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\sum_{t=1}^{x}[PE(C_t)]-\sum_{u=1}^{z}[RAPR(R_u)\cdot YR(R_u)]+YoGE

BE(B_s)=\sum[PE(workers)+ASL(workers)]+PPC(B_s)

\sum_{t=1}^{x}[{CoL(C_t)+\sum_{n=1}^{YW}ASL(C_t,y_n)}]+\sum_{s=1}^{y}[CoP(B_s)

+SNL(B_s)]-\sum_{t=1}^{x}[CoL(C_t)]-\sum_{u=1}^{z}[RAPR(R_u)\cdot YR(R_u)]+YoGE

At the end of the month, before payday, we see that:

\sum_{s=1}^{NoB}[BE(B_s,M_{c+1})]=\sum_{t=1}^{NoWC}[PE(C_t,M_{c+1})+ESU(C_t,M_{c+1})

+SSA(C_t,M_{c+1})]+\sum_{s=1}^{NoB}PPC(B_s,M_{c+1})

And since

\sum_{t=1}^{NoWC}[PE(C_t,M_{c})+ESU(C_t,M_{c})]

+\sum_{s=1}^{NoB}PPC(B_s,M_c)\rightarrow \sum_{all}Businesses

If for all functions of Mc, the same function calculated at Mc+1 is the same, then the deficit for all

businesses in month c+1, disregarding the Safety Net, is:

\sum_{t=1}^{NoWC}[SSA(C_t,M_{c+1})]

Supposing this deficit is present month to month, where the money gets stored in a Savings Account, the

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deficit would amount to

\sum_{t=1}^{NoWC}\sum_{m=1}^{NoMW(C_t)}[SSA(C_t,m)]

This savings deficit is funded by recycling itself. All money, even saved money, goes somewhere;

furthermore, once its there, it goes somewhere else. Thus all Stored Savings Amounts are recycled (chiefly

during ones retirement. Suppose that Stored Savings Amounts for all people are depleted upon the end of

retirement (or death). Then clearly,

\sum_{p=1}^{NoRP}\sum_{m=1}^{NoMW(R_p)}

[SSA(R_p,m)]=\sum_{p=1}^{NoRP}\sum_{m=1}^{NoMR(R_p)}[PE(R_p,m)]

Now, we know that:

\sum_{p=1}^{NoRP}\sum_{m=1}^{NoMR(R_p)}[PE(R_p,m)]\rightarrow Businesses

Now, the Citizens Reserved Savings Amountis, as seen above (3), negative. And so, keeping the same

supposition (of retired citizens having had died), the money from those retired can be used to offset thedeficit (the negative amount).

CRSA(\bigcup_{all\: s}B_{s})=-\sum_{t=1}^{NoWC}\sum_{m=1}^{NoMW(C_t)}[SSA(C_t,m)]

+\sum_{p=1}^{NoRP}\sum_{m=1}^{NoMW(R_p)}[SSA(R_p,m)]

Now, suppose that for all Rp, there are citizens, Ct such that SSA(Rp,m)=SSA(Ct,m) (ie. Suppose that for

each retired person, there is a citizen who has the same Savings Amount Reserved)

CRSA(\bigcup_{all\: s}B_{s})=-\sum_{t=1}^{NoWC}\sum_{m=1}^{NoMW(C_t)}[SSA(C_t,m)]

+\sum_{t=1}^{NoRP}\sum_{m=1}^{NoMW(C_t)}[SSA(C_t,m)]

Then,

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CRSA(\bigcup_{all\: s}B_{s})=-\sum_{t=1}^{NoWC-NoRP}\sum_{m=1}^{NoMW(C_t)}[SSA(C_t,m)]\\

\\ for\; NoWC\geq NoRP

Or

CRSA(\bigcup_{all\: s}B_{s})=\sum_{t=1}^{NoRP-NoWC}\sum_{m=1}^{NoMW(C_t)}

[SSA(C_t,m)]\\ \\ for\; NoRP\geq NoWC

We see that if theNumber of Retired People andNumber of Working Citizens is the same, then the Citizens

Reserved Savings Amountis balanced (or zero) - meaning absent of a deficit or surplus. And since theStored Savings Amountaddressed above is the cumulative value of earnings for a retired citizen, their

Stored Savings Amount, having would been recycled back into the economy would supply a newly

employed citizens Stored Savings Amountfor life (assuming they require the same amount). Therefore, if

the count of the deceased is equivalent to the number of new workers (receiving the same pay as the

aforementioned deceased), no money needs to be created (making the Citizens Reserved Savings Amount

zero). If there happen to be more new workers than deceased, then the government should assume the

responsibility of making money to replenish the deficit as it would be calculated in the Citizens Reserved

Savings Amount. (Note: we could create a more complicated function to determine the exact amount ofmoney needed, however this method (of comparing the number of deceased and newly employed) yields

the same results - that is: when records are kept of the difference between the actual value and the expected

value - so as to balance the equation).

Another way to look at the amount of money needed is by the following calculation