# Duality-symmetric Finance

Duality-symmetric Finance (DSF) is a modern hyperinflation-proof finance and monetary policy system, developed by S. Iriene in 2015. The DSF involves a systematic change to a country's financial system, from leaf to branch, but has many advantages over ordinary financial systems. It has been rumoured that the Zimbabwean government considered changing to the DSF in order to combat hyperinflation in the Zimbabwean economy in the 2010s.

In an ordinary financial system (OFS), the central government controls the money supply by minting currency (and destroying old or unusable currency) in a fixed denomination system. The central government then raises taxes from its populace, to varying degrees of success amongst the very wealthy in particular. For example, the Taiwanese government mints the New Taiwan dollar (NT$) as its currency in values 1/2, 1, 5, 10, 20 and 50. This is typical of most OFS currency systems. Such systems have been eminently prone to hyperinflation, as evinced by history, and tax evasion. The DSF can effectively combat these problems and more. ## The Duality-symmetric Finance System In the DSF, the only currency that needs to be minted is a single type of coin (or banknote), known as "the coin" (or "the banknote), which is the currency. That coin can take either a very low value (for example 1) or a very high value (for example 1,000,000) depending on the choice of the person who possesses the coins. When a monetary transaction occurs between two people, the person that holds the coins to be transferred decides which of the two values they wish the coin to have before exchanging it. The receiving party must accept this choice, but once is in possession of the coin can likewise choose its value to be either of the two currency values. For example, say two people want to enter into a financial transaction involving a DSF-based economy. Let us say the currency used in this economy is the "New Dollac" (N$). Suppose person A holds 100 coins and wishes to by a factory from person B. They agree on a price of N$10,000,080. Person A decides that ten of their coins will have the high value of N$1,000,000 and eighty of their coins will take the low value of N$1. Person A then exchanges a total of 90 coins to person B. Person B now possesses 80 coins that can take lots of values from N$80 to N$80,000,000 depending on their choice. The primary advantage of this system is that hyperinflation is neutralized since there is no impetus to raise prices because everybody is simultaneously rich and poor, and therefore already wealthy: there is no need to raise prices for necessary goods and services. Other advantages include: • No need to mint many different denomination of coins or notes, thus making enormous production cost savings. • No need to worry about currency forgery since, again, there is no impetus to forge coins. This is also a massive cost saving. Additionally, taxation is also not a problem since any individual can afford to pay even enormous tax bills. Thus, tax receipts would asymptote to 100% compliance. This would reduce the need for costly taxation regulation, legislation and enforcement costs by a substantial amount. Indeed, tentative cost estimates for a medium-sized economy are that the implementation of the DSF system would lead to a cost reduction of 92% for these sectors. For a country with a GDP per capita of$1000, this is estimated to be a cost saving of approximately \$135.2bn per year, depending on the exact size and type of the economy in question.

### Notes

The DSF system has some quirks that might not be immediately apparent. First is the question of why only a very small or very high amounts for the coin is permitted. This is to ensure that the poorer members of the populace are not priced out of the economy by a high denominatorial value of the base coin. Similarly, a very large amount is required so that the function of the low-value is still required to be utilized. Clearly, if every coin had a low-high value of, say, 1 and 100, then nobody would bother to use the low value since the high value is not so high that it is unpractical. Indeed, the delta between the two values helps to ensure the efficacy of the hyperinflation-neutralizing effects of the DSF. The fact that in order to pay for goods or services that cost much less than the high value, one would need many coins taking the low value would necessarily put a pressure on goods and services to keep the prices stabilized.

## Economics

It can be shown that for a DSF currency that has a low value of ${\displaystyle A}$ and a high value of ${\displaystyle \phi }$ that the average price of goods and services tends towards a stability value that is given by:

${\displaystyle \langle P\rangle =\log \left(e^{A}\log \phi {\sqrt {\frac {\phi +A}{\phi -A}}}\right)}$

assuming that the distribution of goods is such that the relative proportion of goods at price ${\displaystyle x}$ to those at price ${\displaystyle X}$ is given by:

${\displaystyle _{x}n_{X}={\frac {N_{X}}{N_{x}}}={\frac {X}{x}}e^{x-X}}$.

This model, the so-called "A-model", is a good model for the prices and distribution of diverse goods in an economy, but of course real economies may deviate from this model, especially if they are particularly unequal between poorer and richer classes, or is highly specialized in a particular industry; although even then the model may still be applicable to first approximation.

With an A-model economy, it can also be shown that the standard deviation of price fluctuations can be given by:

${\displaystyle \langle \sigma \rangle _{t}=\log \log \left[{\sqrt {\frac {A}{\phi }}}\left({\frac {\phi -A}{\phi +A}}\right)^{t}\right]}$.

This gives an expected lifetime until the system will decay to where the price fluctuation will exceed the value of ${\displaystyle \phi }$ as:

${\displaystyle \langle T_{\phi }\rangle =\exp \exp \left({\sqrt {\frac {\phi }{A}}}+{\frac {1}{2}}+O\left(\phi ^{-1}\right)\right)}$

which is obviously very large for large ${\displaystyle \phi }$.