analysis of Hybrid Economic Systems—Tokens and Money" Mathematics 9, no. 20: 2607. https://doi.org/10.3390/math9202607