Mathematical Model


#1

This section from the economics whitepaper introduces the mathematical model. Use this thread to discuss, debate and suggest improvements.

Alternatively, if you have a detailed improvement suggestion, please follow the steps to do so here: https://forum.radixdlt.com/t/radix-economic-model-improvement-proposals-remip/181


#4

In the “Positive Surplus Section” of the white paper, there seems to be a couple of errors. Or perhaps I’m just not understanding something.

The first error is here:

Pmin(t+1) =( R(t’) + W * nR(t’) ) / M(t’)

But the new Pmin(t+1) should be the amount remaining in the reserves at the end of the period, minus the amount taken out for the redistribution:

Pmin(t+1) = ( R(t’) - (1 - W) * nR(t’) ) / M(t’) = ( R(t) - dR(t’) + W * nR(t’) ) / M(t’)

Also, the next formula multiplies R(t’) by M(t’) which is obviously wrong. However, it seems like the rM(t’) is just the amount that we didn’t use to increase Pmin. Simply:

rM(t’) = (1 - W) * nR(t’)

Am I missing something?


#5

Hey Schew - thank you for your comments.

Pmin(t+1) = R(t+1)/M(t+1): Pmin also covers all newly created redistribution. You should not minus what is taken out for redistribution.

The interim formula Pmin(t+1) =( R(t’) + W * nR(t’) ) / M(t’) is essentially looking at what % of New Reserves are being pushed to increase Pmin for the next period, where the remainder will be used for redistribution. The M(t’) also includes any new supply created over that period prior to re-distribution.

You are right, the next formula is:

rM(t’) = (R(t’)/Pmin(t+1)) - M(t’)

It is missing the all important (-)!!

Redistribution supply = (Reserves at end of period/next period Pmin) MINUS period end Rad supply

Thanks for picking up that error!


#6

I know that there is the He3 one now, but there’s a bug in the Price Stabilization tab of the economics spreadsheet. The formula for sR(t’) XRI, starting on line 5 is:

=(G5*($O$4-E5))-$O$11

But it should be:

=(G5*($O$4-E5))-$O$11*E5


#7

Piers, I think you mean (R(t) - dR(t’)) rather than R(t’). R(t’) is defined as:

R(t’) = R(t) + nR(t’) - dR(t’)

If you substitute that into the Pmin equation, you get:
Pmin(t+1) = ( R(t) + nR(t’) - dR(t’) + W * nR(t’) ) / M(t’)

This isn’t right since it includes both nR(t’) and W * nR(t’). nR(t’) is defined as nM(t’) * Pmax so it already includes the “extra surplus” from having sold at the Pmax price. R(t+1) will be R(t’) minus the amount sent for redistribution. This results in:

Pmin(t+1) = ( R(t’) - (1 - W) * nR(t’) ) / M(t’)

which is the same as:

Pmin(t+1) = ( R(t) - dR(t’) + W * nR(t’) ) / M(t’)


#8

In the “Stage 3 Model: Mature Growth” section, page 31, I believe that the descriptions of the M(t+1) and rM(t) are reversed.

Also, I don’t understand why the surplus reserve sR(t) is divided by 0.9 to calculate the rM(t) during stage 3. If sR(t) represents the actual surplus, then it seems that that amount is all that can be redistributed.

Thanks for any clarification.


#9

Yep, good catch, thank you.

0.9 is the Pmin; if the system is going to print more Rads but maintain Pmin, then any new Rads it prints must have corresponding Reserves.

If Surplus Reserves are Reserves that can be Redistributed by printing new Rads, then given an amount of Reserves I can print (Surplus Reserves)/(Pmin) amount of Rads to maintain the Pmin for the new Rads printed.


#10

No - because dR(t’) is already accounted for in M(t’) as if dR occurs it also affects M(t’). Please have a look at the sR calculations as the maths is (sort of) covered there.