Detractors of Adam Smith's Real Bills Doctrine

By: Antal E. Fekete | Wed, Jul 13, 2005
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Credit versus clearing

Strictly speaking a bill of exchange, pejoratively called "real bill" by Milton Friedman following his mentor Lloyd Mints, is not a credit instrument. It is a clearing instrument. It enables the market to clear goods in most urgent demand without needlessly invading the pool of circulating gold coins that would cause monetary contraction whenever division of labor is further refined and production processes are made more "roundabout" (to use the phrase of Bëhm-Bawerk) by the most progressive elements in the ranks of entrepreneurs and inventors. Lending and borrowing are not involved. The real bill circulates on its own wings and under its own steam by virtue of the urgent demand for the underlying consumer good.

Self-liquidating credit

In spite of the conceptual difference between credit and clearing, it is customary to extend the concept of credit to include, in addition to credit arising out of the propensity to save that finances fixed capital, self-liquidating credit arising out of the propensity to consume that finances circulating capital in the final phases of production of merchandise moving sufficiently fast to the final, gold-paying consumer. Thus, then, the bill of exchange is the embodiment of self-liquidating credit, so called as the credit is liquidated directly with the gold coin surrendered by the consumer in 91 days or less, 91 days being the length of the seasons of the year. With the change of seasons the type of merchandise demanded most urgently by the consumer also changes in the temperate zones where spontaneous bill circulation has taken its origin during the Renaissance. For this reason bills of exchange are limited to maturities 91 days or less. Under no circumstances would a bill circulate after maturity. If the underlying merchandise couldn't be sold during the current season, then it wouldn't be sold until the same season comes around again the following year.

Chicken or egg?

Detractors of the Real Bills Doctrine (RBD) studiously avoid reference to its prestigious pedigree and its author, Adam Smith. No less are they anxious to avoid reference to self-liquidating credit and to clearing. They also ignore the fact that, as a matter of merchant custom, producers and distributors would hardly ever pay the producers of higher order goods cash. The terms "91 days net" are standard and part of the deal. It is understood by everyone concerned that the bill will not be paid in full until the underlying merchandise is sold to the final consumer. Yet the supplier can use the bill to pay his own suppliers. Endorsed on the back, the bill can be passed along a number of times, the endorsement indicating that title to the proceeds has thereby been transferred from payer to payee. This transaction is also called "discounting" as the payee applies an appropriate discount, calculated at the current discount rate, to the face value of the bill proportional to the number of days remaining to maturity. Upon maturity the last payee presents the bill for payment to the producer on whom the bill is drawn.

Such bill circulation was wide-spread in the city-states of Italy in the Quattrocento and, more recently, in the 18th century in Lancashire, before the Bank of England opened its branch in Manchester, as observed by Ludwig von Mises in his 1912 treatise Theorie des Geldes und der Umlaufsmittel, although he stopped short of investigating the economic forces animating spontaneous bill circulation.

Unlike the question whether the chicken was first or the egg, the question whether bills or banks came first has a definite answer. There can be no doubt that the former did. Logically and historically, the bill predates the bank. What is more, it is perfectly feasible to have an economy without any commercial banks at all wherein circulating bills of exchange emerge as the supplier delivers semi-finished consumer goods to the producer. Instead of recognizing this fact, detractors link bills and banks as if they were Siamese twins. In refraining from ever mentioning the self-liquidating nature of the bill detractors of the RBD insist that credit has been created "out of nothing" and the bill is the engine driving paper-money inflation. Their methodology consists in summarily denouncing any and all as a "monetary crank" who is searching for and disseminating truth pertaining to bill circulation, without the slightest effort to examine the evidence for spontaneity. In doing so they betray their ignorance. Their blinkers do not let them notice the extensive body of scholarly literature on clearing and self-liquidating credit.

A "fairy" tale

Let us look at another instance of clearing and self-liquidating credit that was vitally important in the Middle Ages: the institution of city-fairs. Among the most notable ones were the fairs of Lyon in France, and those of Seville in Spain. They were annual events lasting up to a month. They attracted fair-goers from places as far as 500 miles away who brought their merchandise to sell, as well as their shopping-list of merchandise to buy. One thing they did not bring was gold to pay for the purchase of goods on their shopping list. They would leave it home for fear of highwaymen. They hoped to pay for their purchases with the proceeds of their sale. However, this presented problems. The fact is that there were far fewer gold coins available at the fair than the total value of merchandise waiting to be sold. Fairs would have been a total failure but for the institution of clearing. Buying one merchandise while selling another could be consummated perfectly well without the physical mediation of the gold coin. Gold was needed to finalize the deal only to the extent of the difference between the purchase price and the sale price.

In the absence of clearing the merchant arriving from a far-away place would have to sell before he could buy. Moreover, he would have a hard time selling because of the dearth of gold coins in the hands of prospective buyers. But even if he could sell out his wares, by the time he has done so the cream of the offering at the fair would be gone, and he might be left with the choice between seconds and rejects.

To avoid this, organizers of the fair set up a clearing house. Merchants from afar registered their merchandise upon arrival and received a quota of scrip money in proportion to its value at the clearing house. Scrip money could be used right away to make purchases, even before the purchaser sold any part of his registered merchandise. The quota had to be returned to the clearing house at the end of the fair. Scrip money in excess of the quota was redeemed, and shortfall made up, in gold coin. The marvelous institution of the clearing house and the invention of scrip money could move a far greater amount of merchandise than scarce gold coins ever could.

Those who call the issuance of scrip money "credit created out of nothing" are utterly blind to the true nature of the transaction. Fair-goers did not need a loan. What they needed was an instrument of clearing. The clearing house was not an engine of inflation. Its scrip money represented self-liquidating credit that was extinguished just as soon as the fair was over. As this example clearly demonstrates, a loan is very different from an advance to the seller of wares with a ready market at hand. The advance, scrip money, circulated spontaneously at the fair, while other credit instruments such as loan contracts and mortgages would never do.

Goods in bottoms

Or look at one other example of clearing that was important before World War I. Suppose a cargo ship is ready to sail from Tokyo to Hamburg carrying in its bottom consumer goods in urgent demand in Western Europe. The sea-voyage takes up to 30 days. Does the importer need to raise a loan to pay the supplier for the shipment prior to sailing? Hardly. The goods are known to be in high demand and to have a ready market upon arrival. The cargo is insured against losses at sea. Accordingly, the supplier bills the importer for value received f.o.b. Tokyo, payable in 30 days in London. The importer endorses the bill, attaches the insurance documents, and sends it back to the supplier. The boat is now ready to sail. The supplier has an instrument he could use as ready cash to pay for goods needed in order to replenish his depleted inventory. When the boat docks in Hamburg, the wholesale merchant pays for the cargo with a sight bill on London, with which the importer meets his maturing obligation. This is self-liquidating credit "on the go". No loan is involved. There is no need to invade the pool of circulating gold coins and to tie up savings for 30 days in moving goods in urgent consumer demand.

If you insist that this is credit expansion as money has been created out of nothing without recourse to saved funds to finance the movement of cargo across the high seas, and if you say that the bill drawn on the importer has been misused to fan the fires of inflation, then you have failed to grasp how foreign trade is financed.

Vanishing risks

It is true that production and distribution of consumer goods, no less than that of producers goods, involve risks. However, there is a difference. Risks of dealing in consumer goods in urgent demand vanish as the "journey" of the "maturing" good is coming to an end, and the final cash-paying consumer is already in sight, so that the consummation of sale can no longer be doubted. From this point on the last leg of the journey can be financed with self-liquidating credit. By contrast, for producers goods, risks do not disappear even after the sale.

Of course, not every consumer good has the quality that risks disappear during the last leg of its journey. Luxury goods and specialty items, for example, fall into this second category. So do consumer goods sold on instalment plans. The production and distribution of these have to be financed out of savings through loans, as is done in case of producers goods. Merchandise of the first category may occasionally have to be downgraded to the second, if demand for it slackens. Conversely, consumer goods of the second category could be upgraded to the first if demand for them picks up sufficiently. The bill market is the final arbiter to draw the shifting line of demarcation separating the two categories. If a bill can find takers and is readily discounted, then the underlying merchandise belongs to the first category. Otherwise it belongs to the second.

"Telescoping" payments

We have seen that the RBD has nothing to do with credit expansion by the banks. On the contrary, the remarkable fact is precisely that the RBD works also in an economy bereft of banks. It deals with the singular phenomenon that bills drawn on emerging goods sufficiently close to the ultimate cash-paying consumer circulate on their own wings and under their own steam, provided only that those goods are in urgent demand.

For this reason, if you want to refute the RBD, then it is not good enough to attack the banks for their part in credit expansion. You have to refute the phenomenon, acknowledged by Mises himself, that the bill of exchange is, in and of itself, fully capable of spontaneous monetary circulation. Typically, it is used in payment for higher-order goods by the producer of lower-order goods. In more details, bills drawn on the producer of an (n 1)-st order good, by virtue of his being that much closer to the ultimate gold-paying consumer, become a means of exchange in the hand of the producer of n-th order goods when he pays the producer of (n + 1)-st order goods for supplies. As the final product is sold to the consumer, his gold coin will liquidate all claims that have arisen along its journey through the various stages of production. Several payments have been, as it were, telescoped into one. This is clearing at work. This is the meaning of the assertion that the credit represented by the bill of exchange is self-liquidating. This is credit the volume of which flows and ebbs with the propensity to consume.

Can circulating capital be financed out of savings?

Moreover, as I shall now show, it is not possible to finance all of society's circulating capital out of savings. It would put inordinate demand on savings that simply could not be met. Consider a hypothetical product called "miltonic". It is in urgent demand as a medicine that helps preventing cancer. Its production cycle takes 91 days, with as many as 90 firms participating, so that the sojourn of the semi-finished product at every one of the 90 stops takes one day. The ultimate consumer is willing to pay $100 for a bottle while the producer of the 90th order good has paid $11 for raw materials. We shall also assume that the value added to the maturing product at every stop is $1. Now if you want to finance the movement of one bottle of miltonic through the various stages of production, then the pool of circulating gold coins will have to be invaded 90 times, and you have to withdraw savings in the amount of

11 + 12 + 13 + ... + 98 + 99 + 100 = ½(11 + 100)x90 = 45x111

or $4995, almost 50 times retail value. In other words, there must be savings in existence in the amount of almost $5000 to move just one bottle of miltonic through the production process all the way to the consumer. This sum does not include fixed capital that also has to be financed out of savings! And what about other items of food, fuel, and clothes, also urgently demanded by the consumer? Let me suggest it to you that no conceivable economy can generate savings so prodigiously as to move all the indispensable items to the consumer. I conclude that the division of labor could have never been refined, and the "roundaboutness" of the production process could have never been lengthened, beyond the level reached by the cottage industries of the medieval manors, wherein every family had to produce not only its own food and fuel, but also its clothes and shelter.

If it did not happen that way, and production has become vastly more efficient, was in large part due to the invention of the bill of exchange, heralding the end of the Middle Ages. Clearing has been put to work making it entirely unnecessary to invade the pool of circulating gold coins and divert savings, to finance the movement of consumer goods through an ever more refined and roundabout process, provided only that those goods be demanded by the consumer urgently enough.

Detractors of the RBD, above all Nobel prize laurate Milton Friedman, put his foot into his mouth when he ridiculed the idea of bill circulation suggesting that it was inflationary. It is hard to see how thoughtful people can treat the notion, that circulating capital no less than fixed capital must be financed out of savings, with respect.

Rate of interest versus discount rate

Although Mises was fully cognizant with the bill of exchange, he failed to come to grips with the idea that there was no credit expansion involved in its spontaneous circulation. Bills emerged together with the emergence of marketable merchandise, and were extinguished when the latter was removed from the market by the consumer. At no point did the bill increase the amount of purchasing media relative to the available supply of merchandise. The bill is an instrument of clearing or, if you will, self-liquidating credit. It is one of the marvelous creations of the human genius, fully commensurate in importance with the evolution of indirect exchange, arising spontaneously and opening up new avenues to human progress. Unfortunately, Mises was not interested in the concepts of clearing and self-liquidating credit. He dismissed them as paraphernalia belonging to credit expansion. In this way Mises missed his chance to make his theory of money and credit withstand the ravages of times.

His error of omission led to several errors of commission, the most conspicuous of which was his assumption that the discount rate at which maturing commercial paper changed hands was simply a subset of the rate of interest, in particular, the rate on short-term borrowing. This was a most serious error indeed, as the rate of interest and the discount rate were governed by entirely different, sometimes diametrically opposing, economic forces. They could move independently of one another, frequently in opposite directions, subject to the only constraint that the rate of interest can never be lower than the discount rate. If it were, the propensity to save would outstrip the propensity to consume. But saving becomes pointless if human life cannot be sustained for lack of spending on the wherewithal of life. If you save too much, then you die of starvation. No one ever has done so, rumors notwithstanding. The anecdotal miser is just that, anecdotal. This also explains why the rate of interest cannot go to zero. However, the discount rate may, whenever consumer confidence becomes most exuberant making shop-windows spill over their contents to the curbside.

To recapitulate: the rate of interest is governed by the propensity to save and, by contrast, the discount rate is governed by the propensity to consume. In either case the rate changes inversely with the propensity. For example, the higher the propensity to save, the lower is the rate of interest; the lower the propensity to consume, the higher is the discount rate. That the two propensities are not rigidly linked is due to the existence of a cushion, the propensity to hoard.

Irredeemable currency: present good or future good?

But Mises spurned the idea that there was a theory of an independent discount rate. In consequence his theory of interest is flawed. This fact cannot be swept under the rug, as it has led to further curious errors and contradictions. For example, Mises concluded that fiduciary money, i.e., money originating in the credit expansion of banks, was a present good on exactly the same terms as was the gold coin, and not a future good as was the bill of exchange. In his eyes even irredeemable currency was a present good, in spite of the fact that it could be created at the pleasure of the government ad libitum. Elsewhere Mises rightly ridicules irredeemable currency by saying that only the government is capable of the feat of taking two perfectly useful goods, such as paper and ink, and make the former perfectly worthless by sprinkling some of the latter on it. But if we declare irredeemable currency a present good, then we credit the government with power to create wealth out of nothing, a notion antithetical to Mises' opus.

Had Mises admitted that a discount rate existed independently of the rate of interest, then he could have avoided such contradictions. Fiduciary money and irredeemable currency belong to the species of a promissory note and as such are not a present good but a future good. Even a gold certificate is a future good: "there's many a slip between cup'n lip". Only a gold coin qualifies as a present good among the multifarious forms of purchasing media. This makes the gold coin sui generis, one of a kind, in the context of the theory of interest. In fact, a theory of interest without gold is "Hamlet without the prince". The interest rate on a loan repayable in irredeemable currency can never be the benchmark on which to build a theory of interest, no matter how many armored divisions the government foisting off currency on the world may have at its disposal. Debt repayable in irredeemable currency is nothing but an interest-bearing promise to pay that is exchangeable at maturity for a non-interest-bearing one. Bonds at maturity are exchanged but for an inferior instrument, insofar as interest-paying debt is considered preferable to non-interest-paying debt. The time-preference theory of interest is vacuous unless it explicitly stipulates that interest and principal be payable in gold coin. Without this provision prestidigitation is involved: future goods are juggled to make the impression that debt is being retired through the surrender of a present good.

But debt can never be retired under the regime of irredeemable currency. At maturity it is shifted from one debtor to another. People are constructing a Debt Tower of Babel destined to topple in the fullness of times.

The Lady of Threadneedle Street

It is commonplace to badmouth the Bank of England for her role in the corruption of the gold standard of Sir Isaac Newton, the Master of the Royal Mint from 1699 to his death in 1727. But whatever one can say of the low circumstances of her birth in 1696, and of her most recent role as the "Bag Lady of Threadneedle Street" in selling her gold reserve to the drumbeat from the paper mill on the Potomac, we must give the Bank of England credit for financing Pax Britannica for a period of one hundred years between the close of the Napoleonic Wars and the outbreak of World War I. Authors often wondered how the Bank of England could run the international gold standard on a shoestring of a gold reserve.

The mystery readily finds its solution if we contemplate that the Bank of England acted as the clearing house for real bills financing world trade between 1815 and 1914. This was history's most successful episode demonstrating the power and the potential of the RBD. By 1913 world trade in consumer goods had reached a high mark that was not surpassed until the 1990's. In whichever countries they were domiciled, the exporter billed the importer and the terms of the bill "91 days net payable in London" were standard. The importer endorsed the bill, attached shipping and insurance documents, and sent it back to the exporter. Thereafter the bill circulated world-wide in lieu of gold till it matured. Hardly ever did a default occur, and even then it was in consequence of violations of bill trading rules. Gold was shipped only to the extent of the difference between imports and exports. The modest size of the gold reserve of the Bank of England was no fetter on a most prodigious increase in world trade, a monument to the triumph of clearing. Goods in bottoms did not have to sail anywhere near England to be eligible for financing through bills drawn on London.

It is incumbent on the detractors of the RBD to explain how the phenomenal increase of world trade in consumer goods, on which the remarkable prosperity of the world before World War I depended, was possible with only a negligible amount of gold changing hands.

The permanent crisis of the world's monetary system

The outbreak of World War in 1914 put an end to international bill circulation and wiped out world trade in consumer goods almost entirely. When the war ended, the garrison states that emerged did not allow real bill trading to recover. Bill trading assumes that the gold is outside of the banks, in the hands of the people. Strategic imperatives called for the concentration of monetary gold in bank vaults. People had to be weaned from the gold coin. Nor was the reintroduction of real bill trading considered an option at the Bretton Woods conference in 1944 that was charged with the task to regenerate the world economy and trade after the ordeal of World War II. The world is still doing without the benefits of real bills. Trade has been placed under the direct control of governments. Political, not economic considerations govern the flow of consumer goods across international boundaries. Government regimentation of the lives of the people has become virtually complete.

The expulsion of real bills and the failure of world trade to recover after World War I, together with the advent of "cash and carry" mentality, was one of the main causes of the failure of the international gold standard and the Great Depression about a dozen years after the cessation of hostilities. A strong case could be made that if bill circulation had been allowed to return, then world trade would have quickly recovered, too, and the international gold standard would not have collapsed. Collapse it did because, without the clearing mechanism provided by real bills, it could not cope with world trade, much reduced though it was. People were talking about an "acute shortage of monetary gold". Money doctors rose with a phony diagnosis that the malady was due to the increase in the price level that was not accompanied by a commensurate increase in gold reserves. This diagnosis holds no water. It is based on the Quantity Theory of Money, a flawed theory that is applicable only in a world where all changes are in a linear relationship with their causes. In reality, however, changes in our world are a non-linear function of causes. There is no way of telling how much trade a given amount of monetary gold can support at any given price level. The volume of trade depends, not on the stock of monetary gold, but on the clearing system which can be improved to meet the challenge. Instead of improving it, governments conspired to sabotage the clearing system by blocking international trade in real bills that had worked so efficiently before the war. The proper prescription should have been the restoration of the clearing mechanism through real bills. Please remember that you have seen it here first: the main cause of the Great Depression of the 1930's was government sabotage of the Real Bills Doctrine of Adam Smith. The world's monetary and payments system is still limping from crisis to crisis, and will continue doing so until the RBD is fully rehabilitated.

The pipedream of the 100 percent gold standard

Some detractors of the RBD advocate what they call the "100 percent gold standard" in which they leave no room for real bill circulation. They maintain that real bills must be superseded by loans financed out of savings.

This is a momentous issue that must be addressed adroitly and fairly by all protagonists of sound money. We must put aside prestige, rancor, and personal ambitions in order to bring about a consensus concerning the shape of the gold standard that we all hope will arise from the ashes of the regime of irredeemable currency. We must all cooperate that the new gold standard will not only survive but flourish as well.

The first thing to be observed about the "100 percent gold standard" is that nothing approximating it has ever been tested in practice. All historical metallic monetary standards had a supporting clearing system, more or less developed, which limited the actual payment in the monetary metal to net trade, that is, the difference between the value of total purchases and that of total sales. It follows from my analysis above that a "100 percent gold standard" will not be able to survive for reasons having to do with the burden it unnecessarily puts on savings. There isn't, nor will ever be, savings in sufficient quantity to finance circulating capital in full, given our highly refined division of labor and roundabout processes of production. Luckily, this is no problem, as so much circulating capital to move merchandise in sufficiently high demand by the final consumer can be financed through self-liquidating credit. Advocates of the "100 percent gold standard" must realize that they have grossly underestimated the degree of sophistication of the structure of production in the modern economy. They must also come to grips with the fact that financing circulating capital with real bills is not inflationary. Real bills enter and exit circulation pari passu with the emergence and ultimate sale of consumer goods.

Only if we approach our differences with sufficient humility can we prevail against the evil forces opposing freedom armed, as they are, with the formidable weapon of irredeemable currency. Given the stakes, I am convinced that Ludwig von Mises would, if he were alive today, put pride aside and admit that his 1912 judgment in dismissing the discount rate as an independent variable, distinct from the rate of interest, was a mistake.

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Further reading

In addition to Adam Smith's The Wealth of Nations I recommend my Adam Smith's Real Bills Doctrine that was published on the internet as Monetary Economics 101 in the Gold Standard University series in 2002, see the website


The Mises Institute's broadside on Nelson Hultberg and myself, see Real Bills, Phony Wealth by Robert Blumen calling us "monetary cranks" fails to meet the standards of polite academic debate. Our sin: we had the temerity to suggest that a proper monetary system for the United States should incorporate not only a gold standard but also a clearing system based on Adam Smith's Real Bills Doctrine (see: Breaking the Demopublican Monopoly by Nelson Hultberg, published by Americans for a Free Republic, P.O.Box 801212, Dallas, TX 75380,

The present paper was written as a rejoinder, explaining why a "100 percent gold standard" was a pipedream, and that it was not good enough to put gold coins into circulation (which would promptly go into hiding). One would also have to make provisions for a clearing system, without which the gold standard could not function in a complex economy.

Unfortunately Lew Rockwell and Jeffrey Tucker at the Mises Institute have refused to post my rejoinder, letting the attack on my theoretical work go unchallenged making it appear that no reasonable answer to the detractors of the Real Bills Doctrine is possible. To say the least, this is a most peculiar procedure for an institute that pretends to support the search for and dissemination of truth.

It is difficult if not impossible to enter into a debate on the Real Bills Doctrine with people who are not conversant with the modern literature on clearing and self-liquidating credit. I just mention the names of a few 20th-century authors who have written on the subject: Charles Rist, Melchior Palyi, Benjamin M. Anderson, Heinrich Rittershousen, Ulrich von Beckerath, Henry Meulen; the complete list is too long for inclusion here.

In the 1930's University of Chicago economist Lloyd Mints wrote a book on real bills in which he reviewed the literature on the subject written in English only. This is not unlike writing a medical treatise on tuberculosis reviewing the contributions of English researchers only. If you cast your net so narrow, then you miss the German bacteriologist Robert Koch, the discoverer of what has come to be known the Koch bacillus which today is recognized as the cause.of tuberculosis. It may be of interest to note that for a number of years Koch was ridiculed for suggesting a single cause for "consumption", the earlier name for this devastating disease.

Latter-day detractors of the RBD have obviously missed the contribution of Ritterhousen who in 1934 published a paper Zahlungsverkehr, Einkaufsschaffung und Arbeitsbeschaffung in the journal Annalen der Gemeinwirtschaft. In it he makes a defense of the "Banking School"and the Real Bills Doctrine against the inflationists, deflationists, and adherents of the "Currency School". He also discusses how the first departure in 1909 from the RBD by Germany was later imitated verbatim by other countries, which was the major cause of unemployment world-wide in the 1930's. It is not fashionable nowadays to read papers that have been written and passed by the Nazi censorship during the Third Reich. Yet you may ignore them at your own peril. Economist and monetary scientist Rittershousen survived the Nazi witch-hunt by a fluke. He continued to teach after the war until his retirement as Dean at the University of Këln in 1966.

For all open-minded Americans my rejoinder will demonstrate why Murray Rothbard and the Misesians are mistaken in their denigration of the Real Bills Doctrine and the Banking School, and why their uncritical embracing of the never-ever-tried idea of the so-called "100 percent gold standard" would impart a congenital disease to the new metallic monetary standard after the collapse of the regime of irredeemable currency. In fact I would go so far as to suggest that no greater favor to the enemies of freedom in America could be done than pursuing the present policy of the Mises Institute. The enemies of freedom, the managers of the unconstitutional irredeemable dollar, are rubbing their hands in joy while getting ready to shout from the rooftop that "we have told you so". They understand what the Misesians do not: the "100 percent gold standard" is doomed to failure. If implemented, it would cause depression, bankruptcies, and unemployment. The Great Depression of the 1930's would be repeated, which was due, not to fractional reserve banking, but to government sabotage of the market's clearing system, the international real bill market.

The "100 percent gold standard" is but a blueprint to discredit the gold standard 100 percent.


Author: Antal E. Fekete

Antal E. Fekete
Professor, Intermountain Institute of Science and Applied Mathematics, Missoula, MT 59806, U.S.A.

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