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:

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:

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.

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.