“IS-LM (with endogenous money)”

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Paul Krugman posted on a familiar topic yesterday—the failure of most inflation hawks to admit that they were wrong—and included praise for one such hawk who has indeed changed his mind and said so:

There’s an interesting contrast with one of the real intellectual heroes here, Narayana Kocherlakota of the Minneapolis Fed, who has actually reconsidered his views in the light of overwhelming evidence. In our political culture, this kind of switch is all too often made into an occasion for gotchas: you used to say that, now you say this. But learning from experience is a good thing, not a sign of weakness. (“A Tale of Two Fed Presidents“)

If this was all there was to the article, I would have finished the (as usual) enjoyable read, and moved on to the next link from Twitter. But then there was this statement:

Look, some of us came into the crisis with a more or less fully formed intellectual framework — extended IS-LM (with endogenous money) — and substantial empirical evidence from Japan…

Huh? “extended IS-LM (with endogenous money)”??? Paul has of course exposited on and promoted IS-LM many times in the past. But “with endogenous money“? Normally this is something he has derided. In the past, his perspective has been “IS-LM with Loanable Funds”, not “with Endogenous Money”.

Now I could be reading too much into this phrase. As Nick Rowe said in the very intelligent and civil discussion on his excellent post “What Steve Keen is maybe trying to say“, the phrase can mean different things to different people:

I don’t find the “exogenous vs endogenous money” distinction helpful in this context, simply because different people seem to mean many different things by that. (Nick Rowe)

Paul could mean something quite different to what I mean by “endogenous money” too, and I could be reading far too much into this single phrase (heck, it could even be a typo!). But if he is shifting his position in the “money and banks don’t matter” and “money and banks are crucial” debate, even a little, that’s something to be applauded in precisely the same manner in which he praised Kocherlakota for moving on inflation. And if not—if he meant something entirely different to the interpretation I put on that statement—well then doubtless we’ll find out. We’ll surely get a clarification in due course.

Whatever that clarification turns out to be, this unexpected phrase has motivated me to publish, ahead of schedule, a model comparing Loanable Funds to Endogenous Money that I promised to provide in the discussion on Nick’s blog:

If the lender is a non-bank, then the repayment of a debt lets the lender spend because both debt and loan are on the liability side of the banking system’s ledger; but if the lender is a bank, then the repayment of the loan takes money out of circulation (I prefer that expression to “destroys money”) because the debt is on the asset side of the ledger. That’s the essential difference between Loanable Funds & Endogenous Money, which I’m trying to illustrate in a pair of very simple models that I’ll post on my blog shortly—and link to Nick’s discussion here. (A comment by me on Nick Rowe’s post)

I have since developed that pair of models; there’s much more analysis needed before I’m willing to publish an academic paper on the topic, but here’s what I think is the simplest possible model contrasting Loanable Funds—in which banks, money and (except during a liquidity trap) private debt don’t matter to macroeconomics—and Endogenous Money—in which banks, debt and money are crucial to macroeconomics at all times.

A monetary model of Loanable Funds

My starting point is Krugman’s description of the essence of lending as being a transfer between Patient and Impatient agents:

Think of it this way: when debt is rising, it’s not the economy as a whole borrowing more money. It is, rather, a case of less patient people—people who for whatever reason want to spend sooner rather than later—borrowing from more patient people. (Paul Krugman, 2012, pp. 146-47. Emphasis added)

In the New Keynesian model of a liquidity trap that he and Eggertsson developed (Gauti B. Eggertsson and Paul Krugman, 2012), lending was for the purposes of consumption, and while there was debt, there were neither banks nor money:

We assume initially that borrowing and lending take the form of risk-free bonds denominated in the consumption good. (Gauti B. Eggertsson and Paul Krugman, 2012, p. 1474)

My model of Loanable Funds embeds this vision of lending as being a transfer from Patient to Impatient agents in a monetary model of the economy—one in which all transactions involve the transfer of money in bank accounts—and one in which “Patient agents” and “Impatient agents” are both capitalists, who need money to hire workers and also buy inputs from each other. Though the banking sector exists in this model it is entirely passive: it is just where “Patient agents” deposit their cash, and lending is seen as a transfer from the deposit accounts of the Patient agents to the deposit accounts of the Impatient agents.

I also treat lending as being primarily for production rather than consumption. Both Patient and Impatient agents are capitalists who need money to hire workers and buy inputs for production (as well as for consumption) from each other. The basic financial operations are:

  • An initial deposit of 90 by the Patient agents and loan to the Impatient agents of 10, both of which are stored in bank accounts;
  • Lending by the Patient Agents to the Impatient Agents;
  • Payment of interest;
  • Repayment of the debt;
  • Hiring of workers by both groups of agents;
  • Consumption by all agents from both Patient and Impatient.

The operations are shown below in Table 1, following the conventions in the Minsky program that assets are shown as positives, liabilities and equity are shown as negatives, the source of any flow is a positive and its destination is a negative: these conventions ensure that all rows have to sum to zero to be correct in accounting terms (the program also supports the accounting approach of using DR and CR).

Table 1: Financial transaction in Loanable Funds on banking system’s ledger



Reserves Patient Impatient Workers NWBank
Initial conditions 100 -90 -10 0 0
Lend money Lend -Lend
Pay Interest -Int Int
Repay Loans -Repay Repay
Patient hires workers WagesP -WagesP
Impatient hires workers WagesI -WagesI
Worker consume from Patient -ConsWP ConsWP
Worker consume from Impatient -ConsWI ConsWI
Patient buys inputs/consumes ConsP -ConsP
Impatient buys inputs/consumes -ConsI ConsI
Bankers buy inputs/consume (P) -ConsBP ConsBP
Bankers buy inputs/consume (I) -ConsBI ConsBI


Loans themselves don’t turn up on the banking sector’s ledger because they are transfers between the Patient and Impatient agents. Instead loans are assets of the Patient agents and a liabilities of the Impatient agents. Table 2 shows Loans from the Patient agents’ perspective, while Table 3 shows the same operations from the Impatient agents’ perspective.

Table 2: Lending, repayment and interest from the Patient agents’ perspective


Patient Loans NWPatient
Initial conditions 90 10 -100
Lend money -Lend Lend
Pay Interest Int -Int
Repay Loans Repay -Repay

Table 3: Lending, repayment and interest from the Impatient agents’ perspective



Impatient Loans NWPatient
Initial conditions 10 -10 0
Lend money Lend -Lend
Pay Interest -Int Int
Repay Loans -Repay Repay


The Minsky program (click here for the latest beta build) is primarily designed for numerical simulation—and I’ll get to that shortly—but it also generates the dynamic equations in the model, and they are instructive enough for those who don’t suffer the MEGO effect (“My Eyes Glaze Over”) when looking at equations (if you do, skip most of this and just check the simulations below). The equations of motion of the key accounts in this model (click here to download the model) are shown in Equation . The first four equations describe the dynamics of money in this model; the last equation describes the dynamics of debt.

The key points from these equations are:

  • The total amount of money in the system is the sum of the four accounts Impatient, Patient, Workers and NWBank (for “Net Worth of the Banking sector”, which is zero in this model), and this doesn’t change: the sum of the first 4 equations is zero:

  • The total amount of money in the firm sector is the sum of the first two accounts—Patient and Impatient—and the annual turnover of this amount is the annual GDP of this model. It is unaffected by lending, repayment and debt service, so GDP is also unaffected by lending, repayment and debt service:

  • Finally, the dynamics of debt in this model are

This structure means that, no matter what behavioral relations are used to model lending, repayment, consumption, etc., changes in the level of debt have no impact on the macroeconomy. This is confirmed by the relations I used to simulate this model, which used simple time constants to specify all flows. In Figure 1 I ran the model with a time constant of 7 years for lending and 9 years for repayment until the debt to GDP ratio stabilized at 0.24 (which took about 60 years), and then altered time constants—firstly simulating a slump in lending, then a boom, and finally a return to the initial rates. The level of debt and the debt to GDP ratio varied dramatically, but GDP sailed on undisturbed. So if Loanable Funds accurately characterized actual lending, banks, money and (except during a liquidity trap) debt would indeed by irrelevant to macreoeconomics.

Figure 1: Simulation of Loanable Funds

Endogenous Money proponents, on the other hand, insist that most lending is not between non-banks, but from banks to non-banks, and that this makes all the difference in the world. That is easily illustrated by making just 3 simple changes to this model:

  • Lending is shown as being a flow from Banks to Impatient Agents;
  • Interest payments go not from Impatient to Patient but from Patient to the NWBank; and
  • When the model is simulated, lending is related to the current level of lending rather than to the amount of money in the Patient Agents’ accounts.

So what difference did these simple structural changes make? A lot.

A monetary model of Endogenous Money

The monetary system from the banking sector’s point of view is shown in Table 4: Loans are now an asset of the banking sector, while lending, repayment and debt service are all relations between the Impatient agents and the banking sector. The differences of this model with Loanable Funds are highlighted in bold in the Table (click here to download the model).

Table 4: Financial transaction in Endogenous Money on banking system’s ledger



Reserves Loans Patient Impatient Workers NWBank
Initial conditions 90 10 -90 -10 0 0
Lend money Lend -Lend
Pay Interest Int -Int
Repay Loans -Repay Repay
Patient hires workers WagesP -WagesP
Impatient hires workers WagesI -WagesI
Worker consume from Patient -ConsWP ConsWP
Worker consume from Impatient -ConsWI ConsWI
Patient buys inputs/consumes ConsP -ConsP
Impatient buys inputs/consumes -ConsI ConsI
Bankers buy inputs/consume (P) -ConsBP ConsBP
Bankers buy inputs/consume (I) -ConsBI ConsBI



The equations of motion of this system are:

There are three significant ways in which this model differs from Loanable Funds:

  • The total amount of money in the system is, as before, the sum of the four accounts Impatient, Patient, Workers and NWBank (for “Net Worth of the Banking sector”, which is not zero in this model), and this now is altered by the change in debt:

  • The total amount of money in the firm sector is the sum of the first two accounts—Patient and Impatient—and the annual turnover of this amount is the annual GDP of this model. It is also altered by lending, repayment and debt service, and therefore so is GDP:

  • Finally, the dynamics of debt in this model are the same as in Loanable Funds, but now this is also identical to the dynamics of the money supply:

I simulated the model for 250 years with constant parameters (it took that long for the debt to GDP ratio to stabilize at 0.32), and then repeated the experiment of a slump in lending followed by a boom and then a return to normality. The results in Figure 2 shows how different an Endogenous Money view of the world is to Loanable Funds.

Firstly, in Endogenous money, the growth of debt is not macroeconomically neuteal but causes GDP to grow: rather than the change in debt being irrelevant to the macroeconomy as in Loanable Funds, in Endogenous Money it alters the level of demand. Secondly, alterations in the rate of change of debt had drastic effects on the economy: a decline in lending caused a slump and an increase in lending caused a boom.

Figure 2: Simulation of Endogenous Money

IS-LM and Endogenous Money?

If—and it’s a big if—this phrase signifies a shift in how Krugman models IS-LM, then it will surely mean something very different to what I’ve shown above. For starters, it’s likely to be an equilibrium model, when as Nick Rowe rightly concluded, my story is a disequilibrium one (something that Hicks argued long ago can’t be done with IS-LM—see (John Hicks, 1981)):

We are talking about a Hayekian process in which individuals’ plans and expectations are mutually inconsistent in aggregate. We are talking about a disequilibrium process in which people’s plans and expectations get revised in the light of the surprises that occur because of that mutual inconsistency. (Nick Rowe)

Of course, it could signify no more than a rebadging of Krugman’s established approach—or even a typo. We’ll have to await an elaboration. But I do hope that it does signify a further thawing in the relations between orthodox economists and those from the non-orthodox end of the spectrum after Nick Lowe’s recent contribution.

Nick’s post—a reminder

As I acknowledged in “An outbreak of communication“, Nick’s post accurately stated my arguments on the creation of aggregate (or effective) demand via the creation of money by loans from the banking system to the public:

So with that very big caveat understood, here’s what I think Steve Keen is maybe trying to say:

Aggregate planned nominal expenditure equals aggregate expected nominal income plus amount of new money created by the banking system minus increase in the stock of money demanded. (All four terms in that equation have the units dollars per month, and all are referring to the same month, or whatever.)

And let’s assume that people actually realise their planned expenditures, which is a reasonable assumption for an economy where goods and productive resources are in excess supply, so that aggregate planned nominal expenditure equals aggregate actual nominal expenditure. And let’s recognise that aggregate actual nominal expenditure is the same as actual nominal income, by accounting identity. So the original equation now becomes:

Aggregate actual nominal income equals aggregate expected nominal income plus amount of new money created by the banking system minus increase in the stock of money demanded.

Nothing in the above violates any national income accounting identity. (Nick Rowe)

This is, from my perspective, the essence of the significance of Endogenous Money. If this wasn’t true—if the creation of new money by the banking system didn’t somehow impact on actual income and demand—then by Occam’s Razor, there would be no macroeconomic significance to Endogenous Money, and we’d be better off ignoring the banking sector in macroeconomics, as the model of Loanable Funds does. Nick provided an excellent verbal statement of this—and a logical argument behind it which I think any economist should be able to follow, regardless of his/her school of thought:

Start with aggregate planned and actual and expected income and expenditure all equal. Now suppose that something changes, and every individual plans to borrow an extra $100 from the banking system and spend that extra $100 during the coming month. He does not plan to hold that extra $100 in his chequing account at the end of the month (the quantity of money demanded is unchanged, in other words). And suppose that the banking system lends an extra $100 to every individual and does this by creating $100 more money. The individuals are borrowing $100 because they plan to spend $100 more than they expect to earn during the coming month.

Now if the average individual knew that every other individual was also planning to borrow and spend an extra $100, and could put two and two together and figure out that this would mean his own income would rise by $100, he would immediately revise his plans on how much to borrow and spend. Under full information and fully rational expectations we couldn’t have aggregate planned expenditure different from aggregate expected income for the same coming month.

But maybe the average individual does not know that every other individual is doing the same thing. Or maybe he does know this, but thinks their extra expenditure will increase someone else’s income and not his. Aggregate expected income, which is what we are talking about here, is not the same as expected aggregate income. The first aggregates across individuals’ expectations of their own incomes; the second is (someone’s) expectation of aggregate income. It would be perfectly possible to build a model in which individuals face a Lucasian signal-processing problem and cannot distinguish aggregate/nominal from individual-specific/real shocks.

So at the end of the month the average individual is surprised to discover that his income was $100 more than he expected it to be, and that he has $100 more in his chequing account than he expected to have and planned to have. This means the actual quantity of money is $100 greater than the quantity of money demanded. And next month he will revise his plans and expectations because of this surprise. How he revises his plans and expectations will depend on whether he thinks this is a temporary or a permanent shock, which has its own signal-processing problem. And these revised plans may create more surprises the following month. (Nick Rowe)


Eggertsson, Gauti B. and Paul Krugman. 2012. “Debt, Deleveraging, and the Liquidity Trap: A Fisher-Minsky-Koo Approach.” Quarterly Journal of Economics, 127, 1469–513.

Hicks, John. 1981. “Is-Lm: An Explanation.” Journal of Post Keynesian Economics, 3(2), 139-54.

Krugman, Paul. 2012. End This Depression Now! New York: W.W. Norton.



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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15 Responses to “IS-LM (with endogenous money)”

  1. NeilW says:

    “If the lender is a non-bank, then the repay­ment of a debt lets the lender spend because both debt and loan are on the lia­bil­ity side of the bank­ing system’s ledger;”

    You have to be careful here – because of the buffering effect of the banking transaction system.

    So if you have a classic building society, or other financial institution like a payday lender, without a central bank account, but with an account at a clearing bank. The clearing bank will then have a floating charge over the assets created by the building society.

    That means the clearing bank essentially offers an infinite intraday overdraft to the building society – which allows the building society to (figuratively) advance loans in the morning, and backfill the deposits in the afternoon via Treasury Processes in the same way that the clearing bank does. And it is the advancing the loans first and backfilling in an asynchronous manner – connected only by a target interest rate margin – that causes the forward demand impulse of endogenous money.

    For there to be any loanable funds effect of subtracting from demand first and then advancing demand via a loan or credit, there has to be somebody in the banking system who is prepared to say ‘no’ to the asynchronous option – and force serialisation of the process in time.

    And I don’t see that happening anywhere any more.

    It used to do, for example when building societies had ‘so much to lend’ each month and invited offers on that basis. But since the advent of computerisation and the use of Treasury processes ISTM that secondary lenders operate pretty much like primary ones.

  2. TruthIsThereIsNoTruth says:


    I think you are sort of correct, but might be a bit misleading in the context of the post. Banks will generally run a generous liquidity buffer and the settlement period for most loans allows plenty of time to maturity match the loan funding.

    While the role of the clearing bank you describe is not incorrect, banks view this source of funding as cleaning up the very marginal transactions, particularly in trading, and only if other funding cant be obtained.

  3. TruthIsThereIsNoTruth says:

    had to rush off, to finish the previous post.

    It is not to say banks will exactly maturity match their funding, it is more a case of matching the desired capital and liquidity strategy. But it’s certainly not the case that a bank lends you money for a home loan and then goes to the rba to clear it. This was a picture which for a while was being portrayed by the ‘banks lend money out of thin air’ argument (which may well be the case in a systemic sense, but this was extremely poorly understood and misrepresented by the proponents of the argument.)

  4. Steve Hummel says:

    “This was a pic­ture which for a while was being por­trayed by the ‘banks lend money out of thin air’ argu­ment (which may well be the case in a sys­temic sense, but this was extremely poorly under­stood and mis­rep­re­sented by the pro­po­nents of the argument.)

    This is very true. Conflating and advocating INDIVIDUAL virtues like frugality (especially its excessive and puritanical form, austerity) and SYSTEMIC economic policy as a solution is utterly mistaken.

    Scarcity as both an individual and systemic monetary concept must be correctly identified as the real source of economic disequilibrium, and modern profit making economies must embrace the concept of individual monetary grace the free gift. The failure/irrelevance of velocity theory coupled with the accelerating pace of technological innovation will create increasing economic/monetary instability unless this transforming idea becomes more real in the minds of economists. Reform is not sufficient to solve the problem. Transformative ideas and policies are required.

  5. TruthIsThereIsNoTruth says:

    SH, what’s the antonym for you make sense?

  6. Pingback: Paul Krugman, Nick Rowe and an Endogenous Money Model | Credit Writedowns

  7. Steve Hummel says:

    Apparently you don’t even like it when I agree with you about something. Reminds me of an ex-wife who even after I said I was sorry…the rant just kept right on coming.

    Let’s try again. Trying to make individual moral judgments fit into systemic situations that call for the opposites of those (actually confused) judgments….won’t work. They particularly won’t work when austerity is confused with frugality. This is what the garden variety monetary reformers who rant on about “money out of thin air” do. Actually ex nilhilo money is fine if you address the real underlying problem (systemic scarcity of total individual purchasing power (not to be confused with total money) and you are not hemmed in by habitual pet hates like “central planning!!!!!!” but instead understand that adult, responsible and actual control of the economic and money systems is required simply because they are fundamentally….broken.

  8. Steve Hummel says:

    The physics of economics and money systems is cost. This is why cost accounting is so significant. It gets to the nitty gritty of where the problem lies. If total costs exceed total individual incomes right at the initial creation of a product or service, and that elemental fact is also true at every commercial stop the product/service makes on its journey up to and including retail sale to an individual, and also whenever it re-enters the economy….how can total individual incomes ever equate with total prices? Velocity theory is flimsy in view of the empirical evidence just sighted and despite the following, but if the above is true velocity would have to be god knows 20 or 30 to be even be close to adequate. I suggest economics focus on the empirical evidence to be found in the cost accounting data of any enterprise and worry less about the abstractions of theory less. The discipline would be closer to being a science and getting a better grasp of more fundamental realities would enable us to dispense with a lot of the things that tend to confuse everyone….including economists.

  9. ceviche says:

    Steve, is Rowe’s statement
    “…amount of new money cre­ated by the bank­ing sys­tem minus increase in the stock of money demanded” really consistent with your model?
    I would have thought that ‘new money created…’ represents loans from banks to borrowers (for the purpose of expenditure by them) and that is precisely that which is the “increase in the stock of money demanded” IN THAT PERIOD.

  10. Pingback: IS-LM and Endogenous Money | Colectivo Burbuja

  11. Steve Hummel says:

    There is a 100% correlation between recessions/depressions, the slow down in lending and the drop off in the velocity of money. Doesn’t that point at velocity largely if not entirely representing/being the amount of money borrowed?

    That then would mean that the cost accounting empirical reality that total INDIVIDUAL incomes (effective demand)….not being all costs, and yet all costs must go into price….as a fundamental reality of commerce/the economy. That would also mean that the economy not only is NOT tending toward equilibrium, but for the individual (and for businesses as a result), is radically monetarily unstable.

    And of course, the solution to this scarcity is the equalizing of total INDIVIDUAL incomes with total prices via a direct and consequently commercially costless payment of money to the individual. Think universal dividend.

    Then, because commercial life is an adventure and costs may indeed go up for legitimate reasons, and also because (especially) in a profit making economic system where effective demand is not scarce the tendency will be to increase prices…a policy of equating the cost of consumption (spending) and the cost of production (prices) via a discount to consumers equal to the ratio of cost of consumption over cost of production would do just that….mathematically. Of course the amounts of their discounts to consumers would be rebated back to participating merchants so they could be whole on their overheads and margins and so the system would truly and finally be free to operate on all cylinders in perpetuity and the price reducing effect of innovation would also not be sabotaged so that prices would be free to go down without economic harm. Eventually money would gravitate toward its most rational and sane form, that of a ticket for the distribution of production.

  12. Steve Hummel says:

    The difficult thing about change is mostly just the decision to actually change itself. This is especially true when the change that needs to be made is one that simultaneously trans forms the entire discipline/body of thought….and also leaves many if not most of the structures/basics of that discipline/body of thought virtually intact. So it would be if a change in the consumer financial paradigm of loan only were complemented by the addition of a policy of individual monetary grace, the free gift. This simple and singular change would utterly transform economics and economic theory. It would also leave profit, free enterprise, private property etc. completely unchanged. And actually, incorporating individual monetary grace in a world of abundance made imminently possible/necessary due to the acceleration of technological innovation….would evolve and so insure the the stability and even the survival….of profit making economic systems. After all…if a profit making system not only now cannot rationally create enough jobs/individual incomes for the system to function properly, but with the acceleration of innovation/efficiency will only make the system less able to be balanced, then without evolution it is inevitable that such a system will devolve into either a socialist or a fascist work state.

    Transformative ideas….are transformative. Let us have them.

  13. Steve Hummel says:

    Regarding your bet on Australian housing prices:

    You’d right even when you’re wrong….if you’d cognite on the fact that, ultimately, the financial paradigm is what is important. Australia did good by the first home buyers credit. However, they will not ultimately do good….unless that momentary policy of monetary grace, the free gift is generalized and perpetuated for the consumer, relatively speaking, that is for a middle class lifestyle whether one works or not.

    Do you not see that fact when you look at the Australian housing market….and then extrapolate it outward to the markets in general? Supplementing individual purchasing power directly is necessary…no matter whether the end price of a product is $1,000,000 or $100. You’ve advocated a modern jubilee which is wisdom. Just make it permanent and mathematically equillibrating policy…and the system will flow as freely as truly free market theory can be.

    As I say on your blog, monetary grace and actual and unobtrusive, adult control of the money system as ideas and as a policies…are powerfully transformative. Let us have them….in perpetuity. You really should have the faith….as in confidence to acknowledge that truth.

  14. Steve Hummel says:

    The time for transformative changes never arrives for the self interested or the terminally orthodox, and generally, even for those only slightly too cozy with long held ideas. Habit is actually the worst enemy of present time experience and willingness and ability to look, not the two former obvious flaws.

    The truth is individual monetary grace probably could have been implemented in the first century AD as well as now. In fact the problematic abstractions of feudalism, capitalism and socialism probably would not have be-deviled mankind’s history at all if such would have been the case. Transformative ideas are transformative…no matter how or when they are implemented.

    Science as a dominant mindset is so passé. Of course, so is religion. It’s Wisdom that we’ve always needed, and up until now, foolishly believed was unrealistic. But now the economic and monetary systems require it, so how can one sit back and say that we must progress gradually or even deny the need for it altogether? Oh ye of little faith, repent! For the kingdom of monetary Grace is at hand!

    By the way Wisdom encompasses and ethically integrates both the scientific and the religious mindset.

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