Steve Keen University of Western Sydney Debunking Economics wwwdebtdeflationcomblogs wwwdebunkingeconomicscom Circuit Theory Conundrums If on the other hand wageearners decide to keep part of their savings in the form of liquid balances firms will get back from the market less mone ID: 533198
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Slide1
Solving Circuit Theory Conundrums
Steve KeenUniversity of Western SydneyDebunking Economicswww.debtdeflation.com/blogswww.debunkingeconomics.comSlide2
Circuit Theory Conundrums
“If on the other hand, wage-earners decide to keep part of their savings in the form of liquid balances, firms will get back from the market less money than they have initially injected in it … firms will be unable to repay to the banks the whole of their debt.” (Graziani 1989)“For the sake of simplicity, we exclude the payment of interest to the banks.” (Bellofiore et al, 2000)“The existence of monetary profits … has always been a conundrum for theoreticians of the monetary circuit. If money is created from bank credit, how can we explain profits if firms borrow just enough to cover wages that are simply spent on consumption goods and returned to firms to extinguish their initial debt … In other words,
how can M become M+?” (Rochon 2005)Slide3
Mathematical logic to the rescue...
Circuit conundrums result from “thinking in statics”Financial cycle too complex to follow verballyEven “stock-flow consistent” modelling not suitableSolution is to think dynamically in continuous timeConsider flows set in motion by a loanSee what the flows tell youUse appropriate mathematics to modelProblem with neoclassical economics not maths
per seBut “teleological mathematics”Work out what you want to believe
Torture common sense until you “prove” itAppropriate maths is a system of differential equations...Slide4
Consider simplest possible pure credit economy
As in Graziani 1989 & 2003:No Central Bank or fiat money3 sectorsFirms/CapitalistsWorkers/HouseholdsBankers/BanksSingle loan of $L to Firm sectorCreates $
L of debt and $L money simultaneously
Initiates several flows between accountsDebt compoundingLoan and deposit interest payments
Wages
Consumption...Slide5
Accounting
Mathematical logic to the rescue...
Develop model
from the flows aloneStocks (system states) derived from integrating flows
Accounts
(Stocks) &
Operations (Flows)
Firm Loan
F
L
Firm Deposit
F
D
Worker Deposit
WDBank Income BILoan interestA-A=0-A+ADeposit Interest+B-BWages-C+CDeposit Interest+D-DConsumptionE+F-E-F
Analysing the flows... Rates of change of accounts:
Rate of change...Verbal descriptionOf FL = 0Debt remains constantOf FD = B+E+F-(A+C)Deposit interest + consumption flows – (Debt interest + wages)Of WD = C+D-EWages + Workers’ deposit interest - Workers' consumptionOf BI = A-(B+D+F)Loan interest – (Deposit interest + Bankers' consumption)
Accounts stable if “flows in” equal “flows out”:
$ transferSlide6
Mathematical logic to the rescue...
So system can be stable if:Account
Condition
Verbal Description
F
D
B+E+F=A+C
Deposit
interest plus
consumption flows = Debt
interest plus wages
W
D
C+D=E
Wages plus Workers’ deposit interest = Workers' consumptionBIA=B+D+FLoan interest = Deposit interest plus Bankers' consumptionNot obviously onerous conditions... Exploring further:A is the loan interest rate (rL) times Firm debt (FL)B is the deposit interest rate (rD) times Firm savings (FD)C is some rate per year (say w) times FDD is the deposit interest rate on Worker savings (WD)E is some consumption rate (say w) times Worker savingsF is some consumption rate (say b) Banker savings (BI)Equilibrium values are:Slide7
Mathematical logic to the rescue...
Solved with symbolic algebra program:
Two key conditions:
All accounts are positive if
b
>
r
L
and
w
>
r
D
Which means???If (for example)...The (after inflation) interest rate on loans is 5%; The interest rate on deposits is 1%; andBankers spend their account balance more often than once every 20 years; andWorkers spend theirs more often than once every centuryThen the system can be stableSlide8
Common sense (and Marx) to the rescue...
It’s actually very simple:Capitalist borrows $100Generates $400 (money turns over 4 times in a year)Pays $300 in wages + inputs, keeps $100 in profitUses $5 to pay interest on $100 debtPockets $75 (M+-M) after paying debt down by $20Expressed in terms of time lags, conditions under which credit-financed business is profitable are quite broad
tS
time lag from M to M+
(1/4
th
year standard setting)
t
W
time lag in workers consumption (1/26
th
year)
tB time lag in bankers consumption (1 year)Positive bank balances (and hence incomes—shown later) for broad range of parameter values...Slide9
Conditions for positive bank balances over time
Wide range of valid values:
Bank balances are positive if:
Surplus generated in
production
& workers consume
&
bankers spend
Fairly basic conditions for positive profits, wages, etc...
Viable even if turnover period is 7-10 yearsSlide10
Conditions for positive incomes over time
Banker gross income easy to calculateInterest on outstanding debt per year = rL.FLWorker gross income also easyWage flow per year = w.FD
But what is w? Back to Marx & Sraffa:Workers share of surplus (
1-s)Divided by time lag in going from M to M+ (t
S
)
So w= (
1-s
)/
t
S
What about capitalist profits?
Capitalists share of surplus (s)Divided by time lag in going from M to M+ (tS )So Profits= FD.(1-s)/tS Also derivable from Price times Quantity minus WagesSlide11
Common sense (and Marx) to the rescue...
A Simulation (click here for software)...Slide12
Conditions for positive incomes over time
Banker gross income = rL.FLWorker gross income = FD.(1-s)/tS
Capitalist gross income = FD.s/
tSAll positive so long as FD
> 0
.
System so far purely monetary
Presumes physical system producing net surplus
Easily linked with basic production system
Output = Labour times labour productivity
Labour = Wage flow/Wage
What about prices?
Derive from equilibrium conditions:
Wage set by “Phillips curve”Slide13
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Basic financial and physical equilibrium conditions
In equilibrium, physical output
Q
= physical demand
D
Physical Output
Q =
a.L
Where L = Wage flow/Wage
So
Equilibrium physical demand will beFlow of monetary demand divided by Price levelD = (Wages+Profits)/Price(net interest cancels out)D = (FD.s/tS)/PEquating D and Q:Solve for P:Surplus the source of profitPrice converts capitalist share of surplus in production into monetary sumSlide14
Simulation:
Basic financial and physical equilibrium conditions
Dynamic price relation is
Time-lagged convergence
to equilibrium value
Full monetary production
model can now be examined
Equilibrium conditions are (for given wage W):Slide15
Common sense to the rescue...
Capitalists can thereforeborrow money;pay interest;repay debt;& still make a profitAggregate profit exceeds zeroAs do wages and interest incomePrice converts capitalist surplus in production into moneyM becomes M+ via the price mechanism(if
there is a surplus in production)Fixed stock of money can finance constant outputRising M not needed to sustain constant outputSlide16
Common sense (and Marx) to the rescue...
Contrary Circuit conclusions resulted fromConfusion of stocks & flows:Initial Loan (stock) is not the limit of financial transactions the money it creates can cause (Flow/Year)Forgetting about surplus in productionSource of both physical and financial profitForgetting about turnover period of capital:“Let the period of turnover be 5 weeks, : the working period 4 weeks... In a year of 50 weeks ... Capital I of £2,000, constantly employed in the working period, is therefore turned over 12½ times. 12½ times 2,000 makes £25,000.” (
Capital II, Part II: The Turnover of Capital)Slide17
A new approach to dynamic modelling
Inspired by Godley/Lavoie Stock-Flow Consistent tablesPlus comments by Scott Fullwiler at UMKC 2006Rendition of SAM tabular concept in continuous timeWith bank account fundamental unit of analysisFar more suitable for asynchronous real-worldAll investment does not occur at same time
Discrete “t”, “t-1” period modelling imposes this
Does not require artificial time-delaysAllows processes to occur at different frequenciesConsumption fortnightly, investment 2-yearlySee my
Rossi-
Ponsot
2009
chapter for more details
Easily implemented in any symbolic algebra program
(
Mathcad—
www.ptc.com
/
mathcad
—shown here...)Slide18
Accounting
A new approach to dynamic modelling
Input table of accounts and flows between them:
Substitute
functions for placeholders A, B, etc.:
Automatically build “coupled ODE” model
$ transferSlide19
Conclusion: The Circuit “Works”
Long-believed conundrums must be forgotten... ButSolving conundrums strengthens Circuit TheoryCan explain where monetary profit comes fromSystem stable in the absence of Ponzi finance!Model expands to growth, multiple sectors, fiat moneyExplains:
Endogenous credit money creation;Credit system’s desire to extend too credit;Bank surplus rises if Debt rises
Basis of “inherent instability” in Financial Instability TheoremNot just a Hypothesis!Model here merely start of modelling monetary dynamics...Slide20
The Circuit can be extended...
To general monetary dynamic disequilibrium model...
Mixed credit-fiat
money...
Comparing different policies