In this equation we can see that, when \(V\)moves faster than \(T_{real}\), we are faced with inverse change in the money supply, \(M\). This is desired since growth in \(V\) exceeding \(T_{real}\) is very likely a sign of asset bubbles or other economic overheating. On the other hand, \(V\) decreasing faster than \(T_{real}\) is a likely indicator of a financial crash. Finally, any changes in \(T_{real}\) unmatched by changes in \(V\) should be taken as signs of real economic change which should be matched by changes in the money supply to allow the velocity of money to return to its previous equilibrium.
Calculating M dt
Having decided upon a rule upon which to base changes in our money supply we must now determine how to obtain our necessary inputs and how to distribute money into or remove money from the economy.
Determining Inputs
Turning first to the issue of obtaining \(T_{real}/V\ dt\), we can quickly see that only one piece of this will prove difficult, the calculation of \(T_{real}\ dt\).11 Interestingly, since we have required that we can precisely measure all other variables in the equation of exchange, we could quite easily solve for \(T\). However, this would provide us no insight into the financial and non-financial makeup of our total transaction value. To accomplish this, we must first calculate a price level for non-financial assets:
- In a given period \(t_0\), we analyze our transaction data to determine the \(n\) most valuable assets by total volume, which also occupy places among the \(m\) most valuable assets by total volume in period \(t_{-1}\). We denote this basket as \(B_0\left(P_0\right)\).
- The total value and proportionate makeup of this basket in period \(t_{-1}\) is then scaled to match that found in period \(t_0\) and denoted as \(B_{-1}\left(P_{-1}\right)\).
- Taking the ratio \(B_0\left(P_0\right)\ /\ B_{-1}\left(P_{-1}\right)\), we multiply it by the total value of all non-financial transactions in period \(t_{-1}\), \(T_{nf,-1}P_{nf,-1}\cdot\left(B_0\left(P_0\right)\ /\ B_{-1}\left(P_{-1}\right)\right)\), to obtain \(T_{nf,-1}P_{nf,0}\).
- Finally, we calculate \(T_{nf,0}P_{nf,0}-T_{nf,-1}P_{nf,0}\). Since the price level in both terms is now identical it can be ignored and we have therefore obtained \(T_{nf,0}-T_{nf,-1}=T_{nf}\ dt\).
Distributing M dt
Having successfully extracted \(T_{real}/V\ dt\), we must now determine how to distribute changes in the money supply when necessary. The first determination that must be made towards the adjustment of our currency supply that of the relevant time frames. Each supply adjustment requires three time periods, two to calculate movement in \(T_{real}/V\ dt\) and one to adjust the supply. As described above, we utilize periods \(t_{-1}\) and \(t_0\) to calculate the necessary adjustment. Once we have determined the required \(\Delta M\), we adjust our supply in period \(t_1\). For simplicity, we propose that as this cycle iterates, it always begins with period \(t_{i+1}\), where \(t_i\) was the distribution period of the previous cycle.
Having defined our three step process, let us first consider the case where \(\Delta M\) is positive. In these scenarios, \(\Delta M\) will be distributed pro rata to each existing positive Poly balance. Importantly, this distribution will be randomly distributed in time over the period \(t_1\) in order to avoid excessive market activity attempting to benefit from known supply adjustments. Turning now to cases where \(\Delta M\) is negative, we are faced with a more challenging problem, how to contract the money supply. Leveraging the fact that the movement of funds and value through the described Protocol must be paid in Polys, we propose that in times of monetary contraction, transaction fees are increased and the Polys collected as fees are not immediately transferable. The specific algorithms of this process are still being tested in simulations.
Conclusion
Although significant work remains, including the calculation of ideal values for key variables introduced, we believe that the Poly represents a promising new model of currency. First, as a single token stablecoin system, the Poly is designed to be free of well-known concerns involving the use of collateral as well as the lesser known problem of inequality created in multi-token systems. Second, by relying on endogenous information involving transaction value and velocity instead of on external price feeds, the Poly is first and foremost a new currency unto itself, not a crypto-peg to an existing currency. Taken together, these two considerations lead us to an optimistic assessment of the unique potential of the Poly.