Perpetual Public Deficits and Debts

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Perpetual Public Deficits and Public DebtsDebt-JCS JCSEngineering

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Jean-Claude Schmitz Management & Energy Consultancy [email protected] 25-09-13 Page 1 / 41

A treatise on

Perpetual Public Deficits and Debts

by Jean-Claude Schmitz Luxembourg

Consultant

Dipl Ing ETH Zrich BBA GSBA Zrich

version V0; septembre 25, 2013

Comments & Corrections are welcome at the following email-address :[email protected]


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Introduction.................................................................................................... 3

Abstract ......................................................................................................... 4

1) Maastricht table M1: stable deficit % & growth % ...................................... 7

2) Maastricht table M2: varying deficit % & growth % ................................. 10

3) Maastricht table M3, Nominal Growth Rate for stable debt ratio ............. 12

4) Maastricht table M4 : varying NGR% versus NGRT% ............................. 14

5) Maastricht table M5 : involving the interest rate....................................... 16

6) Maastricht table M6 : Surplus Deficit SD und Surplus Multiplicator.......... 19

7) Maastricht table M7 : Paying back the principal ? ................................... 22

8) M8 : targeting Interest rate, Surplus Multiplicator, Surplus Deficit, Public Debt ...... 24

9) Debt or Savings....................................................................................... 27

10) Debt Ratio Stabilization: easy or difficult................................................ 28

11) zero interest debt ratio limit.................................................................... 30

12) Background of the Surface Multiplicator SM ......................................... 32

13) Natural Debt ratios with little growth and little inflation ........................... 33

14) Comments to Maastricht Criteria and ECB goals................................... 36

15) Solving the Problem with Positive Money .............................................. 38


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Introduction

In Maastricht , in february 1992, the European Leaders did define a couple of criteria forpublic debt management that if adhered to should ensure financial stability throughout theEuroZone.

MC1: Public DeBt / GDP


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Abstract1) Maastricht table M1 : stable deficit % & growth %

In a first table (M1), the first Maastricht Criterium (MC1) of 60 % public debt as comparedto GDP is used as a starting point, and 5 % interest to be paid on that debt every year.

In the first year, that will mean 5% * 60 % = 3% additional public deficit, which is ok withthe second Maastricht Criterium (MC2).

The following years are not so reassuring, as last years deficit is added to this years debt,and debt grows faster and faster.

2) Maastricht table M2 : varying deficit % & growth %

Table M2 shows the effects of varying deficits and growth rates against debt.

3) Maastricht table M3 : Nominal Growth Rate for stable debt ratio

Since it is clear that only enough growth can make the rising debt levels look smaller, thequestion was: what is enough growth ?

A formula has been derived that gives the target growth rate in % of GDP, where the risingdebt would keep the same debt-to-GDP ratio thanks to the rising GDP.

The formula is: target growth rate >= deficit / debt

On table M3, it can be seen that as soon as the growth rate falls below that value, the debtratio rises and vice-versa.

Also, the bigger the debt with respect to GDP, the easier it is to stabilize that ratio

4) Maastricht table M4 : varying NGR% versus NGRT%Table M4 shows the effect of nominal growth rates varying against the target ratesmentioned above.

5) Maastricht table M5 :involving the interest rateThe formula defined above is used in table M5, in the special case where new debt is

contracted only to pay for the interest of the old debt.Again, it is interesting to see under which circumstances the debt ratio can stay constantor not, here the formula can be simplified to: target growth rate >= interest rate

6) Maastricht table M6 : Surplus Deficit SD und Surplus MultiplicatorIn order to plug new budget holes, and sustain the economy, public deficits are oftenbigger than just the interest that has to be paid on the old debts.

We define Surplus Deficit (SD) that extra amount, and Surplus Multiplier (SM) the factorbetween that amount and growth in GDP. This makes actual growth a result of these twovalues, while the rise or fall of debt ratio still depends on the relationship between actual

growth so produced and targeted growth. Table M6.


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7) Maastricht table M7 : Paying back the principal ?An attempt is made to pay not only the interest on the debt, but also the principal over 20years. The result is recession as GDP contracts, and a higher debt ratio as GDP contractsfaster than debt.

8) M8 : targeting Interest rate, Surplus Multiplicator, Surplus Deficit, Public Debt ratioA set of formulas are derived that connect interest rate, surplus deficit, surplus multiplicatorand debt. If you fix three out of these four, the last can be calculated and is over timeunavoidable, whatever the starting point.

9) Debt or SavingsDepending on the set of parameters, like when the interest rate is higher than the growthrate, public debt had better be negative, that means public wealth, as there may be nostable point to be found in the debt area. Any excursion below the calculated value of

wealth will then lead into relentlessly growing debt .

10) Debt Ratio Stabilization: easy or difficultWhere we confirm that large debt ratios are easier to stabilize than small ones, and thatbigger Surplus Multiplicators do help. Rogoff-Reinhard got it all wrong with their 90%discussion.

11) zero interest debt ratio limitWhere we calculate the minimal Surplus Multiplicator needed to render debt ratiostabilization possible. Again, the bigger the debt, the smaller SM is needed, and the easierit is to stabilize the debt ratio. And small debts do require SM values that might beunachievable in real life. A 60 % debt or below may thus be impossible to hold as itrequires an SM bigger than 1,66, even if the interest is zero.

12) Background of the Surface Multiplicator SM

The real life meaning of the Surplus Multiplicator SM is explained as the tendency of thepopulation involved to let their money circulate, and not hide or hoard it. It is thus a matterof culture and discipline.


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13) Natural Debt ratioswith little growth and little inflation

We use the formulas mentioned above to determine natural debt ratios for givenproductivity and inflation rates, so that nominal growth is in line with the ECB criteria and

economic reality. We use 2% productivity + 2 % inflation to have 2 + 2 = 4% nominalgrowth NGR , and calculate the Surplus Deficit SD from there backwards with SM as input.SD = NGR / SM, in this case SD% = 4% / SM.Doing that with the interest rate as parameter shows again how impossible it is to stabilizelow debt ratios.Once you get into debt, within our economic system, you can only stabilize at high debtlevels. The Japanese seem to have understood just that .(Abenomics; 2013)

14) Comments to Maastricht Criteria and ECB goals

How it becomes clear that the Maastricht criteria and the ECB targets are not consistent,and that within our system they can push any troubled economy only further down.

15) Solving the Problem with Positive Money

Since it becomes clear that a system that relies on ever getting further into perpetual debtis incompatible with any level of common sense, the proposal is to end the drama by:

having the Central Bank generate Positive Money-no-debt to

pay for the public debts interest, to

pay down the public debt itself over the years, and to

provide some extra into the economy in order to enable a few % of growth

as compatible with inflation targets and productivity improvements

How well that would work is shown on table PM1.

The handling of the existing debt should be coordinated with the finance ministry, the extrafor growth should be equally distributed to all citizens of the EuroZone.

At the same time, Money-debt should be fed into the commercial banks, so that these canlend out money-debt, but without creating any on their own. (no fractional reserveanymore!). The amounts available for each bank would have to be backed by 25 .. 33 %equity.


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1) Maastricht table M1: stable deficit % & growth %

We assume that the government already has a 60% debt, has and keeps a 3 % deficit,and has to pay 5% interest on its debt at any moment in time.

The situation is described by the following formulas:

Formulas used in Table M1

YY Year YY = YY + 1

GDP Gross Domestic Product GDP = GDP + NGRPDB Public Debt PDB = PDB + PDF

BI% Bank Interest % BI% : input

PDF% Public DeFicit% PDF% : input

NGR% Nominal Growth % NGR% : input

PDF Public DeFicit PDF = PDF% * GDP

BI Bank Interest BI = BI% * PDB

NGR Nominal Growth NGR = NGR% * GDP

PDB% Public DeBt % PDB% = PDB / GDP

Note: in case the same value is on both sides of the equation, the value on the right is theold one from the line above, from the year before.

Also, at this level, the interest BI is not fed into one of the other formulas, that will be doneat a later stage.

Values used in Table M1:

We start out with the 60 % Maastricht limit, 3 % deficit, 5 % interest rate and assume 1 %nominal growth.


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M1 Perpetual Public Deficits and Public Debts jcs;28-8-13 M1

startvalue

Year

Gro

ss

Dom

estic

Pro

du

ct

Public

Debt

Bank

Intere

st%

Public

DeFicit%

Nomin

alGrow

th

%

Public

DeFicit

Bank

Intere

st

Nomin

alGrow

th

Public

DeB

t%

startvalue

inputvalue

YY=YY+1

GDP=

GDP+N

GR

PDB=

PDB+PDF

BI%:in

put

PDF

%:in

put

NGR

%:in

put

PDF=PDF

%*

GDP

BI=

BI%*PDB

NGR=

NGR

%*

GDP

PDB

%=

PDB/

GDP

inputvalue

YY GDP PDB BI% PDF% NGR% PDF BI NGR PDB%

0 100 60 5,0% 3,0% 1,0% 3,0 3 1 60%

1 101 63 5,0% 3,0% 1,0% 3,0 3,2 1,0 62%

2 102 66 5,0% 3,0% 1,0% 3,1 3,3 1,0 65%

3 103 69 5,0% 3,0% 1,0% 3,1 3,5 1,0 67%

sameasabove

4 104,1 72 5,0% 3,0% 1,0% 3,1 3,6 1,0 69%

sameasabove

5 105,1 75 5,0% 3,0% 1,0% 3,2 3,8 1,1 72%

6 106,2 78 5,0% 3,0% 1,0% 3,2 3,9 1,1 74%

7 107,2 82 5,0% 3,0% 1,0% 3,2 4,1 1,1 76%

8 108,3 85 5,0% 3,0% 1,0% 3,2 4,2 1,1 78%

9 109,4 88 5,0% 3,0% 1,0% 3,3 4,4 1,1 81%10 110,5 91 5,0% 3,0% 1,0% 3,3 4,6 1,1 83%

11 111,6 95 5,0% 3,0% 1,0% 3,3 4,7 1,1 85%

12 112,7 98 5,0% 3,0% 1,0% 3,4 4,9 1,1 87%

13 113,8 101 5,0% 3,0% 1,0% 3,4 5,1 1,1 89%

14 114,9 105 5,0% 3,0% 1,0% 3,4 5,2 1,1 91%

15 116,1 108 5,0% 3,0% 1,0% 3,5 5,4 1,2 93%

16 117,3 112 5,0% 3,0% 1,0% 3,5 5,6 1,2 95%

calculationwith/withinaboveline

17 118,4 115 5,0% 3,0% 1,0% 3,6 5,8 1,2 97%


18 119,6 119 5,0% 3,0% 1,0% 3,6 5,9 1,2 99%

19 120,8 122 5,0% 3,0% 1,0% 3,6 6,1 1,2 101%

20 122 126 5,0% 3,0% 1,0% 3,7 6,3 1,2 103%

21 123,2 130 5,0% 3,0% 1,0% 3,7 6,5 1,2 105%

22 124,5 133 5,0% 3,0% 1,0% 3,7 6,7 1,2 107%

23 125,7 137 5,0% 3,0% 1,0% 3,8 6,9 1,3 109%

24 127 141 5,0% 3,0% 1,0% 3,8 7,0 1,3 111%

25 128,2 145 5,0% 3,0% 1,0% 3,8 7,2 1,3 113%

26 129,5 149 5,0% 3,0% 1,0% 3,9 7,4 1,3 115%

27 130,8 152 5,0% 3,0% 1,0% 3,9 7,6 1,3 117%

28 132,1 156 5,0% 3,0% 1,0% 4,0 7,8 1,3 118%

29 133,5 160 5,0% 3,0% 1,0% 4,0 8,0 1,3 120%

calculationwith/withinsameline

30 134,8 164 5,0% 3,0% 1,0% 4,0 8,2 1,3 122%



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Comments to Table (M1):

With 1% nominal growth, 5 % Bank Interest rate, and 3% deficit at any moment in time,interests get compounded, debt rises faster than GDP and reaches 122 % of GDP after30 years.

Perpetual Public Deficits and Public Debts : Table (M1)

0

100

200

300

400

500

0 5 10 15 20 25 30 year

Gross Domestic Product

Public Debt

60% Public Debt at the start,

5% interest, 3 % Deficit; 1 % nominal growth,


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2) Maastricht table M2: varying deficit % & growth %It is obviously interesting to change the input parameters and see what happens to GDPand Debt .

This has been done on table M2, with a change every few years that can be seen asdarker green number.

The formulas are the same as for M1, we start out with the same numbers as on M1, andchange something every 5 years.

0 years : deficit 3 % debt ratio PDB % goes up

5 years : deficit from 3 % downto 2 %; goes up slower

10 years : deficit from 2 % downto 0 % goes up slower

15 years : growth from 1 % up to 2 % comes down

20 years : deficit from 0% up to 2 % goes up

25 years : growth from 2 % up to 4 % goes down

Comments to Table M2:

Depending on the set of parameters chosen as inputs, GDP & Debt do vary a lot.The higher the deficit and the lower the nominal growth, the worse it gets


0

50

100

150

200

1 3 5 7 911

13

15

17

19

21

23

25

27

29

31

0

1

2

3

4Gross Domestic Product

Public Debt

Public DeFicit

Public DeBt %

60% Public Debt, 5% interest,

with varying deficit and growth


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startvalue

Year

Gross

Dom

estic

Product

PublicD

ebt

BankIn

tere

st%

PublicD

eFicit%

Nomin

alGrow

th

% PublicD

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BankIn

tere

st

Nomin

alGrow

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PublicD

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t%

startvalue

inputvalue

YY=YY+1

GDP=

GDP+N

GR

PDB=

PDB+PDF

BI%:in

put

PDF

%:in

put

NGR

%:in

put

PDF=PDF

%

*

GDP

BI=

BI%*PDB

NGR=

NGR

%*

GD

P

PDB

%=

PDB/

GDP

inputvalue

YY GDP PDB BI% PDF% NGR% PDF BI NGR PDB%

0 100 60 5,0% 3,0% 1,0% 3,0 3 1 60%

1 101 63 5,0% 3,0% 1,0% 3,0 3,2 1,0 62%

2 102 66 5,0% 3,0% 1,0% 3,1 3,3 1,0 65%

3 103 69 5,0% 3,0% 1,0% 3,1 3,5 1,0 67%

sameasabove

4 104,1 72 5,0% 3,0% 1,0% 3,1 3,6 1,0 69%

sameasabove

5 105,1 75 5,0% 2,0% 1,0% 2,1 3,8 1,1 72%

6 106,2 77 5,0% 2,0% 1,0% 2,1 3,9 1,1 73%

7 107,2 80 5,0% 2,0% 1,0% 2,1 4,0 1,1 74%8 108,3 82 5,0% 2,0% 1,0% 2,2 4,1 1,1 75%

9 109,4 84 5,0% 2,0% 1,0% 2,2 4,2 1,1 77%

10 110,5 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 78%

11 111,6 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 77%

12 112,7 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 76%

13 113,8 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 76%

14 114,9 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 75%

15 116,1 86 5,0% 0,0% 2,0% 0,0 4,3 2,3 74%

16 118,4 86 5,0% 0,0% 2,0% 0,0 4,3 2,4 73%


17 120,8 86 5,0% 0,0% 2,0% 0,0 4,3 2,4 71%


18 123,2 86 5,0% 0,0% 2,0% 0,0 4,3 2,5 70%

19 125,7 86 5,0% 0,0% 2,0% 0,0 4,3 2,5 68%

20 128,2 86 5,0% 2,0% 2,0% 2,6 4,3 2,6 67%

21 130,7 89 5,0% 2,0% 2,0% 2,6 4,4 2,6 68%

22 133,4 91 5,0% 2,0% 2,0% 2,7 4,6 2,7 68%

23 136 94 5,0% 2,0% 2,0% 2,7 4,7 2,7 69%

24 138,7 97 5,0% 2,0% 2,0% 2,8 4,8 2,8 70%

25 141,5 99 5,0% 2,0% 4,0% 2,8 5,0 5,7 70%

26 147,2 102 5,0% 2,0% 4,0% 2,9 5,1 5,9 69%

27 153,1 105 5,0% 2,0% 4,0% 3,1 5,3 6,1 69%

28 159,2 108 5,0% 2,0% 4,0% 3,2 5,4 6,4 68%29 165,6 111 5,0% 2,0% 4,0% 3,3 5,6 6,6 67%


30 172,2 115 5,0% 2,0% 4,0% 3,4 5,7 6,9 67%



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3) Maastricht table M3, Nominal Growth Rate for stable debt ratio

One good question is what growth rate will be needed to keep the debt ratio constant, as afunction of debt & deficit, and whatever else.

We call that growth rate NGRT%, the formula is derived below.

Starting from the requirement to keep the debt ratio constant:

PDB% = PDB / GDP = constant

=> PDB / GDP = (PDB+PDF) / (GDP + NGRT)

PDB*(GDP + NGRT ) = GDP*(PDB + PDF )

PDB*GDP+ PDB * NGRT = PDB * GDP+ PDF * GDP

PDB * NGRT = GDP * PDF

NGRT = GDP * PDF / PDB

NGRT% = NGRT / GDP

NGRT% = PDF / PDB (F1)

So, as long as Nominal GRowth is at least equal or bigger than the ratio of Public DeFicitto DeBt, the debt ratio does not rise and trouble is contained.

In the next table M3, while otherwise using the same numbers than on table M2, wecalculate this value NGRT% for any moment in time, by adding a column on the right withformula (F1)

We see that every time NGR% is bigger or at least equal to the target value NGRT%, thedebt ratio PDB% does not rise. For these occasions, NGRT% has been put to darkergreen in the table.


0,0%

0,5%

1,0%

1,5%

2,0%

2,5%

3,0%

3,5%

4,0%

4,5%

5,0%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

NGR%

NGRT%

PDB%

60% Public Debt, 5% interest,

with varying deficit and growth debt service.


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startvalue

Ye

ar

Gr

oss

Dom

estic

Pro

duct

Pu

blicD

ebt

Ba

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tere

st%

Pu

blicD

eFicit%

No

minalGrow

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startvalue

inputvalue

YY=YY+1

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GR

PDB=

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PDF

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BI=

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%=

PDF/PDB

inputvalue

YY GDP PDB BI% PDF% NGR% PDF BI NGR PDB% NGRT%

0 100 60 5,0% 3,0% 1,0% 3,0 3 1 60% 5%

1 101 63 5,0% 3,0% 1,0% 3,0 3,2 1,0 62% 5%

2 102 66 5,0% 3,0% 1,0% 3,1 3,3 1,0 65% 5%

3 103 69 5,0% 3,0% 1,0% 3,1 3,5 1,0 67% 4%

sameasabove

4 104,1 72 5,0% 3,0% 1,0% 3,1 3,6 1,0 69% 4%

sameasabove

5 105,1 75 5,0% 2,0% 1,0% 2,1 3,8 1,1 72% 3%

6 106,2 77 5,0% 2,0% 1,0% 2,1 3,9 1,1 73% 3%

7 107,2 80 5,0% 2,0% 1,0% 2,1 4,0 1,1 74% 3%

8 108,3 82 5,0% 2,0% 1,0% 2,2 4,1 1,1 75% 3%

9 109,4 84 5,0% 2,0% 1,0% 2,2 4,2 1,1 77% 3%

10 110,5 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 78% 0%

11 111,6 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 77% 0%

12 112,7 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 76% 0%

13 113,8 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 76% 0%

14 114,9 86 5,0% 0,0% 1,0% 0,0 4,3 1,1 75% 0%

15 116,1 86 5,0% 0,0% 2,0% 0,0 4,3 2,3 74% 0%

16 118,4 86 5,0% 0,0% 2,0% 0,0 4,3 2,4 73% 0%

calc

ulationwith/withinaboveline

17 120,8 86 5,0% 0,0% 2,0% 0,0 4,3 2,4 71% 0%

calc


18 123,2 86 5,0% 0,0% 2,0% 0,0 4,3 2,5 70% 0%

19 125,7 86 5,0% 0,0% 2,0% 0,0 4,3 2,5 68% 0%

20 128,2 86 5,0% 2,0% 2,0% 2,6 4,3 2,6 67% 3%

21 130,7 89 5,0% 2,0% 2,0% 2,6 4,4 2,6 68% 3%

22 133,4 91 5,0% 2,0% 2,0% 2,7 4,6 2,7 68% 3%

23 136 94 5,0% 2,0% 2,0% 2,7 4,7 2,7 69% 3%

24 138,7 97 5,0% 2,0% 2,0% 2,8 4,8 2,8 70% 3%

25 141,5 99 5,0% 2,0% 4,0% 2,8 5,0 5,7 70% 3%

26 147,2 102 5,0% 2,0% 4,0% 2,9 5,1 5,9 69% 3%

27 153,1 105 5,0% 2,0% 4,0% 3,1 5,3 6,1 69% 3%

28 159,2 108 5,0% 2,0% 4,0% 3,2 5,4 6,4 68% 3%29 165,6 111 5,0% 2,0% 4,0% 3,3 5,6 6,6 67% 3%


30 172,2 115 5,0% 2,0% 4,0% 3,4 5,7 6,9 67% 3%



14/41


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -


4) Maastricht table M4 : varying NGR% versus NGRT%

On this table, starting out with the usual 60% debt, 3% deficit, 5 % interest,

we have initially 1% growth, but we calculate that the

target growth rate would be 5 % at year zero, and

coming down to 3,6 % after 10 years.

Due to

NGRT%( 5 .. 3,6%) > NGR% (1%) ,

the debt ratio grows from 60 % to 83 % during that time.

On year 10, we set the growth rate to exaclty the target rate, and we see that the debt ratiostays constant from there on, while GDP and debt are rising synchronously.

So the formula (F1) is correct and sets the right target.

It is interesting to see that higher debt ratios seem to demand lower target growth rates tokeep the debt ratio stable


0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

0%

1%

2%

3%

4%

5%

6%

Gross Domestic Product

Public Debt

Public DeBt %NGR%

NGRT%

60% Public Debt to start,

nominal growth gets to the target after 10 years.


15/41


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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -



startvalue

Ye

ar

Gr

oss

Dom

estic

Pro

duct

Pu

blicD

ebt

Ba

nkIn

tere

st%

Pu

blicD

eFicit%

No

minalGrow

th

%

Pu

blicD

eFicit

Ba

nkIn

tere

st

No

minalGrow

th

Pu

blicD

eB

t%

No

minalGR

ow

th

Ta

rget%

startvalue

inputvalue

YY=YY+1

GDP=

GDP+N

GR

PDB=

PDB+PDF

BI%:in

put

PDF

%:in

put

NGR

%:in

p

ut

PDF=PDF

%*

GDP

BI=

BI%*PDB

NGR=

NGR

%*

GDP

PDB

%=

PDB/

GDP

NGRT

%=

PDF/PDB

inputvalue


0 100 60 5,0% 3,0% 1,0% 3,0 3 1 60% 5,0%

1 101 63 5,0% 3,0% 1,0% 3,0 3,2 1,0 62% 4,8%

2 102 66 5,0% 3,0% 1,0% 3,1 3,3 1,0 65% 4,6%

3 103 69 5,0% 3,0% 1,0% 3,1 3,5 1,0 67% 4,5%

sameasabove

4 104,1 72 5,0% 3,0% 1,0% 3,1 3,6 1,0 69% 4,3%

sameasabove

5 105,1 75 5,0% 3,0% 1,0% 3,2 3,8 1,1 72% 4,2%

6 106,2 78 5,0% 3,0% 1,0% 3,2 3,9 1,1 74% 4,1%

7 107,2 82 5,0% 3,0% 1,0% 3,2 4,1 1,1 76% 3,9%

8 108,3 85 5,0% 3,0% 1,0% 3,2 4,2 1,1 78% 3,8%

9 109,4 88 5,0% 3,0% 1,0% 3,3 4,4 1,1 81% 3,7%

10 110,5 91 5,0% 3,0% 3,6% 3,3 4,6 4,0 83% 3,6%

11 114,5 95 5,0% 3,0% 3,6% 3,4 4,7 4,2 83% 3,6%

12 118,6 98 5,0% 3,0% 3,6% 3,6 4,9 4,3 83% 3,6%

13 122,9 102 5,0% 3,0% 3,6% 3,7 5,1 4,5 83% 3,6%

14 127,4 105 5,0% 3,0% 3,6% 3,8 5,3 4,6 83% 3,6%

15 132 109 5,0% 3,0% 3,6% 4,0 5,5 4,8 83% 3,6%

16 136,8 113 5,0% 3,0% 3,6% 4,1 5,7 5,0 83% 3,6%

calc


17 141,7 117 5,0% 3,0% 3,6% 4,3 5,9 5,1 83% 3,6%

calc


18 146,9 122 5,0% 3,0% 3,6% 4,4 6,1 5,3 83% 3,6%

19 152,2 126 5,0% 3,0% 3,6% 4,6 6,3 5,5 83% 3,6%

20 157,7 130 5,0% 3,0% 3,6% 4,7 6,5 5,7 83% 3,6%

21 163,4 135 5,0% 3,0% 3,6% 4,9 6,8 5,9 83% 3,6%

22 169,4 140 5,0% 3,0% 3,6% 5,1 7,0 6,1 83% 3,6%

23 175,5 145 5,0% 3,0% 3,6% 5,3 7,3 6,4 83% 3,6%

24 181,9 150 5,0% 3,0% 3,6% 5,5 7,5 6,6 83% 3,6%

25 188,5 156 5,0% 3,0% 3,6% 5,7 7,8 6,8 83% 3,6%

26 195,3 162 5,0% 3,0% 3,6% 5,9 8,1 7,1 83% 3,6%

27 202,4 167 5,0% 3,0% 3,6% 6,1 8,4 7,3 83% 3,6%

28 209,7 174 5,0% 3,0% 3,6% 6,3 8,7 7,6 83% 3,6%29 217,3 180 5,0% 3,0% 3,6% 6,5 9,0 7,9 83% 3,6%


30 225,2 186 5,0% 3,0% 3,6% 6,8 9,3 8,2 83% 3,6%



16/41


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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -


5) Maastricht table M5 : involving the interest rate

We have to recognize that deficit and interest rate are certainly connected, as part of thedeficit is to pay for these interests, and the rest of the deficit is to help growth come about.

We introduce the concept of Surplus Deficit SD, meaning the deficit that goes beyondpaying for the interest.

We then have the formula:

PDF = BI + SD

Where

PDF : Public DeFicit

BI : Bank Interest

SD : Surplus Deficit

We set the Surplus Deficit as a function of GDP, with the factor SD% :

SD = SD% * GDP

And we have from before :

BI = BI% * PDB

So we can express formula F+ now as follows:

(F1) : NGRT% = PDF / PDB

=>

NGRT% = ( BI + SD ) / PDB = BI / PDB + SD / PDB

NGRT% = BI% + SD / PDB

Since both SD% and PDB% are defined relative to GDP, we can also state:

(F2) : NGRT% = BI% + SD% / PDB%

The bigger the debt, the smaller NGRT%, but growth % always has to be bigger than theinterest rate BI% ! Welcome to Abenomics

On (F2), we have a special case when the Surplus Deficit is zero, that means if Deficit ismade only to pay for the interest on the existing debt.

In that case, we can simplify towards:

(F3) : NGRT% = BI %

So if we do not need to support our economy with more deficit, the debt ratio stays thesame if the growth rate equals the interest rate.

That sounds simple enough, whether growth will get there by itself is another matter.


17/41


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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -


Table M5 shows that, starting again from 60 % and 3 % deficit, and now having deficitpaying for interest only, we see that growth needs to equal the interest rate at 5 %.

After year 0, growth % equals interest % and the debt ratio is constant

After year 10, we set growth lower and the debt ratio rises,

after year 20, we set growth higher than BI% and the debt ratio comes down again.

In reality, the difficulty will be to have the economy grow at such a fast pace withouthelping it with any surplus deficit.

It is therefore very likely that growth wiill not be so high, and that the debt ratio will runaway.


0

100

200

300

400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

0%

2%

4%

6%

8%

GDP PDB

PDB% NGR%

BI%

60% Public Debt to start, no surplus deficit SD =0;

nominal growth changes every 10 years.


18/41


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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -



startvalue

Ye

ar

Gr

oss

Dom

estic

Pro

duct

Pu

blicD

ebt

Ba

nkIn

tere

st%

Pu

blicD

eFicit%

No

minalGrow

th

%

Pu

blicD

eFicit

Ba

nkIn

tere

st

No

minalGrow

th

Pu

blicD

eB

t%

No

minalGR

ow

th

Ta

rget%

startvalue

inputvalue

YY=YY+1

GDP=

GDP+N

GR

PDB=

PDB+PDF

BI%:in

put

PDF

%=

PDF/

GDP

NGR

%:in

put

PDF=BI

BI=

BI%*PDB

NGR=

NGR

%*

GDP

PDB

%=

PDB/

GDP

NGRT

%=

BI%

inputvalue


0 100 60 5,0% 3,0% 5,0% 3,0 3 5 60% 5,0%

1 105 63 5,0% 3,0% 5,0% 3,2 3,2 5,3 60% 5,0%

2 110,3 66 5,0% 3,0% 5,0% 3,3 3,3 5,5 60% 5,0%

3 115,8 69 5,0% 3,0% 5,0% 3,5 3,5 5,8 60% 5,0%

sameasabove

4 121,6 73 5,0% 3,0% 5,0% 3,6 3,6 6,1 60% 5,0%

sameasabove

5 127,6 77 5,0% 3,0% 5,0% 3,8 3,8 6,4 60% 5,0%

6 134 80 5,0% 3,0% 5,0% 4,0 4,0 6,7 60% 5,0%

7 140,7 84 5,0% 3,0% 5,0% 4,2 4,2 7,0 60% 5,0%

8 147,7 89 5,0% 3,0% 5,0% 4,4 4,4 7,4 60% 5,0%

9 155,1 93 5,0% 3,0% 5,0% 4,7 4,7 7,8 60% 5,0%

10 162,9 98 5,0% 3,0% 2,5% 4,9 4,9 4,1 60% 5,0%

11 167 103 5,0% 3,1% 2,5% 5,1 5,1 4,2 61% 5,0%

12 171,1 108 5,0% 3,1% 2,5% 5,4 5,4 4,3 63% 5,0%

13 175,4 113 5,0% 3,2% 2,5% 5,7 5,7 4,4 64% 5,0%

14 179,8 119 5,0% 3,3% 2,5% 5,9 5,9 4,5 66% 5,0%

15 184,3 125 5,0% 3,4% 2,5% 6,2 6,2 4,6 68% 5,0%

16 188,9 131 5,0% 3,5% 2,5% 6,5 6,5 4,7 69% 5,0%

calcu

lationwith/withinaboveline

17 193,6 138 5,0% 3,6% 2,5% 6,9 6,9 4,8 71% 5,0%

calcu


18 198,5 144 5,0% 3,6% 2,5% 7,2 7,2 5,0 73% 5,0%19 203,4 152 5,0% 3,7% 2,5% 7,6 7,6 5,1 75% 5,0%

20 208,5 159 5,0% 3,8% 7,5% 8,0 8,0 15,6 76% 5,0%

21 224,2 167 5,0% 3,7% 7,5% 8,4 8,4 16,8 75% 5,0%

22 241 176 5,0% 3,6% 7,5% 8,8 8,8 18,1 73% 5,0%

23 259 184 5,0% 3,6% 7,5% 9,2 9,2 19,4 71% 5,0%

24 278,5 194 5,0% 3,5% 7,5% 9,7 9,7 20,9 69% 5,0%

25 299,3 203 5,0% 3,4% 7,5% 10,2 10,2 22,5 68% 5,0%

26 321,8 213 5,0% 3,3% 7,5% 10,7 10,7 24,1 66% 5,0%

27 345,9 224 5,0% 3,2% 7,5% 11,2 11,2 25,9 65% 5,0%

28 371,9 235 5,0% 3,2% 7,5% 11,8 11,8 27,9 63% 5,0%

29 399,8 247 5,0% 3,1% 7,5% 12,3 12,3 30,0 62% 5,0%

calculationwith/withinsame

line

30 429,8 259 5,0% 3,0% 7,5% 13,0 13,0 32,2 60% 5,0%

calculationwith/withinsame

line


19/41


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -


6) Maastricht table M6 : Surplus Deficit SD und Surplus Multiplicator

The growth rate is certainly influenced by the Surplus Deficit, so let us define theeffectiveness of that Surplus Deficit to generate growth as a factor SM, the Surplus

Multiplicator.

NGR = SM * SD or NGR% = SM * SD%

The higher SM, the more bang for the buck.

Table M6 includes SD% and SM as input values, from which NGR and therefore NGR%are derived.

Since we do not restrict ourselves to paying just the interest with the new deficit, the target

NGRT% is again calculated with formula(F1): NGRT% = PDF / PDB

But F1 is equivalent to F2,

(F2) : NGRT% = BI% + SD% / PDB%

which shows that at any moment the requirement NGRT% depends directly on BI% andon SD%, but seemingly not on SM.

SM comes in when real growth rate is calculated, as NGR% = SM * SD%.

Since SD feeds directly to more deficit and debt, a high value of SM makes it easier toreach the desired NGR at lower NGRT%.

Also, according to F2, the bigger the debt, the smaller NGRT%!

Table 6 starts again with the same values as before, and adds the complexity with

SD% and SM = 2,5 changing over time ( dark green marks the change )

The formulas have been modificated as necessary for the purpose.

YY YY = YY + 1 Year

GDP GDP = GDP + NGR Gross Domestic ProductPDB PDB = PDB + PDF Public DebtBI% BI%: input Bank Interest %PDF% PDF% = PDF / GDP Public DeFicit%NGR% NGR % = NGR / GDP Nominal Growth %PDF PDF = BI + SD Public DeFicitBI BI = BI% * PDB Bank InterestNGR NGR = SM * SD Nominal GrowthPDB% PDB% = PDB / GDP Public DeBt %SD% SD% : input Surplus Deficit %


20/41


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M6 Perpetual Public Deficits and Public Debts cs;28-8-13 M6

startvalue

Year

Gro

ss

Dom

estic

Pro

duct

PublicD

ebt

BankIn

tere

st%

PublicD

eFicit%

Nomin

alGrow

th

%

PublicD

eFicit

BankIn

tere

st

Nomin

alGrow

th

PublicD

eB

t%

Sur

plusD

eficit

%

Sur

plusD

eficit

Sur

plus

Mu

ltiplic

ator

Nomin

alGR

ow

th

Tar

get%

startvalue

inputvalue

YY=YY+1

GDP=

GDP+N

GR

PDB=

PDB+PDF

BI%:in

put

PDF

%=

PDF/

GDP

NGR

%=

NGR/

GDP

PDF=BI+

SD

BI=

BI%*PDB

NGR=

SM*

SD

PDB

%=

PDB/

GDP

SD

%:in

put

SD=

SD

%*

GDP

SM:in

put

NGRT

%=

PDF/PDB

inputvalue

YY GDP PDB BI% PDF% NGR% PDF BI NGR PDB% SD% SD SM NGRT%

0 100 60 5,0% 3,0% 0,0% 3,0 3 0,0 60% 0,0% 0,0 2,0 5,0%

1 100 63 5,0% 3,2% 0,0% 3,2 3,2 0,0 63% 0,0% 0,0 2,0 5,0%

2 100 66 5,0% 3,3% 0,0% 3,3 3,3 0,0 66% 0,0% 0,0 2,0 5,0%

3 100 69 5,0% 3,5% 0,0% 3,5 3,5 0,0 69% 0,0% 0,0 2,0 5,0%

sameasabove

4 100 73 5,0% 3,6% 0,0% 3,6 3,6 0,0 73% 0,0% 0,0 2,0 5,0%

sameasabove

5 100 77 5,0% 6,3% 5,0% 6,3 3,8 5,0 77% 2,5% 2,5 2,0 8,3%

6 105 83 5,0% 6,4% 5,0% 6,8 4,1 5,3 79% 2,5% 2,6 2,0 8,2%

7 110,3 90 5,0% 6,6% 5,0% 7,2 4,5 5,5 81% 2,5% 2,8 2,0 8,1%

8 115,8 97 5,0% 8,2% 8,0% 9,5 4,8 9,3 84% 4,0% 4,6 2,0 9,8%

9 125 106 5,0% 8,3% 8,0% 10,3 5,3 10,0 85% 4,0% 5,0 2,0 9,7%10 135 117 5,0% 8,3% 8,0% 11,2 5,8 10,8 86% 4,0% 5,4 2,0 9,6%

11 145,8 128 5,0% 8,4% 8,0% 12,2 6,4 11,7 88% 4,0% 5,8 2,0 9,6%

12 157,5 140 5,0% 8,5% 8,0% 13,3 7,0 12,6 89% 4,0% 6,3 2,0 9,5%

13 170,1 153 5,0% 8,5% 8,0% 14,5 7,7 13,6 90% 4,0% 6,8 2,0 9,4%

14 183,7 168 5,0% 8,6% 9,4% 15,7 8,4 17,3 91% 4,0% 7,3 2,4 9,4%

15 201 184 5,0% 8,6% 9,4% 17,2 9,2 18,9 91% 4,0% 8,0 2,4 9,4%

16 219,9 201 5,0% 8,6% 9,4% 18,8 10,0 20,7 91% 4,0% 8,8 2,4 9,4%


17 240,5 220 5,0% 8,6% 9,4% 20,6 11,0 22,6 91% 4,0% 9,6 2,4 9,4%


18 263,1 240 5,0% 8,6% 9,4% 22,5 12,0 24,7 91% 4,0% 10,5 2,4 9,4%

19 287,9 263 5,0% 8,6% 9,4% 24,7 13,1 27,1 91% 4,0% 11,5 2,4 9,4%

20 314,9 288 5,0% 8,6% 9,4% 27,0 14,4 29,6 91% 4,0% 12,6 2,4 9,4%

21 344,5 315 5,0% 7,6% 7,1% 26,1 15,7 24,3 91% 3,0% 10,3 2,4 8,3%

22 368,8 341 5,0% 7,6% 7,1% 28,1 17,0 26,0 92% 3,0% 11,1 2,4 8,2%

23 394,8 369 5,0% 7,7% 7,1% 30,3 18,4 27,8 93% 3,0% 11,8 2,4 8,2%

24 422,7 399 5,0% 7,7% 7,1% 32,6 20,0 29,8 94% 3,0% 12,7 2,4 8,2%

25 452,5 432 5,0% 7,8% 7,1% 35,2 21,6 31,9 95% 3,0% 13,6 2,4 8,1%

26 484,4 467 5,0% 7,8% 7,1% 37,9 23,3 34,1 96% 3,0% 14,5 2,4 8,1%

27 518,5 505 5,0% 7,9% 7,1% 40,8 25,2 36,6 97% 3,0% 15,6 2,4 8,1%

28 555,1 545 5,0% 7,9% 7,1% 43,9 27,3 39,1 98% 3,0% 16,7 2,4 8,1%

29 594,2 589 5,0% 8,0% 7,1% 47,3 29,5 41,9 99% 3,0% 17,8 2,4 8,0%

ca

lculationwith/withinsameline

30 636,1 637 5,0% 8,0% 7,1% 50,9 31,8 44,8 100% 3,0% 19,1 2,4 8,0%

ca

lculationwith/withinsameline


21/41


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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - -


Comments on Table M6

Things start to get really interesting on table M6, where faced with an interest rate of 5%,we need at least NGRT% = 5% growth to keep the debt ratio at 60 %.

When that does not happen by itself, as during the first 5 years, the debt ratio will grow.

We will then inject Surplus Deficit into the economy.

At the start, we assume a Surplus Multiplicator of SM = 2, meaning every Euro more willgive 2 Euros worth of growth, this year.

So the first thought is to inject SD% = NGRT% / SM = 5% / 2 = 2,5 % as surplus.

We do that after year 5, but immediately the required NGRT% changes as well, and goesup, the debt ratio is also still rising.

In desperation, we inject more money and put the level of SDF% to 4%, again the requiredNGRT% goes up, now towards 9,8%.

The only way to get out of this vicious circle is to increase SM, putting it to SM = 2,4solves the problem, raises growth rate to the desired 9,4 % , and stabilizes the debt ratio.

However, since the growth rates are all nominal, they are very likely to include a good dealof inflation, if productivity goes up by say 2 % per year, that still leaves 9,4 2 = 7,4 %inflation, which may not be to everybodys taste.

Lowering SD% later on, on year 21, will lower inflation and growth rate, but induce agrowing debt ratio again.

So In a situation like that, there is no easy way out.


0

100

200

300

400

500

1 3 5 7 9 1 1 1 1 19 21 2 2 2 2 3

0

1

2

3

4

5

GDP

PDB

PDB%

SD%

SM

60% Public Debt to start, SD% & SM varying


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7) Maastricht table M7 : Paying back the principal ?

Since the formulas work both ways, we can try to get out of trouble by paying not only theinterest, but also the principal of the Public debt, over time.

Unless the money to do that falls from the sky or from the outside world, it will be taken outof the economy, out of GDP, just the same way as on the page before we have addedsome by borrowing more.

SD% is calculated so to cover the interest + the 5 % of the debt at any moment in time.

It is then obviously negative.


0

50

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

0

1

2

3

4

5

GDP

PDB

PDB%

BI%

SM

60% Public Debt to start, SD%= - 2%;

Paying back the debt over 20 years

This is another road to disaster, as the debt comes down as intended, GDP comes downas well, mostly even faster.

With SM = 1, initial interest is set to BI% = 5 %, and we change that to 2 % after year 7.

The debt ratio goes up at the first since GDP collapses faster than the debt.

Only with lower interest rates does the debt come down a bit faster than GDP, the debtratio decreases slowly while GDP is still collapsing.

If SM is halved to 0,5, the negative effect on the economy is halved as well, (after year15), if it is doubled to SM = 2; the effect is doubled as well.

So much for austerity and taking the rot out of the system


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M7 Perpetual Public Deficits and Public Debts cs;28-8-13

startvalue

Year

Gross

Domestic

Product

PublicDebt

BankInterest%

PublicDeFicit%

NominalGrowth%

PublicDeFicit

BankInterest

NominalGrowth

PublicDeBt%

SurplusDeficit%

SurplusDeficit

Surplus

Multiplicator

NominalGRowth

Target%

inputvalue

YY=YY+1

GDP=

GDP+NGR

PDB=

PDB+PDF

BI%:input

PDF%=

PDF/GDP

NGR%=NG

R/

GDP

PDF=BI+S

D

BI=

BI%*PDB

NGR=SM

*SD

PDB%=

PDB/GDP

SD%:inpu

t

SD=

(BI+PDB/20)

SM

:input

NGRT%=

PDF/PDB

YY GDP PDB BI% PDF% NGR% PDF BI NGR PDB% SD% SD SM NGRT%

0 100 60 5,0% -3,0% -6,0% -3,0 3 -6,0 60% -6,0% -6,0 1,0 -5,0%

1 94 57 5,0% -3,0% -6,1% -2,9 2,9 -5,7 61% -6,1% -5,7 1,0 -5,0%

2 88 54 5,0% -3,1% -6,1% -2,7 2,7 -5,4 61% -6,1% -5,4 1,0 -5,0%

3 83 51 5,0% -3,1% -6,2% -2,6 2,6 -5,1 62% -6,2% -5,1 1,0 -5,0%

sameasabove

4 78 49 5,0% -3,1% -6,3% -2,4 2,4 -4,9 63% -6,3% -4,9 1,0 -5,0%

5 73 46 5,0% -3,2% -6,4% -2,3 2,3 -4,6 64% -6,4% -4,6 1,0 -5,0%

6 68 44 5,0% -3,2% -6,5% -2,2 2,2 -4,4 65% -6,5% -4,4 1,0 -5,0%

7 64 42 2,0% -3,3% -4,6% -2,1 0,8 -2,9 66% -4,6% -2,9 1,0 -5,0%

8 61 40 2,0% -3,3% -4,6% -2,0 0,8 -2,8 65% -4,6% -2,8 1,0 -5,0%

9 58 38 2,0% -3,3% -4,6% -1,9 0,8 -2,6 65% -4,6% -2,6 1,0 -5,0%

10 55 36 2,0% -3,2% -4,5% -1,8 0,7 -2,5 65% -4,5% -2,5 1,0 -5,0%

11 53 34 2,0% -3,2% -4,5% -1,7 0,7 -2,4 64% -4,5% -2,4 1,0 -5,0%

12 51 32 2,0% -3,2% -4,5% -1,6 0,6 -2,3 64% -4,5% -2,3 1,0 -5,0%

13 48 31 2,0% -3,2% -4,5% -1,5 0,6 -2,2 64% -4,5% -2,2 1,0 -5,0%

14 46 29 2,0% -3,2% -4,4% -1,5 0,6 -2,0 63% -4,4% -2,0 1,0 -5,0%

15 44 28 2,0% -3,2% -2,2% -1,4 0,6 -1,0 63% -4,4% -1,9 0,5 -5,0%

16 43 26 2,0% -3,1% -2,1% -1,3 0,5 -0,9 61% -4,3% -1,8 0,5 -5,0%

calcu


17 42 25 2,0% -3,0% -2,1% -1,3 0,5 -0,9 60% -4,2% -1,8 0,5 -5,0%

18 41 24 2,0% -2,9% -2,0% -1,2 0,5 -0,8 58% -4,0% -1,7 0,5 -5,0%

19 40 23 2,0% -2,8% -2,0% -1,1 0,5 -0,8 56% -3,9% -1,6 0,5 -5,0%

20 40 22 2,0% -2,7% -1,9% -1,1 0,4 -0,8 54% -3,8% -1,5 0,5 -5,0%

21 39 20 2,0% -2,6% -1,8% -1,0 0,4 -0,7 53% -3,7% -1,4 0,5 -5,0%

22 38 19 2,0% -2,5% -1,8% -1,0 0,4 -0,7 51% -3,6% -1,4 0,5 -5,0%

23 38 18 2,0% -2,5% -1,7% -0,9 0,4 -0,6 49% -3,4% -1,3 0,5 -5,0%

24 37 18 2,0% -2,4% -6,7% -0,9 0,4 -2,5 48% -3,3% -1,2 2,0 -5,0%

25 34 17 2,0% -2,4% -6,8% -0,8 0,3 -2,3 48% -3,4% -1,2 2,0 -5,0%

26 32 16 2,0% -2,5% -6,9% -0,8 0,3 -2,2 49% -3,5% -1,1 2,0 -5,0%

27 30 15 2,0% -2,5% -7,0% -0,8 0,3 -2,1 50% -3,5% -1,1 2,0 -5,0%

28 28 14 2,0% -2,6% -7,2% -0,7 0,3 -2,0 51% -3,6% -1,0 2,0 -5,0%

29 26 14 2,0% -2,6% -7,4% -0,7 0,3 -1,9 53% -3,7% -0,9 2,0 -5,0%

calculationwith/withinsamelin

e

30 24 13 2,0% -2,7% -7,6% -0,6 0,3 -1,8 54% -3,8% -0,9 2,0 -5,0%


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8) M8 : targeting Interest rate, Surplus Multiplicator, Surplus Deficit, Public Debt

After the introduction of SM, SD% and SD,

SD% Surplus Deficit % to GDP

SD Surplus Deficit SD = SD% * GDPSM Surplus Multiplicator SM = NGR / SD

the requirement for stable debt ratios can be reformulated as follows:

PDB / GDP = constant => ( stable debt ratio)

(a) PDB/GDP = (PDB + PDF ) / ( GDP + NGR )

NGR = NGR% * GDP =>

PDB/GDP = (PDB + PDF ) / ( GDP + NGR% * GDP )PDB * (GDP + NGR% * GDP ) = GDP * (PDB + PDF )

PDB * GDP ( 1 + NGR% ) = GDP * ( PDB + PDF ) / GDP

PDB * ( 1 + NGR% ) = PDB + PDF

PDB + PDB * NGR% = PDB + PDF - PDB

PDB * NGR% = PDF

(b) NGR% = PDF / PDB ( = formula F1 in previous pages )

PDF = BI + SD

BI = BI% * PDBSD = SD% * GDP

(c) PDF = BI% * PDB + SD% * GDP

PDB * NGR% = BI% * PDB + SD% * GDP

NGR = SD * SM / GDP

(d) NGR% = SD% * SM

NGR% = PDF/PDB = SD% * SM (b) & (d)

PDF = BI% * PDB + SD% * GDP (c) / PDB

(e) PDF/PDB = BI% + SD% *GDP/PDB

NGR% = BI% + SD% / PDB% (b) & (e)

SD% * SM = BI% + SD% / PDB% (d) * PDB%

F4: PDB% * SD% * SM = BI% * PDB% + SD%

F4 has 4 variables : PDB%; SD%; BI%; SM

and leads to 4 different formulas F5 .. F8 depending on the outcome variable desired,

the other 3 are then inputs:

PDB% * ( SD% * SM BI%) = SD%


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F5: PDB% = SD% / ( SD% * SM BI%)

SD% ( SM 1 / PDB% ) = BI%

F6: BI% = SD% * ( SM 1 / PDB% )

F7: SD% = BI% / (SM 1/PDB%)

F8: SM = BI% / SD% + 1 / PDB%

Here is the complete list of formulas so far, that all describe the conditions for stablePDB%with different levels of complexity:

F1 : NGRT% = PDF / PDB

F2 : NGRT% = BI% + SD% / PDB%

F3 : NGRT% = BI % (when SD% = 0)

F4: PDB% * SD% * SM = BI% * PDB% + SD%

Note: an T is attached to the variable names to mark the Targeted values

F5 PDB%T = SD% / (SM * SD% - BI%) Public Debt ratio

F6 BI%T = SD% * (SM - 1/PDB%) Bank Interest rate

F7 SD%T = BI% / (SM - 1/PDB%) Surplus Deficit %

F8 SMT = BI% / SD% + 1/PDB% Surplus Multiplicator

With the last 4 formulas, any three parameters will give a value for the fourth that wouldkeep the debt ratio stable, the table M8 below shows exactly that.

The first of these lines states that with interest at BI% = 3%, SD% =2 and SM =1, yourstable point is savings of 200 % rather than any level of debt, anything less than that will

lead to trouble.

The second line here states that you can avoid more trouble if withDebt PDB% = 60 %

Table M8:conditions for stable PDB%

BankInterest%

SurplusDeficit

%toGDP

Surplus

Multiplicator

NominalGRowth

%

DeLta

StablePublicDebt

level

BI%:input

SD%=

input

SM

:in

put

NGR%

=

SM

*S

D%

DL=

SM*SD

%-BI%

PDF%

T=

NGR%

-BI%

BI% SD% SM NGR% DL PDF%T

F5 PDB%T = SD% / (SM * SD% - BI%) PDB%T = 3,0% 2,0% 1,0 2,0% -1,0% -200%

F6 BI%T = SD% * (SM - 1/PDB%) BI%T = 0,7% 2,0% 2,0 4,0% 3,3% 60%

F7 SD%T = BI% / (SM - 1/PDB%) SD%T = 2,0% 7,4% 1,0 7,4% 5,4% 137%

F8 SMT = BI% / SD% + 1/PDB% SMT = 2,0% 1,0% 2,7 2,7% 0,7% 135%


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Surplus Multiplicator of SM = 2

Surplus Deficit of SD% = 2 % if you have an

interest rate at BI% = 0,7 %

Comments to M8:

With given values of interest rate, surplus deficit and surplus multiplicator, there will beonly one stable debt ratio, and things will over time evolve towards that ratio whether it ishigh or low.


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9) Debt or Savings

Formula (F5) gives the natural debt ratio towards which an economy will drift if SD%, BI%,SM are given.


It has a singularity at : SM * SD% = BI%since SM * SD& = NGR%that can be expressed as: NGR% = BI%

Since:F2 : NGRT% = BI% + SD% / PDB%

That can only happen if SD% = 0, or if the debt is huge.

- If the interest rate is higher than the growth rate, the result for Public Debt isnegative, that means the stable point is in savings and not in debt.

If you do not have high enough savings as given by the formula, you will get, and thenever deeper, into debt.

BI% > SM * SD% = NGR% => PDF%T < 0

better have public savings than debt

- If the interest rate is lower than the growth rate, you may be able to manage yourpublic debt : BI% < SM * SD% = NGR% => PDF%T > 0

Conclusions:

PDB%T negative : no stable point when in debt

PDB%T positive : a stable point for that level does at least exist

What the formula also means that for a given set of SD%, SM and BI%, the debt willevolve towards a natural point as given by the formula, whether the starting point asabove or below that level.


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10) Debt Ratio Stabilization: easy or difficult

F6 : BI%T = SD% * (SM - 1/PDB%)

has a zero point at SM = 1/PDB% or PDB% = 1 / SM;

below the level of debt given by the inverse of SM, it is almost impossible to find a stablepoint, as negative interest rates would then be required

SD% = 2 % Chart M10A

For this chart, the Bank Interest Rate for stable debt ratio is calculated as a function of thedebt ratio, and the Surplus Multiplicator SM.The Surplus Deficit SD% is held constant at 2%

The chart shows that stabilizing a debt ratio is easier with higher surplus multiplicators,as they allow for higher interest rates to prevail.

It is also easier to stabilize a bigger debt than a smaller one, as again higher interest ratesare allowed for that.

The intersection points with zero interest rates are each given by PDB% = 1 / SM.


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F6 : BI%T = SD% * (SM - 1/PDB%) SD% = 3 % Chart M10B

,0%

Same chart as before, this time with the Surplus Deficit SD% set to 3%

If the Surplus Deficit is bigger at 3%, then the points at zero interest are the same, but thecurves above that allow for higher interest rates, which will be coupled with higher growthand higher inflation.


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11) zero interest debt ratio limit

F6 BI%T = SD% * (SM - 1/PDB%) Bank Interest rate

In order to find a point that might be stabilized, it is interesting to know where the stabledebt ratio eventually might be within a given set of circumstances.

We have seen that F6 comes up with interest rates that go through zero at the point

SM = 1/PDB% orPDB% = 1 / SM

With a debt level below the inverse of SM, negative interest rates would be required tohold the debt ratio. Negative interest rates may or may not be realistic, but they are noteasily put into practice.

So the difficulty with which the debt ratio can be stabilized depends on how close thesituation is to asking for zero interest rates. The further away the situation is fromdemanding negative interest rates, the easier things will be.

This underlines the importance of the Surplus Multiplicator in any economy.

If SM is small, than only large debt ratios can be stabilized.

To avoid negative interest rates while stabilizing some well-known debt ratios, thefollowing minimum SMs are needed:

60 % => SM > 1,66 ( Maastricht )80 % => SM > 1,25 ( Germany in 2013 )90 % => SM > 1,11 ( Reinhard-Rogoff )

125 % => SM > 0,8 ( Italy, for decades )175 % => SM > 0,57 ( Greece, 2013 ? )

Higher Surplus Multiplicators tend to be more difficult to achieve, so it is easier to stabilizea 90% than a 60% debt, as the curve comes back to lower SM levels with bigger ratios.(see chart below)

Small debt ratios have a hard time maintaining themselves without negative interest rates.

Only negative surplus, like paying back debt, can achieve that, at the cost of seriousrecession, year by year, leading to the destruction of any economic activity after a while.

Note: an enforcable or desirable debt level of 60% or 90 % for everyone is thus completelymisguided, as it does not take account of the nature of an economy, namely its SM factor.

Interesting finding in times of "austerity".


31/41


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Chart M11 : PDB% = 1 / SM ; zero interest point of formula (F6)


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12) Background of the Surface Multiplicator SM

The Surplus Multiplicator stands for the amount of times that the extra money, and moneyin general, circulates in the home economy, per year.

In principle, it should be spent on average once per month, like the salaries of most of us.That would mean SM =12.

Reality is likely to be very far from that, as the extra cash has to first overcome the cashdisappearing into savings, financial investments, fiscal paradises, and only after that it isable contribute to GDP in a noticeable manner.

So the factor is closer to 1, if not below...

SM represents the willingness of the citizens to support their own economy byspending their money, by keeping it in circulation, by paying their taxes.

Countries with positive trade and current accounts have an easier time as cash is comingin, at the expense of others. And vice-versa.

The factor is a rough simplification of what is really going on, but a useful one withsufficient amount of information at this level of modelling detail.

The higher the value for SM, the easier it is to stabilize debt at any level, and to pay higherinterest rates.

The higher the debt, the lower SM is needed to keep it stable. And vice-versa.The higher the debt, the easier it is to maintain its level.


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13) Natural Debt ratioswith little growth and little inflation

The EuroZone has given its Central Bank (ECB) at price stability as the target, andeverybody agrees that

inflation IF% = 2% is a good target as it avoids both deflation and real inflation.

If we assume that the number of economic participants stays roughly the same, thennominal growth will be the sum of inflation (IF%) and productivity (PR%) increases.

F9 : NGR% = PR% + IF%

For productivity,

PR = 2 % is also a pretty good number, so the target for nominal growth is

NGR% = PR% + IF% = 2% + 2% = 4%.

On the other hand, by our previous definition, NGR% is also : NGR% = SD% * SM

Bringing both formulas together sets a value for SD %:

SD% = NGR% / SM = (PR% + IF%) / SM = 4% / SM in this case.

Our set of formulas loses one degree of liberty, but we are now able to analyze thesituation under these additional rules.


F9 : NGR% = PR% + IF%

F5 PDB%T = SD% / (SM * SD% - BI%)

= ((PR% + IF%) / SM ) / (SM*SD% - BI%))= ((PR% + IF%)/SM) / (SM*(PR%+IF%)/SM - BI%)= ((PR% + IF%) / SM) / (PR% + IF% - BI%)

with PR% + IF % = 4%

= 4% / (SM * (4% - BI%) ) ; singularity at BI% = 4%

The calculation of theNatural DeBt ratio PDB%N= f (SM; BI%)

for an economy was done for a row of values

Surplus Multiplicator : SM = 0,5 4, and for

Interest rates : BI% = 5% 3% 2% 1% 0%

Results on table M14 and the attached chart:


34/41


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Comments:

This chart mans that in order to stay at 60 %, you need very high SM values or very lowinterest rates, or rather both.With an SM = 1; you can live with a debt ratio of 133% and a 1 % interest rate, all the whilegenerating 2 % growth and 2 % inflation.

If the interest rate happens to be 2 %, you will have to live with 200 % debt, or evolvetowards that state of affairs.

Again, a 90 % debt is easier to live with than trying to hold onto a 60 % debt, and 100% iseasier than 90%.So much for the Reinhard-Rogoff discussion.

It all comes down to "natural values " that you cannot escape, if you try anyway, disastersloom.If you are below the natural ratio, you will slowly get there, if you are above, you will comedown to it by the forces of financial gravity.

If the interest rate is higher than the growth rate, only savings are ok, debt cannot bemanaged and will run away.

The chart also shows that 3 % interest is already more than any state can carry, when wewant a bit of growth and not more than a couple of % inflation.

Small wonder that these days (2013) Central Banks bring down the interest rates, and thatbond rates are coming down with them.

PDB% = f ( SM ; BI% ) with SD% = 4% / SM

NGR% = (2% Productivity + 2% Inflation) = 4%

-200%

-100%

0%

100%

200%

300%

0 1 2 3 4 5

SM

Debt Ratio

BI%=3%

BI%=2%

BI%=1%

BI%=0%

BI%=5%


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productivity PR% 2,0% Input Table M14

inflation IF% 2,0% input

nominal growth NGR% = 4,0% PR% + IF%

Surplus Deficit % SD% = NGR% / SM

F5 PDB%N = SD% / (SM * SD% - BI%)

Bank Interest BI% 3,0% 2,0% 1,0% 0,0% 5,0%

SD% SM BI%=3% BI%=2% BI%=1% BI%=0% BI%=5%

8,0% 0,5 800% 400% 267% 200% -800%

6,7% 0,6 667% 333% 222% 167% -667%

5,7% 0,7 571% 286% 190% 143% -571%

5,0% 0,8 500% 250% 167% 125% -500%

4,4% 0,9 444% 222% 148% 111% -444%

4,0% 1,0 400% 200% 133% 100% -400%

3,6% 1,1 364% 182% 121% 91% -364%3,3% 1,2 333% 167% 111% 83% -333%

3,1% 1,3 308% 154% 103% 77% -308%

2,9% 1,4 286% 143% 95% 71% -286%

2,7% 1,5 267% 133% 89% 67% -267%

2,5% 1,6 250% 125% 83% 63% -250%

2,4% 1,7 235% 118% 78% 59% -235%

2,2% 1,8 222% 111% 74% 56% -222%

2,1% 1,9 211% 105% 70% 53% -211%

2,0% 2,0 200% 100% 67% 50% -200%

1,9% 2,1 190% 95% 63% 48% -190%1,8% 2,2 182% 91% 61% 45% -182%

1,7% 2,3 174% 87% 58% 43% -174%

1,7% 2,4 167% 83% 56% 42% -167%

1,6% 2,5 160% 80% 53% 40% -160%

1,5% 2,6 154% 77% 51% 38% -154%

1,5% 2,7 148% 74% 49% 37% -148%

1,4% 2,8 143% 71% 48% 36% -143%

1,4% 2,9 138% 69% 46% 34% -138%

1,3% 3,0 133% 67% 44% 33% -133%

1,3% 3,1 129% 65% 43% 32% -129%

1,3% 3,2 125% 63% 42% 31% -125%

1,2% 3,3 121% 61% 40% 30% -121%

1,2% 3,4 118% 59% 39% 29% -118%

1,1% 3,5 114% 57% 38% 29% -114%

1,1% 3,6 111% 56% 37% 28% -111%

1,1% 3,7 108% 54% 36% 27% -108%

1,1% 3,8 105% 53% 35% 26% -105%

1,0% 3,9 103% 51% 34% 26% -103%

1,0% 4,0 100% 50% 33% 25% -100%


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14) Comments to Maastricht Criteria and ECB goals

In order to stay out of trouble, Nominal GRowth rate NGR% has to

-be bigger or at least equal to the ratio between new Public DeFicit (PDF) andalready existing Public DeBt (PDB).

or,

- as a first, nominal growth rate needs to be bigger than the interest rate,

and if your deficit goes beyond just paying for the interest,

- as a second, the resulting growth rate of the economy has to be bigger than thegrowth rate of debt.

-

Simple enough

That sounds easier than it is, since we do not want high inflation either, so nominal growthis limited to the sum of the targeted inflation + expected productivity increases.

In the EuroZone, 2% inflation is targeted for to keep serious inflation as well as deflation atbay. At the same time, the EuroZone does not want to go beyond 3 % deficits.

All these rules limit the room for manoeuver, and together with the 60% debt limit, it turnsout that they are incompatible with saving any economy that is in trouble. They actually

stand in the way of saving the economy, and push it further into the ground.

MC1: 3% of GDP as maximum Public DeFicit (PDF) for the year, and

MC2 : 60 % of GDP as maximum Public DeBt (PDB )

seem to have been chosen so that

at an 5 % interest rate, which was not unusual at the time (1990) ,

it looked as if the debt would pay for itself: 5 % of 60% is 3%

Unfortunately,

last year's deficit gets added to last year's debt and the sum gives the new debt,

which then stands at 63 % and not 60 % anymore.

Unless there is enough growth to make this 63 look smaller in comparison.

So when no effort is done to jump-start the economy by more debt, it needs

- growth of the same percentage as the interest rate to keep the debt ratio constant

- and growth bigger than that if the debt ratio has to shrink.

This is true whatever the actual debt ratio, but only if all the deficit goes to debt service.

Now since debt service alone does hardly generate any growth, asking for growth of thesame magnitude or bigger than the interest rate is a tall order.


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So it is very likely that the targeted growth is not achieved, and that public debt and itsratio to GDP will grow.

So within our current monetary system, the very existence of Public Debt calls forgrowth that public deficits mostly cannot deliver.

Unless the interest rate comes down, and allows at least nominal growth to get bigger thanthis rate.

Small wonder that this is what is going on these days ( ECB, Fed, BOJ in mid-2013)

Also:

If nominal growth hits spare capacities, growth will happen without inflation.

If nominal growth hits full capacities, productivity increases are needed to avoid inflation.

And without the inflation signals showing which items are becoming rare and look likegood business, investment will not happen.

Wages rising due to shortage of manpower is a goal to achieve, it would mean fullemployment and invite investment for productivity increases. It should not invite theCentral Bank to raise its rates again, as that would only kill the shortage and fullemployment as well. This is however what has happened for most of the last decades,before and after the introduction of the Euro.

Central Banks have de facto set their control loops around wages, instead of aroundgrowth , around monetary mass or even better around circulating monetary mass, which

would mean actual GDP.

One of the reasons why there has been so little growth in Europe all that time.


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15) Solving the Problem with Positive Money

From the pages above on Perpetual Public Deficits and Public Debts it become asclear that such situations very easily get out of hand, that this is no way to run aneconomy.

To get out of that trap and avoid ever getting back into it, we introduce the concept ofPositive Money, Money-no-Debt that is generated by the Central Bank and distributeddirectly into the economy, to its citizens, equally, thus avoiding voracious intermediarieslike politics, bureaucracies and commercial banks.

Introduction of positive money, example:

Table PM1: Simulation of how to get out of trouble with Positive Money

90% Public Debt as a start, 2 % interest

For the exercise of this table, the surplus multiplicator is set low to 0,5 at the start, thenmoves up to 1 at year 7, finally towards 1,3 at year 20.

Positive money for interest on existing debt : IPOS = BIPositive money to pay down the principal PPOS = PPOS% * GDP ; PPOS% = 2%Positive money to facilitate growth GPOS = GPOS% * GDP ; GPOS% = 2%

The formulas have been adapted to reflect these purposes.

YY Year YY = YY + 1GDP Gross Domestic Product GDP = GDP + NGRPDB Public Debt PDB = PDB + PDFBI% Bank Interest % BI%: inputPDF% Public DeFicit% PDF% = PDF / GDPNGR% Nominal Growth % NGR % = NGR / GDPPDF Public DeFicit PDF = BI - DPOSIPOS Positive money to pay for debt interest IPOS = BIIPOS% Positive money to pay for debt interest IPOS% = IPOS / GDPPPOS% Positive money % to pay for debt principal PPOS% : Input

PPOS Positive money % to pay for debt principal PPOS = PPOS% * GDPDPOS Positive money % to pay for debt DPOS = PPOS + IPOSDPOS% Positive money to pay for debt DPOS% = DPOS / GDPGPOS% Positive money % to pay for growth GPOS% : InputGPOS Positive money for growth GPOS = GPOS% * GDPTPOS total positive money TPOS = DPOS + GPOSTPOS% total positive money % TPOS% = TPOS / GDP

APOS Accumulated Positive Money APOS = APOS + TPOSBI Bank Interest BI = BI% * PDBNGR Nominal Growth NGR = SM * GPOSPDB% Public DeBt % PDB% = PDB / GDP

SM Surplus Multiplicator SM : input


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Comments to Table PM1:

So this is what it takes to solve the public debt part of our monetary problem (2013), andavoid trouble in the future as well:

Create enough positive money for the following 3 purposes:(1) pay the interest on the public debt(2) pay back the principal over time(3) inject some % of GDP to enable growth that reflects the possible increases inproductivity and workforce

This last point on workforce is important: If we know that workforce is increasing by say 2,5% per year, and hopefully GDP will increase for that reason as well,

we have to inject money into the system to reflect the target GDP. Failing to do so will justgenerate the next crisis of youth unemployment.How much real growth will eventually result will be up top the economy, whether it keepsthe multiplicator high or not, whether it spends money on reasonable investment or not,

whether it uses the money for inflation or savings. That is not a monetary issue, but moreof a fiscal and a business issue.In the chart, generation of positive money to cover debt has been stopped as soon aspublic debt has been repaid. It is however advisable to continue generating more positivemoney in order to run total private debt down to reasonable levels as well, and then keep itthere.

If inflation goes up too fast, the multiplicator is higher than expected, and the injection ofpositive money for growth can be slowed down. The Central Bank would be managingthese aspects. Or the finance minister can increase taxes.


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Documents

Perpetual Public Deficits and Debts