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The Application of Circuit-consistent Money to

Macroeconomic Modelling

Diarmid J G Weir

University of Stirling

Email: d.j.g.weir@stir.ac.uk

19th October 2005

With thanks to my PhD supervisors Professor Sheila Dow and Dr Alberto Montagnoli for help and support.

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1. Introduction

The premise of this paper is that describing the macroeconomy for the purposes

of illustrative and predictive modelling will be enhanced by the inclusion of money in a

way that is consistent with plausible explanations for the origin, valuation and current

nature of money. The inclusion of money in standard neoclassical models generally

relies on one of three techniques: the insertion of government-liability money in the

utility function eg: Buiter (2005); money as an additional good that lowers transaction

and/or production costs; eg: King and Plosser (1984); or the addition of a ‘Cash-in-

Advance’ constraint to the usual household budget constraint; eg: Cooley and Hansen

(1995). None of these techniques are satisfactory because they suffer from one or both

of the following deficiencies: they do not acknowledge the origin and destruction of

money in the private sector and how this affects private sector budget constraints; they

do not explain why money should be held across periods. In contrast to these

techniques, I believe that the insights provided by the Theory of the Monetary Circuit

(TMC), can lead us to a much more realistic way of integrating money into

macroeconomic models.

We shall start this paper by briefly describing what we believe to be the critical

features of money in a modern economy. We then go on to outline the monetary circuit

and the features that make it a desirable explanation of the nature of modern money.

In the following section we will discuss how the monetary circuit imposes a

constraint on firms, how monetary circuit theorists have envisaged the effect of this

constraint on the behaviour of firms, with particular focus on the issues of investment

and profits and what the consequences of this constraint might be. We will suggest that

the consequences suggested by monetary circuit theorists such as Graziani and Parguez

may not be strictly correct.

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To focus on the issues involved in the interpretation of the TMC in relation to

the macroeconomy we formalise some of the critical relationships between the aims of

firms and those of households from a circuit perspective while leaving open the source

of firms’ profits but assuming utility maximisation of households. The role of central

bank money and the effect of exogenous changes in the interest rate at which this

money is lent to the commercial banks is included in the model.

Finally we draw some conclusions from the preceding discussion and modelling

exercise.

2. The Essential Features of Modern Money

2.1 Money Creation and Economic Activity

There are two critical features of modern money:

1) Money facilitates economic activity because it is a guarantee of receiving a reward

for assisting that activity (providing labour) when that activity is neither its own

reward (that is it has at least relative disutility), nor does it earn an immediate

reward because either:

a) Production takes time

b) Output of the productive activity does not itself match completely the desires of

those who assist in its production.

2) Money represents a guaranteed claim on the output of some production process.

This gives it a reason to be accepted and held by individuals. It is not enough that

there is a positive externality to society as a whole, since every individual

transaction, whether a purely barter transaction or one involving money, is purely

bilateral. No individual will voluntarily accept money for real goods unless she is

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confident that she will be able to convert her money back into the real goods she

requires, as the loss from failing to do so is potentially greater than any liquidity

gain to her as an individual from eliminating the requirement for a double

coincidence of wants. A purely conventional basis for money’s acceptance may be

equilibrium, as Kiyotaki and Wright (1989) have shown, but there can be no

guarantee that it will become one, or that one will be regenerated after some shock

that damages trust in money.

While the two features listed above need not be part of the same process; state

or central bank money is not issued in a production process, and workers are sometimes

paid in kind for their labour, it is the claim of the TMC that in a modern economy the

bulk of money is created in the monetary production circuit.

In a modern economy by far the largest part of transactions and the largest part

of money stocks are in the form of bank deposit money, unbacked by state money

(either in the form of cash or central bank deposits). The only plausible source for this

money is the issue of bank credit to the private sector. The only plausible reason for its

valuation is the prospect of exchange for output valued by households.

The TMC shares with the Post-Keynesian school, eg: Wray (1990), Rousseas

(1992), and the Stock-Flow view, eg: Godley and Lavoie (2000, 2004), Godley (2004),

a consistent view of the nature of money in a modern economy. There is an

acknowledgement that the modern economy has three types of money, whose quantities

are linked in a way that maintains balance sheet equality for all agents at all times. One

of these types of money, cash, I am going to ignore for the sake of clarity and brevity in

this discussion.1 State or central bank deposit money (SBDM) is held by the central

1 Cash is a small and decreasing proportion of modern money, and is essentially a more tangible form of Central Bank Deposit Money.

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bank in the name of individual commercial banks. These deposits come into existence

when the government makes payments into individuals’ bank accounts that are matched

by commercial bank deposit money (CBDM) (defined below), or when commercial

banks borrow from the central bank. These deposits are cancelled by the reverse

operations: when individuals pay taxes from their bank accounts and when banks repay

their central bank loans. Central bank deposits can only directly be used to settle

transactions between different commercial banks and between commercial banks and

the central bank.

The third type of money - commercial bank deposit money (CBDM) - is itself

acceptable as a means of payment and can moreover be created by the lending of

commercial banks. For this latter reason the amount of CBDM exceeds the amount of

central bank money, and is the chief form of money used in transactions and as

precautionary deposits. CBDM is destroyed when the assets for which they are a

matching liability are terminated, whether this is on the repayment of a commercial

bank loan or on the payment of taxes to government, in which latter case a

corresponding quantity of SBDM also disappears from the system.

2.2 A Desert Island Economy

A brief thought-experiment can give us an idea as to how money might

plausibly have arisen and been valued, and serve as a point of reference as we try to

unravel a consistent way of envisaging the modern monetary economy.

We imagine two individuals on a desert island, one of whom is expert at

climbing trees to find fruit (let’s call him F) and the other has a knack for digging to

find water sources (we’ll call him W). They exchange fruit and water but wonder if

there might not be a better way to do things. They consider an arrangement to work

together to plant fruit trees near their living area. W must expend more time and effort

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to find water, and F promises to give him a share of the extra fruit grown. W doesn’t

quite trust F to give him the agreed share when the fruit is ready for gathering, so this

Pareto-improving plan fails to be carried out.

It so happens that a few days later a big, strong, numerate, but otherwise

unskilled individual (henceforth named B) is washed up on the island. When he hears

the plan of the others, he offers to ensure that the fruit-grower fulfils his side of the

bargain in return for his own share of the fruit. All three believe that this will still leave

them better off than before, so now the plan goes ahead. To make it easy for everyone

to remember who owes what to whom, B gives F some specially marked leaves to be

handed to W when the water is handed over. When the crop of new fruit is ripe these

marked leaves are handed back to F by W in exchange for his fruit share. F then returns

the leaves to B along with B’s fruit share as a signal that the fruit production process

has been completed satisfactorily.

As time goes by more unfortunates become shipwrecked on the island. First to

arrive is a talented rock-climber (to be known as R). He is able to get access to the cliffs

on the island where millions of seabirds live and manages to collect a considerable

amount of guano to fertilise the fruit trees and increase the crop. So B gives a few more

marked leaves to F who in turn gives some of these to R in exchange for guano. Like

W, R exchanges these for fruit when the crop is ready. Once again F returns all the

leaves to B, along with his share of the fruit (now increased thanks to the guano).

Despite his climbing skills, however, R finds that his guano-harvesting exploits are not

providing him with enough to eat. He collects some of the eggs he finds on the cliffs,

but doesn’t much like the taste. But he takes them back to W who finds them quite

acceptable. Unfortunately W is a bit low on fruit at the moment, as F is between crops,

and cannot exchange any with R. R suggests to W that he will take some of W’s

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marked leaves, which he knows he will be able to exchange for fruit when it is ready to

be picked.

As the island obtains more residents, who all have different skills and tastes, it

turns out that these sort of transactions involving exchange of the leaves for goods or

services rendered becomes more and more common, since they allow people to delay

their consumption or decisions about consumption and save on the time spent searching

for someone else to make a direct exchange with. Others opt to grow fruit or other food

crops as F did and in each case B (or someone else trusted to enforce production

agreements) is willing to enforce these arrangements in exchange for a share of the

extra output produced, and each time he issues more of his specially marked leaves

which are returned to him as each process is completed.

It should be clear the role that B’s marked leaves are playing here. They are

being used as a means of exchange; when held they are a store of value and it seems

likely they will be used as a unit of account. In other words, the marked leaves are

money, and they are accepted because they always represent a claim on consumption

that has been deferred to a later date as a consequence of the growing (production)

process.2

2.3 Analysing the Desert Island model

No collective agreement or convention is required to establish the acceptance or

valuation of money in this case. Moreover, by ensuring W of his due share in F’s

increased output an improved use of available resources is enabled that allows the

production of goods that would not otherwise have been achieved.

2I think this approach can be differentiated from that of characterising money as ‘assignable debt’. If a debt is a contract to repay money, then I am not sure that defining money as a contract to repay money – even if assignable – provides us with the insight we seek.

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Of course the desert island economy is very different from a modern economy.

There is initially only one productive ‘firm’, only one ‘bank’ and no bank deposits,

government sector or central bank. Given the limited consumption possibilities on the

island, B is happy to accept his ‘interest’ in produced goods rather than cash. It can,

however, be said that B’s leaves follow a circuit.

3. The Monetary Circuit

Proponents of the Theory of the Monetary Circuit insist that money is primarily

an outcome of the production process which cannot take place, because of time and

uncertainty, without an issue of credit, in the form of Commercial Bank Deposit

Money, which allows firms to pay the wages of their workers before production is

completed. The determination of the level of economic activity is thus the process of a

‘triangular’ negotiation over credit between commercial banks and firms. (Graziani

2003, p62) Wage-earners spend the wages thus received and these expenditures (in the

form of CBDM) can return to the firms in payment for their produced goods, or as the

purchase of bonds to individuals at the cost of a long-term interest rate. The Monetary

Circuit allows, however, a third possibility, which is the holding of precautionary

deposits of CBDM.

The two aspects of the circuit can be divided into ‘Initial Finance’, which is the

bank credit supplied at the cost of a short-term interest rate, and ‘Final Finance’ which

is the return of money to firms following sales of production. If consumer goods firms

can capture all of the expenditure arising from their borrowing, then at the end of the

production process (Initial Finance matches Final Finance) they can repay the full value

of their loans and so will be solvent without any further intervention. If CBDM is held

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up in the form of precautionary deposits, then the firms’ solvency (within the pure

TMC described) requires the rolling over of bank credit into the next circuit.

3.1 The Monetary Circuit as a Constraint

The adoption of the Monetary Circuit as the model for money implies a

constraint that must be included in any model of the macroeconomy. At the conclusion

of the term of each production loan, the nominal expenditure by a firm that results from

that loan is matched by an equal nominal quantity of purchases of consumer goods,

capital goods and financial assets; bank deposits being included in the latter category.

In an economy where all money is the issue of commercial banks that insist on the strict

repayment of all loans, then this constraint will apply to any firm that takes out a

production loan.

The problem faced by the Circuit Theorist is to account for profits, saving and

interest payments given this constraint. Augusto Graziani (Graziani 2003, 1989) and

Alain Parguez (Parguez 1996, 2004) have probably put the most effort into resolving

this problem and they have arrived at a similar solution. They allow the price of output

to be determined by firms and/or banks before the start of production, so that given a

fixed labour productivity, when they determine their level of employment and the

nominal wage they also fix their level of sales receipts.

According to Graziani (1989), the marginal theory of distribution, by which the

level of real income is determined by equating the real wage with the marginal

productivity of labour, is thus to be rejected in favour of the power of banks and firms

to determine the allocation of the economy’s real resources. It is not clear whether he

regards this proposition as independently supported by the empirical evidence or

whether it follows inevitably from the constraint imposed by the monetary circuit. He

goes on to endorse the view, put forward by Kalecki, for example Kalecki (1971), that

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real consumption and investment are decided on by capitalists, and that this is achieved

by their setting a price to equalise demand and supply in the consumption goods

market. The higher the price set, the lower is the proportion of consumption goods

going to wage-earners, but the greater nominal quantity of money firms must borrow.

Graziani’s view seems to have shifted slightly between 1989 and 2003, but his

final position is that firms borrow an additional amount of money to purchase capital

goods, and if they have set the price of the goods they sell correctly this money spent

on capital goods will return to the firm as profit.

It is not quite straightforward for firms, however, since wage-earners wish to

save a proportion of their wage-income. If money is thus withdrawn from the circuit in

the form of CBDM, this eats into firms’ profits to the extent that should the wage-

earners’ saving coincidently equal the capital expenditure of the firms, they will make

zero profits. To counter this, firms offer interest-bearing securities to wage-earners. The

cost to them is not in fact the full value of the interest since a proportion of interest

returns to the firms for the purchase of goods. Graziani anticipates a steady state in

which the level of CBDM deposits is constant, and so profits, investment and the

interest rates and price level required to maintain them is constant. Firms can acquire

whatever finance they need as long as no increase in CBDM deposits is anticipated.

Parguez (1996) describes the process similarly. Firms, he states, exist to grow

capital, and thus must make money profits. When they are offered for sale,

consumption goods must have a pre-determined set of values that reflect the profit

constraint determined by agreement between banks and firms. In Parguez’ view the

monetary circuit is an ordered series of stages explaining the determination of the

present state of the economy and so is an open, path-dependent system. Firms borrow

from the banks in two rounds; one for the payment of wages which workers can

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exchange for a pre-determined output of consumption goods, thus allowing the firms to

extinguish this debt, and one for the purchase of additional output of capital goods by

the firms themselves. This allows capital goods firms to repay their debt, and leaves

firms holding an additional amount of real wealth in the form of new capital goods.

Since profits are generated by investment expenditures, they cannot exist before

investment as an available liquid fund and so it cannot be true that saving is required

for investment. Moreover, if wage income and wage rate are the sole adjusting factors

for firms and banks to achieve profits, then wage-earners have no role in their

determination.

Parguez (2004) goes on to suggest that, in conjunction with banks, firms target a

desired monetary growth of their capital since banks target their own accumulation of

wealth in the form of the liabilities of firms (both short and long term). This wealth of

the banks thus depends in turn on the money value of the capital of firms. To avoid

inflation reducing the real value of this capital, banks insist as a condition of lending on

a price level that ensures their targeted growth of capital. The monetary wage rate is set

by the firms’ required rate of return and price level for the target capital accumulation,

not the marginal productivity of labour (MPL). In fact for any given targeted return on

capital, a rise in MPL would presumably simply lower the demand by firms for labour.

In Graziani’s description there is a single product used both for consumption

and as the capital used in production. Firms acquire a fraction of aggregate product for

themselves firms as capital at a price that achieves equilibrium between demand and

supply. The rate of return on expenditure is given by the ratio of capital expenditure to

the monetary cost of production, and Graziani’s result can be shown to be equivalent to

that of Parguez except for an expression for the saving ratio, reflecting the presence of

securities in Graziani’s model.

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3.2 Interest Payment to Banks

There is the additional problem of how interest payments to the banker in

payment for the provision of loans can be accounted for when these payments are

outwith the standard production cycle encompassed by the theory.

There seem to be three possible solutions to the problem:

1) The services of the banker in the model do not require the employment of workers.

Her status is essentially an institutional and non-market acquired one. Since she has

no need to employ workers for their central function as modelled she has no need to

borrow and so interest receipts are pure ‘profits’ and can be spent on the market for

goods and services. Of course if productive output is confined only to that paid for

in wages, then there will be no goods for these bank ‘profits’ to be spent on, with

consequences for the price level. But if the worker/consumers are a party to the

arrangement of a production loan and its consequences and as long as an overall

gain from the availability of the new goods remains, then they will be prepared to

manufacture extra goods, which they will not themselves consume, to the value of

the bank profits. When these goods are purchased from the firm the money with

which the interest is paid returns to the firm and can then be used to pay workers

who purchase the firms output allowing them to repay the loan principal and

complete the production circuit.

2) An alternative assumption is that the interest paid on a loan in one period can only

be paid with money obtained by a further loan in the next period. This would mean

that the amount borrowed would initially increase each period even when the

monetary value of production was constant. However the additional borrowing

would approach an asymptotic value and so an approximate steady-state would be

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reached, in which the loan value was very close to being a constant amount after

each circuit

3) The final option and the one that Graziani (1989) describes is that firms include

their bank interest payment in their targeted surplus, when the price level is fixed.

When the bank pays wages, and other costs this money is returned to the firms who

repay this part of their debt in the usual way. The banks’ employees and

shareholders’ consequent acquisition of real goods will thus further squeeze the real

value of the wages of workers in the real goods sector.

3.3 The Relationship between Capitalists and Wage-earners

Circuit theory generally, assumes as Parguez and Graziani do, that production

and investment decisions and thus decisions about the quantity of credit and thus the

quantity of CBDM, are wholly in the hands of the banks and the firms acting together.

Yet there are some problems with this solution to the questions of the monetary circuit.

(Cartelier 1996) points out that the traditional description of a clear social

division between capitalist entrepreneurs and dependent wage-earners is not necessarily

clear in economic terms. He believes that the relationship between wage-earners and

entrepreneurs is an open question with the following possible solutions:

1. The specificity of the wage relationship is ignored and the wage treated

just like another cost, such as that for fuel or animal feed. This ignores

the freedom of the wage-earner to choose between work and leisure, and

spend his wage as desired.

2. The wage is assumed to be determined in the same way as other

commodities in competitive markets. This, in turn, ignores the unequal

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relationship between entrepreneurs and wage-earners in that only the

former can decide the level and nature of economic activity.

In Cartelier’s view it is the access to the means of payment by entrepreneurs

that shifts the economic relation between them and wage-earners in favour of the

former. But Cartelier emphasises that wage-earners are not slaves and have the same

market power as other economic agents within the limits of their budget constraint.

The Desert Island model, however, illustrates that money is likely to come into

existence from a triangular agreement, so that once the banks and firms have control of

the creation of money and households do not then there must be some strain on the

continuation of a monetary economy. The money received by the agents in the Desert

Island model is acceptable to them because they know exactly how much fruit it

represents and they believe that they are getting a fair share that justifies the extra effort

they have put into producing the extra fruit. Households in the Graziani and Parguez

models, on the other hand, are passive acceptors of whatever real wage is left to them

once the price level has been set by the firms and/or banks, to allow for that part of

output the firms wish to reacquire as profits for re-investment. For this to be plausible

we must completely abandon the possibility that there is any approach to the

equalisation of the marginal utilities of work and leisure for wage-earners. This seems

unlikely in a modern economy, with firms in competition with each other for market

share and for skilled labour. Many skilled workers also have the option of self-

employment, which may well give them access to borrowed funds themselves. There is

in fact much more overlap than the traditional division suggests – with many wage-

earners being direct or indirect shareholders, and many wage-earners the beneficiaries

of the profits of firms.

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Moreover, it is not clear that the sequence of events envisaged by Parguez and

Graziani corresponds to reality. They imagine that investment decisions are made at the

time bank loans are negotiated, and so ‘profits’ are simply that part of the loan that is

spent on acquiring capital goods. But in fact the nature of profits in the real economy is

rather different from this. Profits are ‘retained’ and often not spent immediately as they

must be if already acquired as a consequence of pre-arranged investment, and secondly

they can be quite unpredictable for individual firms.

To accept the Parguez-Graziani picture it may be that we must assume

extraordinarily forward–thinking households that are willing to give up a share in

current production to see production increase in the future as a consequence of the

application of that share to capital investment. In an economy which distinguishes

between the return to capital and the return to labour, this seems most unlikely.

One thing that the monetary circuit allows, that neoclassical models cannot, is to

introduce some separation between firms and households. In most neoclassical models

that do have a production sector decisions about saving and investment are taken at the

same time, whereas the existence of credit and money as explicitly modelled by the

monetary circuit theory allows the possibility of the preferred outcomes to differ

between firms and households. The consequence is that consumption need not match

the output of consumption goods as savings do not automatically become investment

goods but may be held up as deposits.

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4. Elements of a Consistent Monetary Model of the Macroeconomy

4.1 Assumptions of the Model

Bearing in mind the issues we have discussed I want to start to formalise some

of the relationships that will exist in a circuit macroeconomy.

There are a large number of firms and households. In this version of the model

we have not specified a production process, beyond stating that it requires a

combination of labour and capital goods. Thus we make no profit-maximising

assumption, but wish to examine the conditions for a positive money profit and the

maintenance of that particular level of profit under alternative conditions.

Because production takes time, production credit must be borrowed from banks

to the quantity that matches the output created and available for sale to households by

the firm in that cycle. Because this credit is provided by a trusted third party and is

demanded by firms in exchange for goods to allow them to repay their loans, it fulfils

the role of a medium of exchange and so can be used for the purchase of goods already

produced. Indeed it makes such exchanges easier since it eliminates the need to find a

double coincidence of wants for each exchange. In this way the credit issued to

facilitate production becomes money. This money is demanded for a further reason, and

this is because if not immediately exchanged for real goods it represents a store of value

that can be used to allow the delaying of the decision to allocate expended labour or the

proceeds of the sale of other goods to different goods and/or services. It is a critical

insight of the TMC that when this store of value is kept in the form of bank deposits it

is not just withdrawn from consumption but from the monetary circuit as a whole, and

so leaves some firms unable to repay their loans within the circuit in which this

withdrawal takes place.

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When firms find that their sales receipts (including those from other firms) fall

short of that required for them to fully repay their loans, they have the choice of

attempting to have their bank loans ‘rolled over’, or of converting their loans into long-

term securities to be purchased by households. The extent to which each will happen,

depends on the relative interest rates, the liquidity preference of households and the

willingness of banks to extend loans.

By treating the production cycle as a discrete time period and confining our

analysis to the position at the end of each period, transaction balances can be regarded

as zero. Precautionary balances are determined by subjective uncertainty and by the

interest rate that can be earned on the only alternative means of saving: bonds issued by

firms. Bonds are issued by firms for the purpose of economising on the cost of bank

loans. If they can capture money that would otherwise have remained stationary in bank

deposits, then they can repay more of their loans and save on the interest costs. To

capture this money they themselves will offer a rate of return on these bonds. In this

first attempt at outlining the model, all values are in nominal terms, and are represented

by upper-case letters.

4.2 Firms

Irrespective of their production function, in a monetary circuit where money

arises from production agreements only, firms as a whole face the following budget

constraint:

1 1(1 ) (1 ) ( )L L B W W F Ft t t t t t t t t t t t t t t tL i L i W N i B C P N C P F B B− −= + + + + − − − − , (1)

where tL is the outstanding nominal quantity of all loans to firms at the end of period t;

tW is the nominal wage paid to each worker in period t; tB is the outstanding nominal

value of firms’ bonds at the end of period t; is the average nominal consumption per

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wage-earner in the private sector; FtC the average nominal capital expenditure by

firms; Ft the number of firms at time t; WtP is the average price of consumption goods;

FtP is the average price of capital goods; L

ti is the period t interest rate paid by firms to

the banks and Bti is the interest paid by firms to their bond-holders. The period t money

surplus for the firms’ sector as a whole is thus given by:

( ) 1(1 )W W F F F F L L Bt t t t t t t t t t t t t t tC P N C P C P i W N i L i Bπ −= + − − + − − . (2)

The two identical expressions in the brackets cancel each other out as they are

both expenditures and receipts of the firms’ sector, and so have no bearing on the level

of surplus. Assuming that 1W Ft tP P= = , and combining equations (1) and (2), we find

1 1t t t t tB B L Lπ − −= − + − , (3)

which implies that for a positive profit, 0tπ > , even assuming no saving so that Wt =

Ct,

1 1t t t tB B L L− −− > − . (4)

In words, firms can only make a profit in a period if they redeem bonds to a

greater value than their additional borrowing from the banks in this period. Such a

surplus cannot be achieved for an indefinite period. As we have discussed above,

Graziani and Parguez’ addrerss this problem by suggesting that profit is equivalent to

expenditure by firms on investment, citing the work of Kalecki as precedent. Firms

themselves purchase some of their own collective output, thus reducing that proportion

of output available to households. This is achieved either by firms themselves, in the

case of Graziani, or, in the case of Parguez, banks that have a stake in the capital value

of firms requiring a mark-up on prices at which households can purchase the output of

firms. Since firms can borrow their total expenditure, the price level is therefore only a

limit to the purchasing power of wage-earners. It should be clear from examining the

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profit equation (2) how this works, given a fixed nominal wage. Although this results in

a greater proportion of real resources going to firms for investment, it does not achieve

a monetary surplus at the end of the period. But we know that it is an empirical fact that

the firms sector in a modern economy does indeed achieve a surplus of receipts over

their expenditure as shown in the first column of Table 1. The only way to account for

this and maintain the integrity of the monetary circuit is to allow for the possibility of

additional money entering the firms’ budget constraint that is not borrowed by firms.

The two main sources of this are SBDM of the government and central bank, and loans

to households. The possible relative significance of these to profits are suggested by

Table 1 and Chart 1. At any particular price level the proportion of this money that

firms must recycle in wages is pre-determined, but they do not need to repay any of it

to the banks since they did not borrow it. The effect of this additional money is to scale

up the production process, and create a monetary surplus without any further increase

in the price level. Looking at the profit equation we can see that if we increase WtC to

WtC ε+ , and increase Wt to tW ε+ and Pt > 1 has previously been set to allow the firm

to purchase capital goods, then 0WtPε ε− > , and equation (2) will yield a positive

result for �t.

4.3 Money and Production Loans

The money stock created by the private sector at the end of period t must equal

the amount of outstanding loans:

Pt tM L= . (5)

Note that since bonds are long-term loans, movements in bonds are not included in the

calculation of profits, although changes in bond interest will affect them. The money

stock created by the private sector at the end of period t must equal the amount of

outstanding loans:

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Pt tM L= . (6)

All bank loans demanded are supplied at interest rate Lti (determined as shown

below), so that

( )P Lt t tM L i= , 0L

Li

∂ <∂ (7)

4.4 Households Utility and Deposits

Households are assumed to be utility maximisers, subject to a budget constraint.

They divide their income between consumption Ct, and saving St. New saving is

defined as that part of the wage that is not consumed in the period in which it is earned:

1t t t tS S W C−− = − , (8)

where tS is the total amount of saving per worker at the end of the period and where

saving is comprised of two parts; new bond purchases and addition to bank deposits.

Total saving is thus given by

t t tS D B= + , (9)

where tD is the quantity of bank deposits held at the end of the period by each

household. The period budget constraint applying to each household is therefore

1 1( ) ( )Bt t t t t t t tW i B C D D B B− −+ = + − + − . (10)

Bank deposits are assumed to earn zero interest, but are held for precautionary

motives depending on a subjective uncertainty factor tµ . It is important to note that this

factor is one viewed by households as affecting them individually, and not one that

affects the value of money. A constant level of confidence in the production economy

as a whole is assumed. The utility of each household in each period (the felicity

function) is assumed to be

( ) ( ) ;t t t t tU g C h Dµ ωχ= + − (11)

- 21 -

0, 0;g g′ ′′> < 0, 0; 0h h ω′ ′′> < > ;

where �t is the hours of labour performed in each day.

Equation (11) implies that utility increases in consumption and in deposits held,

but with declining marginal utility in each case. Utility declines with constant marginal

utility in the number of hours worked.

If we set up a Lagrangian for the household as follows:

1 1

1 1 1 1 1 1 1 1

( ) ( ) ( ( ) ( )

( ( ) ( )

Bt t t t t t t t t t t t t t t

Bt t t t t t t t t t

L g C h D w C D D B B i B

w C D D B B i B

µ ωχ λ χ

λ χ− −

+ + + + + + + +

� �= − − − − − − − +� �

� �− − − − − − +� �

, (12)

we obtain the following first-order conditions:

) ( )t tL g CC λ∂ ′= +∂ , (13)

1( )t t t tL h DD µ λ λ +

∂ ′= + −∂ , (14)

t tL Wω λχ

∂ = − −∂ , (15)

Setting 0Lχ

∂ =∂ and rearranging equation (4.31) we obtain

t tWω λ= − , (16)

confirming that in our model maximising households will aim to make the marginal

disutility of work equal to the asset-equivalent value of wages.

Setting 0LC

∂ =∂ and combining (13) and (15) we get

( )t tg C Wω ′= , (17)

or that the disutility of labour is equal to additional utility provided by the wage. This

makes it clear that there is a conflict between utility-maximising wage-earners and

Parguez-Graziani motivated firms. Finally, by setting 0LD

∂ =∂ and combining (13)

and (14) we obtain

- 22 -

1( ) ( ) ( )t t t th D g C g Cµ +′ ′ ′= − , (18)

or that the marginal utility of deposit holdings in period t is equal to the change in

marginal utility from consumption between periods t and t+1. Because both ( ) 0th D′′ <

and ( ) 0tg C′′ < , this translates to an association between an increase in the utility from

deposit holding (either because of an increase in deposits Dt or an increase in

uncertainty �t) and decreasing consumption over time.

To analyse the effect of changes in bond interest rates we obtain

1t t t tL iB λ λ λ +

∂ = − −∂ (19)

from the Lagrangian (12). Setting 0LB

∂ =∂ and combining (13), (14) and (19) we can

show that

( )

( )t t

tt

h Di

g Cµ ′

=′

(20)

so that an increase in the interest rate will produce an increase in the ratio of

consumption to deposits, assuming a constant level of subjective uncertainty �t. If, on

the other hand, �t increases while the interest rate remains constant we will see a switch

from consumption to deposits to maintain the equality.

4.5 The Role of Central Bank Money

Central Bank Deposit Money money (SBDM) is issued by the central bank on

behalf of the state. It can enter the economy in two ways. Firstly it is used by the

government to make purchases from households and firms. When this happens the

SBDM issued becomes part of the reserves of the commercial banks and an equal

quantity of commercial bank money is transferred to the accounts of those from whom

the government purchases were made. At the end of each period t

1t

E Et t tH H G T

−= + − , (21)

- 23 -

where EtH is the total quantity of SBDM entering via the government expenditure route

present in the economy at the end of period t; tG is government expenditure in period t

and tT is tax received by the government in period t. In our model, which for the sake

of clarity has no government bonds, if Ht-1 = 0 and Gt - Tt-1 then no SBDM from this

route will be present in the economy.

SBDM adds to the circulating medium of exchange tM so that

Pt t t t tM M H L H= + = + , (22)

In its role as regulator the central bank imposes a minimum reserve ratio φ on the

banks3, so that /t tH L φ≥ . If /EtH L φ< then the banks are required to borrow

additional SBDM from the central bank, at an interest rate of Hti to maintain the reserve

ratio. Clearly the greater the government deficit the less reliant the banks are on

borrowing from the central bank, and the less influence the central bank has of

influencing commercial bank lending through manipulating the interest rate.

5. Conclusions

5.1 Taking the Theory of the Monetary Circuit Seriously

There are strong arguments for taking the TMC seriously as a tool for modelling

the monetary economy in the light of its plausibility as a mechanism for the initiation

and maintenance of the monetary economy.

5.2 The TMC and Profits

The constraint of the TMC presents a problem of accounting for profits. In the

explanations of Parguez and Graziani, there is a clear conflict between the power of

3 In most modern economies, such as that of the UK, there is no prescribed ratio, but banks themselves ensure a prudential reserve ratio to allow for possible cash demands. In our modelled non-cash economy we replace this with an imposed ratio.

- 24 -

firms to control the real distribution of goods and the neoclassical assumption of an

equilibrium equality between the real wage, the marginal productivity of labour for

firms and the marginal disutility of labour to wage earners. Graziani and Parguez

conclude that the conflict is resolved entirely in the favour of firms. But their

conclusion appears not entirely convincing and may in part be as a result of not

considering the possibility of alternative sources of money from the government and

consumption loans. This model shows how this might allow firms to earn a money

surplus without further manipulation of the real economy or the price level.

5.3 The Role of Deposits

The introduction of precautionary deposits into the model which are significant

to the budget constraints of firms and households but not that of the government is

significant for the anticipated effects of exogenous interest rate changes.

5.4 Implications for Interest-rate Policy

An exogenous increase in the interest rate charged by the central bank to

commercial banks may have the following consequences:

a) An increase in the interest rate offered to firms and/or a reduction in the number

of loans offered. Our model suggests this effect can be mediated by the level of

the government deficit.

b) Firms have to meet higher interest-rate payments. They may seek to meet these

by:

i) passing on the extra cost to wage-earners by increasing the prices of

consumption commodities and /or

ii) reducing employment and output levels and/or

- 25 -

iii) offering a higher return on their bonds.

Which of these effects is most prominent will depend on the stance taken on the

relative power of firms and households.

c) Because holding bonds is now less attractive, greater consumption occurs by

households, as indicated by equation (20).

Note that b)i) and c) are potentially inflationary – contrary to the presumed intended

effect of the interest rate increase.

6. Bibliography

Buiter, W. H., "New Developments in Monetary Economics: Two Ghosts, Two

Eccentricities, a Fallacy, a Mirage and a Mythos," Economic Journal 115 (502):

C1-C31 (2005).

Cartelier, Jean. 1996. In Money in Motion: The Post Keynesian and Circulation

Approaches., edited by G Deleplace and E. J. Nell. Basingstoke and London:

Macmillan.

Cooley, Thomas and Greg Hansen. 1995. Business Cycle Models with Money. In

Frontiers of Business Cycle Research., edited by Thomas Cooley. Princeton:

Princeton University Press.

Godley, Wynne. 2004. Weaving Cloth from Graziani's Thread: Endogenous Money in a

Simple (but Complete) Keynesian Model. In Money, Credit and the Role of the

State: Essays in Honour of Augusto Graziani., edited by Richard Arena and

Neri Salvadori. Aldershot: Ashgate.

Godley, Wynne and Lavoie, Mark. Kaleckian Models of Growth in a Stock-Flow

Monetary Framework: A Neo-Kaldorian Model. 2000. Annandale-on-Hudson,

New York. Working paper No. 302, The Levy Economics Institute of Bard

College.

- 26 -

Godley, Wynne and Lavoie, Mark. Features of a Realistic Banking System within a

Post-Keynesian Stock-Flow Consistent Model. 2004. Cambridge, UK.

Cambridge Endowment for Research in Finance.

Graziani, Augusto. The Theory of the Monetary Circuit. 89. London.

Graziani, Augusto. 2003. The Monetary Theory of Production. Vol. . ed. Edited by .

Cambridge, UK: Cambridge University Press.

Kalecki, Michel. 1971. Selected Essays on the Dynamics of the Capitalist Economy

1933-1970. Vol. . ed. Edited by . Cambridge: Cambridge University Press.

King, Robert G. and Charles G. Plosser, "Money, Credit, and Prices in a Real Business

Cycle," American Economic Review 74 (3): 363-380 (1984).

Kiyotaki, Nobuhiro and Randall Wright, "On Money as a Medium of Exchange,"

Journal of Political Economy 94 (4): 927-954 (1989).

Parguez, A. 1996. Beyond Scarcity: A Reappraisal of the Theory of the Monetary

Circuit . In Money in Motion: The Post Keynesian and Circulation Approaches.,

edited by G Deleplace and E. J. Nell.Macmillan.

Parguez, Alain. 2004. The Solution of the Paradox of Profits. In Money, Credit and the

Role of the State: Essays in Honour of Augusto Graziani., edited by Richard

Arena and Neri Salvadori. Aldershot: Ashgate.

Rousseas, Stephen. 1992. Post Keynesian Monetary Economics. Armonk, New York:

M.E.Sharpe.

Wray, Randall. 1990. Money and Credit in Capitalist Economies: The Endogenous

Money Approach. Aldershot: Edward Elgar.

- 27 -

7. Tables and Figures Table 1: UK Gross Operating Surplus, M0 and Household Lending

1986-2003

Gross Operating Surplus of UK

Firms £ millions

Quantity of M0 at year

end £ millions

Amount Outstanding Sterling Net Lending to

Individuals £ millions

1986 95953 15946 48145 1987 108273 16633 62624 1988 121235 18040 77863 1989 131108 19006 116306 1990 136103 19492 126561 1991 137840 20085 133022 1992 144326 20581 138571 1993 160887 21729 148145 1994 180196 23322 158012 1995 191594 24539 186669 1996 213016 26153 209901 1997 224826 27802 364566 1998 231884 29346 386993 1999 234738 32768 420082 2000 235708 34566 470917 2001 241233 37319 514802 2002 258750 39540 575819 2003 277165 42317 620255

0

100000

200000

300000

400000

500000

600000

700000

1986

1988

1990

1992

1994

1996

1998

2000

2002

£ st

erlin

g (m

illio

ns)

Gross OperatingSurplus of UK Firms

Quantity of M0 at yearend

Amount OutstandingSterling Net Lending toIndividuals

Chart 1: UK Gross Operating Surplus, M0 and Household Lending

1986-2003

Sources: ONS, Bank of England