Ponzi Maths–Part 2

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In the previous post, I outlined my basic model of a pure credit economy, in which a single initial loan allowed a continous flow of economic activity (at a constant level) over time. The basic flowtable of that system was:

 

Type 1 -1 -1 -1
Account Firm Loan (FL) Firm Deposit (FD) Bank Deposit (BD) Worker Deposit (WD)
Interest on Loan +A      
Interest on Deposit   +B -B  
Pay Interest on Loan -C -C +C  
Pay Wages   -D   +D
Interest on Deposit     -E +E
Consume   +F+G -F -G

The next stage of the model allows for repayment of loans, and re-circulation of these repayments. For this, another account is needed: a capital account that records the inactive reserves of the banking system–those reserves the banking system has available for lending. The two additional steps that are considered now are:

  1. The firm pays money to the bank that is to be taken off its outstanding debt. This is a transfer of H from the firm’s deposit account to the bank’s capital account, and in recognition of receiving it, the bank is olbiged to reduce the recorded amount of outstanding debt by the same amount; and
  2. The bank can now re-lend existing inactive reserves to firms. This is a transfer of money I from the bank’s capital account to the firm’s deposit account, and in recognition of having given it to the firm, the bank records that the firm’s debt has risen by the same amount.

Adding these new flows to the table generates the following system:

Type 1 0 -1 -1 -1
Account Firm Loan (FL) Bank Reserves (BR) Firm Deposit (FD) Bank Deposit (BD) Worker Deposit (WD)
Interest on Loan +A        
Interest on Deposit     +B -B  
Pay Interest on Loan -C   -C +C  
Pay Wages     -D   +D
Interest on Deposit       -E +E
Consume     +F+G -F -G
Repay Loan -H +H -H    
Relend Reserves +I -I +I    

This is still an equilibrium system–though it operates at a lower level than the previous one where a single injection of credit money circulated indefinitely, because there is less money in active circulation. The next step–and the one that explains how money can expand endogenously–is to introduce the creation of new credit money. The mechanism is extremely simple. As Basil Moore, the pioneer of “endogenous money” theory, argued decades ago, major firms have “lines of credit” that enable them to increase their spending at will, in return for accepting a matching increase in their debt levels. In a growing economy, these “lines of credit” (and their domestic equivalent, the gap between aggregate credit card balances and aggregate limits) are growing all the time.

In this simple model, this simultaneous expansion of both debt and money is captured by the sum J being added to the firm’s deposit account, in return for the bank adding the same sum to the outstanding debt of the firm.

 

Type 1 0 -1 -1 -1
Account Firm Loan (FL) Bank Reserves (BR) Firm Deposit (FD) Bank Deposit (BD) Worker Deposit (WD)
Interest on Loan +A        
Interest on Deposit     +B -B  
Pay Interest on Loan -C   -C +C  
Pay Wages     -D   +D
Interest on Deposit       -E +E
Consume     +F+G -F -G
Repay Loan -H +H -H    
Relend Reserves +I -I +I    
Extend Credit +J   +J    

 

With this extension, we move out of the realm of equilibrium–so long as J is positive, the money supply and the economy will be expanding (we also comprehensively invalidate “Walras’ ‘Law'”, a cornerstone of neoclassical economics–but that’s a topic for a later post). Starting from the equilibrium values of the previous system, the bank balances and incomes in the system grow as indicated by the next two graphs.

All the models so far describe “well behaved” financial systems: the banks make their money out of the spread between loan and deposit rates of interest (other extensions cover non-bank lending, which is part of the explanation of why debt exceeds money; but that’s another topic in itself). Next we introduce a badly behaved financial intermediary: one that pretends to make more money than the others, but in reality makes none at all–a Ponzi Scheme.

This is enough for one post; to be continued in Ponzi Maths–Part 3.

About Steve Keen

I am Professor of Economics and Head of Economics, History and Politics at Kingston University London, and a long time critic of conventional economic thought. As well as attacking mainstream thought in Debunking Economics, I am also developing an alternative dynamic approach to economic modelling. The key issue I am tackling here is the prospect for a debt-deflation on the back of the enormous private debts accumulated globally, and our very low rate of inflation.
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5 Responses to Ponzi Maths–Part 2

  1. marcf999 says:

    Steve,
    1/ Can you expand on the difference you make between Bank Deposit and Bank Reserves? I am not sure I understand the distinction clearly.

    2/ Regarding the sentence: “The next step–and the one that explains how money can expand endogenously–is to introduce the creation of new credit money.”
    a/ You seem to postulate J, the “new credit-money” rather than derive it. In this system credit money growth is a hypothesis not a consequence? Minsky clearly talks of credit money expansion as a consequence of ponzi demand
    b/ furthermore J is defined as nMxFD in the next post, meaning a sort of money multiplier on the deposits of firms alone? Can you expand on this hypothesis?

  2. Steve Keen says:

    Hi Marc,

    Here I’m probably taking a familiarity with some of the endogenous money literature for granted.

    1. On the first point, the difference relates to Graziani’s arguments that, for a credit money system to work, it must be the case that seignorage is not possible. If a bank could spend or consume on the basis of what was in its reserves–if it could in effect spend what was paid to it as repayment for loans–then seignorage would be occurring.

    The division of the banks finances into a Deposit account–really a Profit and Loss account–and a reserve account mimics this. Actual bank finances these days would be far more complicated; this simply implements the basic concept in a hypothetical pure credit economy.

    2a. On the second, there is a substantial literature developed by Basil Moore around how money is endogenously created via the existence of “lines of credit” for major corporations. The same thing applies to overdrafts for small firms, and credit cards for individuals. These are always being extended to new entities, or expanded for existing ones in a growing economy. My model simply formalises that.

    2b. It’s not a multiplier but a flow function–an exponential growth term, the mirror image of the functions used for debt repayment where exponential decay applies. As a differential equation, it simply says that (if nM is 0.1 or 10%) that “the money supply grows at 10% per annum”.

    In a more complex extension to the model, this growth rate would depend on firms’ willingness to take on debt–so it would be driven from the borrower side rather than the lender. For now I simply use a set constant so that my model provides a skeleton of how a financial system works.

    I think you might benefit from reading some of the references I’ve given in the associated paper that I’ve sent you by Moore, Graziani and Minsky, to see where some of these ideas come from.

  3. marcf999 says:

    Steve,

    thanks for the clarification on seignorage (the word seems to throw off you spell checker).

    Yes I understand you are postulating new money creation now. I have read most papers you have sent (not browsed references yet) and was particularly keen on the “not keen on bailouts”. The narrative in there is really good and points at monetary levels that cannot be controlled.
    I looked at the ponzi math in the 3 chapter here I think you are very close to a unified endogenous model of new money creation. My personal graal would be linking monetary levels to prices in dynamics. I am making good progress in my understanding of what your model captures, your narrative is richer than the models and provides a lot of food for thought.

    It is funny I was thinking this morning in the car that a way to capture endogenous creation of credit money would be to model demand for credit money. Ponzi demand as opposed to postulating money creation would introduce a dynamic growth of credit. Demand for credit has got to be a function of price derivative which in your dP=p(D-Q) means that a positive dP means more demand than Q and that in turns increases D by creating money for ponzi. In other words demand for credit increases asset prices which increases demand for credit. Do you have a formula on that? I think that postulate would close the loop.

    I am still searching for a endogenous minsky moment. The endogenous shock… how do we get at it from the dynamics? Will probably follow by email.

  4. marcf999 says:

    regarding seignorage… if I understand your explanation correctly, it means that banks cannot spend the loans that are repaid because it was all credit money that came out of nothing. Bad debt essentially violates the no-seignorage rule. The money is in circulation, WAS SPENT and will not be recovered. Futhermore this money is senior in capital structures to equity capital. So fake money will devour equity capital in bad debt explosions, witness the banks and their equity as we speak. We are floating balance sheets that were composed of credit money that was fake in the first place but needs to be materialized with equity capital as it turns bad. This further depresses the demand and could be a significant factor in the Minsky narrative, we are clearly seeing this at the moment imho.

  5. fidelegas says:

    Thanks for explaining all about the equilibrium values ??, definitely something that everyone dedicated to the economy, private banking and finance should take into account.Fidel Egas

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