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Re: Article : why debt growth must exceed interest payments
From the begining of Part-II of Hudson's paper
From Part - I
From the begining of Part-II of Hudson's paper
The past century’s economic schoolbooks have described a universe running down from entropy. Production is assumed to be plagued by diminishing returns, so that each additional unit of input produces less and less output. Even if technology were recognized to raise the productivity of labor, capital and land over time, neoclassical models hold that each additional unit of consumption or wealth yields diminishing psychological utility.[1] Not only will economies grow less rapidly, they will feel poorer.
Large parts of the population in many countries are indeed becoming poorer and forced into debt, but the pessimistic assumptions cited above make no reference to debt. Their seeming independence from finance – and from social policies to deal with debt problems and wealth distribution – is supposed to make economics scientific. And if the subject is to be a science, of course, it must adopt the scientific hallmark, mathematics. Unfortunately, the only way for economic models to produce a mathematically solvable equilibrium is to use physical production functions that slow down and psychological wealth-seeking utility functions that dissipate rather than become addictive. Economic technocrats thus are taught to use mathematics in a wrongheaded way at the outset, while ignoring the exponential mathematics of debt and the asset-price inflation it feeds.
This blind spot of “learned ignorance” has created economic devastation from Russia and Japan to third world debtor countries. Today’s academic curriculum teaches models that fail to recognize how the economy’s debt overhead mounts up to produce financial shocks. Also ignored is the degree to which wage-earners and industrial investors find a rising share of their incomes diverted to pay debt service. The way to get rich today is not by earning wages and profits, but to benefit passively from the inflation of real estate and other asset prices as interest is credited and other new savings are recycled into mortgage and stock market loans. But even if economic theory recognized these dynamics, the national income and product accounts (NIPA) do not include capital gains, so there is no clear basis for giving a quantitative sense of proportion to the financial, insurance and real estate (FIRE) sector vis-à-vis the rest of the economy.
The neglect of debt is curious, for the subject was placed at the center of economic and indeed, religious policy for most of civilization’s past four thousand years. The mercantile debts and rural usury of Bronze Age Babylonia and classical Greece and Rome saw the accrual of interest double and redouble the sums due, leading to expropriation of indebted families and forcing them into bondage. From feudal Europe’s papal bankers to the emergence of large-scale Dutch, English and French finance capital, the expansion path of public as well as private debts has soared off the charts toward infinity. Money is saved and reinvested to grow without end, regardless of the economy’s ability to pay. Yet the mathematics describing the growth of interest-bearing debt on an economy-wide basis are missing from today’s macroeconomic policy models.
What the Babylonians recognized that modern economists don’t
Mathematics played a major role in training the scribes of Sumer and Babylonia. Most of them were employed in palace and temple bookkeeping, so their schoolbook exercises included manpower allocation problems such as calculations of how many men were needed to produce a given amount of bricks or dig canals of a given size, the expected growth of herds and the doubling times of investments lent out at interest.[2] Surprising as it may seem to modern readers, this mathematical training four thousand years ago was more relevant for dealing with society’s debt overhead than is that given to economics graduates today, for it dealt with exponential functions (as well as astronomical computations and even quadratic equations).
When U.S. bank lending rates peaked at 20 percent in 1980, they reached what had been the normal commercial interest rate from Sumer c. 2500 BC through the Neo-Babylonian epoch in the first millennium. In fact, when Alexander the Great conquered the Near East in 331 BC, the rate had remained remarkably stable at the equivalent of 20 percent for more than two thousand years. It had not been set with any particular reference to profit levels or the ability to pay, but was a matter of mathematical convenience, reflecting the Mesopotamian way of computing fractions by division into 60ths. A bushel of barley was divided into 60 “quarts,” and a mina-weight was composed of 60 shekels. Paying interest at the rate of 1/60th each month added up to 12/60ths per year, or 20 percent in modern decimal notation. A mina lent out at this rate would produce 60 shekels in five years, doubling the original principal.
A model Babylonian scribal exercise from around 2000 BC appears in the Berlin cuneiform text (VAT 8528). It asks the student to calculate how long it will take for a mina of silver to double at the normal rate of one shekel per mina per month. The answer is five years at simple interest. And in fact, the common practice was to lend long-distance traders money for this five-year period. Assyrian trade contracts c. 1900 BC, for instance, typically called for investors to advance 2 minas of gold, getting back 4 in five years. Elsewhere in Mesopotamia commercial contracts normally were denominated in silver, but the interest rate was the same.
This idea that doubling times were determined by the rate of interest was well enough understood to be given a popular imagery. “If wealth is placed where it bears interest, it comes back to you redoubled,”[3] an Egyptian proverb observes. Another compares making a loan to having a baby, viewing the reproduction of numbers in sexual terms. The word for “interest” in every ancient language meant a newborn, either a goat-kind (mash) in Sumerian and the Akkadian language used by the Babylonians, or a young calf – tokos in Greek or foenus in Latin. The “kid” or “calf” was born of silver or gold, not by borrowed cattle as some economists once believed, missing the metaphor at work. What was born was the “baby” fraction of the principal, 1/60th. And only when these accruals of interest had grown to be as large as their parent, after the fifth year, were they deemed “adult” enough begin having new interest “babies” on their own, for everyone knows that only adults can reproduce themselves. Thus, compounding began only after the principal had reproduced itself by the time 60 months had passed. Investors who wanted to keep their loans growing had to draw up new loan contracts.
How long could the process go on at these rates? A relevant scribal problem (VAT 8525) asks how long it will take for one mina to become 64, that is, 26. The solution involves calculating powers of 2 (22 = 4, 23 = 8 and so forth).[4] A mina multiplies fourfold in 10 years, eightfold in 15 years, sixteenfold in 20 years, and 64 times in 30 years, that is, six times the basic five‑year doubling period, expressed in modern notation as 26.
Traders and merchants were able to pay such rates out of their business gains, but serious problems occurred in the agricultural sphere, especially when crops failed or military hostilities interrupted the harvest. Matters were aggravated by the fact that interest rates were higher and more extortionate in the rural sector. The most typical rate was 33 1/3 percent, evidently reflecting the normal sharecropping rate of a third of the crop. Rates of 50 or even 100 percent might be charged, often for only short periods of time. Creditors (mainly palace collectors or other officials) demanded whatever they could get when they found cultivators in distress conditions. Sharecroppers or other individuals who were unable to break even or pay their stipulated rents or fees to the palace were forced to borrow out of need found that once they ran into debt, it was difficult to extricate themselves. The problem was that rural loans were made to pay taxes or get by hard times, not to acquire property or finance investment. Thus, instead of financing the acquisition of property, rural usury led to its forfeiture.
At the interest rate of 33 1/3 percent, Babylonian agricultural debts doubled in three years. Probably reflecting this fact, §117 of Hammurapi’s laws (c. 1750 BC) stipulates that after three years of service, by which time the creditor had received interest equal to the original debt, it should be deemed to have been paid and the bondservant liberated to rejoin the debtor’s family. The implication is that doubling the debt principal represented a moral and indeed, practical limit, largely because it was recognized how quickly debts grew to exceed the rural economy’s ability to pay. Indeed, at no time in history has output grown at sustained rates approaching the typical 33 1/3 percent rate of interest charged for agricultural loans, or even the commercial 20 percent rate. When the loan proceeds were used for consumption or to pay tax arrears, interest charges ate into the needy cultivator’s modest resources, obliging him to pay sums growing exponentially beyond his ability to produce. Under these conditions, creditors were enabled to draw into their own hands the debtor’s family members as bondservants, followed by the land and other assets. This threatened to polarize society self-destructively by expropriating the citizen-army that traditionally supported itself on the land.
.
.
.
.
.
Large parts of the population in many countries are indeed becoming poorer and forced into debt, but the pessimistic assumptions cited above make no reference to debt. Their seeming independence from finance – and from social policies to deal with debt problems and wealth distribution – is supposed to make economics scientific. And if the subject is to be a science, of course, it must adopt the scientific hallmark, mathematics. Unfortunately, the only way for economic models to produce a mathematically solvable equilibrium is to use physical production functions that slow down and psychological wealth-seeking utility functions that dissipate rather than become addictive. Economic technocrats thus are taught to use mathematics in a wrongheaded way at the outset, while ignoring the exponential mathematics of debt and the asset-price inflation it feeds.
This blind spot of “learned ignorance” has created economic devastation from Russia and Japan to third world debtor countries. Today’s academic curriculum teaches models that fail to recognize how the economy’s debt overhead mounts up to produce financial shocks. Also ignored is the degree to which wage-earners and industrial investors find a rising share of their incomes diverted to pay debt service. The way to get rich today is not by earning wages and profits, but to benefit passively from the inflation of real estate and other asset prices as interest is credited and other new savings are recycled into mortgage and stock market loans. But even if economic theory recognized these dynamics, the national income and product accounts (NIPA) do not include capital gains, so there is no clear basis for giving a quantitative sense of proportion to the financial, insurance and real estate (FIRE) sector vis-à-vis the rest of the economy.
The neglect of debt is curious, for the subject was placed at the center of economic and indeed, religious policy for most of civilization’s past four thousand years. The mercantile debts and rural usury of Bronze Age Babylonia and classical Greece and Rome saw the accrual of interest double and redouble the sums due, leading to expropriation of indebted families and forcing them into bondage. From feudal Europe’s papal bankers to the emergence of large-scale Dutch, English and French finance capital, the expansion path of public as well as private debts has soared off the charts toward infinity. Money is saved and reinvested to grow without end, regardless of the economy’s ability to pay. Yet the mathematics describing the growth of interest-bearing debt on an economy-wide basis are missing from today’s macroeconomic policy models.
What the Babylonians recognized that modern economists don’t
Mathematics played a major role in training the scribes of Sumer and Babylonia. Most of them were employed in palace and temple bookkeeping, so their schoolbook exercises included manpower allocation problems such as calculations of how many men were needed to produce a given amount of bricks or dig canals of a given size, the expected growth of herds and the doubling times of investments lent out at interest.[2] Surprising as it may seem to modern readers, this mathematical training four thousand years ago was more relevant for dealing with society’s debt overhead than is that given to economics graduates today, for it dealt with exponential functions (as well as astronomical computations and even quadratic equations).
When U.S. bank lending rates peaked at 20 percent in 1980, they reached what had been the normal commercial interest rate from Sumer c. 2500 BC through the Neo-Babylonian epoch in the first millennium. In fact, when Alexander the Great conquered the Near East in 331 BC, the rate had remained remarkably stable at the equivalent of 20 percent for more than two thousand years. It had not been set with any particular reference to profit levels or the ability to pay, but was a matter of mathematical convenience, reflecting the Mesopotamian way of computing fractions by division into 60ths. A bushel of barley was divided into 60 “quarts,” and a mina-weight was composed of 60 shekels. Paying interest at the rate of 1/60th each month added up to 12/60ths per year, or 20 percent in modern decimal notation. A mina lent out at this rate would produce 60 shekels in five years, doubling the original principal.
A model Babylonian scribal exercise from around 2000 BC appears in the Berlin cuneiform text (VAT 8528). It asks the student to calculate how long it will take for a mina of silver to double at the normal rate of one shekel per mina per month. The answer is five years at simple interest. And in fact, the common practice was to lend long-distance traders money for this five-year period. Assyrian trade contracts c. 1900 BC, for instance, typically called for investors to advance 2 minas of gold, getting back 4 in five years. Elsewhere in Mesopotamia commercial contracts normally were denominated in silver, but the interest rate was the same.
This idea that doubling times were determined by the rate of interest was well enough understood to be given a popular imagery. “If wealth is placed where it bears interest, it comes back to you redoubled,”[3] an Egyptian proverb observes. Another compares making a loan to having a baby, viewing the reproduction of numbers in sexual terms. The word for “interest” in every ancient language meant a newborn, either a goat-kind (mash) in Sumerian and the Akkadian language used by the Babylonians, or a young calf – tokos in Greek or foenus in Latin. The “kid” or “calf” was born of silver or gold, not by borrowed cattle as some economists once believed, missing the metaphor at work. What was born was the “baby” fraction of the principal, 1/60th. And only when these accruals of interest had grown to be as large as their parent, after the fifth year, were they deemed “adult” enough begin having new interest “babies” on their own, for everyone knows that only adults can reproduce themselves. Thus, compounding began only after the principal had reproduced itself by the time 60 months had passed. Investors who wanted to keep their loans growing had to draw up new loan contracts.
How long could the process go on at these rates? A relevant scribal problem (VAT 8525) asks how long it will take for one mina to become 64, that is, 26. The solution involves calculating powers of 2 (22 = 4, 23 = 8 and so forth).[4] A mina multiplies fourfold in 10 years, eightfold in 15 years, sixteenfold in 20 years, and 64 times in 30 years, that is, six times the basic five‑year doubling period, expressed in modern notation as 26.
Traders and merchants were able to pay such rates out of their business gains, but serious problems occurred in the agricultural sphere, especially when crops failed or military hostilities interrupted the harvest. Matters were aggravated by the fact that interest rates were higher and more extortionate in the rural sector. The most typical rate was 33 1/3 percent, evidently reflecting the normal sharecropping rate of a third of the crop. Rates of 50 or even 100 percent might be charged, often for only short periods of time. Creditors (mainly palace collectors or other officials) demanded whatever they could get when they found cultivators in distress conditions. Sharecroppers or other individuals who were unable to break even or pay their stipulated rents or fees to the palace were forced to borrow out of need found that once they ran into debt, it was difficult to extricate themselves. The problem was that rural loans were made to pay taxes or get by hard times, not to acquire property or finance investment. Thus, instead of financing the acquisition of property, rural usury led to its forfeiture.
At the interest rate of 33 1/3 percent, Babylonian agricultural debts doubled in three years. Probably reflecting this fact, §117 of Hammurapi’s laws (c. 1750 BC) stipulates that after three years of service, by which time the creditor had received interest equal to the original debt, it should be deemed to have been paid and the bondservant liberated to rejoin the debtor’s family. The implication is that doubling the debt principal represented a moral and indeed, practical limit, largely because it was recognized how quickly debts grew to exceed the rural economy’s ability to pay. Indeed, at no time in history has output grown at sustained rates approaching the typical 33 1/3 percent rate of interest charged for agricultural loans, or even the commercial 20 percent rate. When the loan proceeds were used for consumption or to pay tax arrears, interest charges ate into the needy cultivator’s modest resources, obliging him to pay sums growing exponentially beyond his ability to produce. Under these conditions, creditors were enabled to draw into their own hands the debtor’s family members as bondservants, followed by the land and other assets. This threatened to polarize society self-destructively by expropriating the citizen-army that traditionally supported itself on the land.
.
.
.
.
.
Today’s economists have a problem analyzing the relationship between the debt overhead and the capacity to pay. Academic orthodoxy holds that economies can adjust to any volume of debt, given sufficient price and income flexibility to facilitate the transfer of revenue and assets to creditors. What is not recognized is that the resulting economic polarization reduces the economy’s ability to function well. In addition to missing this negative feedback (the proverbial vicious circle), modern economists tend to overlook the fact that interest-bearing debt grows according to its own exponential laws of increase. The economy rarely can keep up.
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Ancient economic thought did not endorse the ideal of accumulating wealth and riches. Rather than praising ambition as the mainspring of progress, Mesopotamian religion condemned the amassing of property. Excess was held to be the primary cause of injustice, and it was characteristic above all of creditors abusing the weak and poor and foreclosing on their lands. It was to avenge the economic injustice done by the rich and strong against the weak that the Sumerian goddess Nanshe moved, as would the Greek goddess Nemesis in classical antiquity.
Nearly every ancient society recognized that physical consumption might bring satiety, but that financial riches and property did not. The biblical prophets described how the selfish principle of insatiability led to hubris, a form of wealth addiction whose exponential upsweep in greed was akin to the growth of money at compound interest. When Isaiah declaimed “Woe to you who add house to house and join field to field till no space is left and you live alone in the land,” he was condemning not only the greed of creditors but the inexorability of interest-bearing debt that gave them the power to amass property at the expense of the society around them
.
.
.
.
.
The hubristic spirit of evil was that of insatiability, a wealth addiction that led its prey to victimize the rest of society – what Martin Luther depicted the drive for usury as the all-consuming monster, Cacus. Today’s world seems to be embracing this spirit, viewing moderation as uneconomic behavior. In its place is being put a self-referential economics of moral obesity. Ivan Boesky is reported to have announced in 1986 to a seminar convened at Stanford University that “There is nothing wrong with greed.” If the fictional corporate raider Gordon Gekko elaborated this passage more overtly in the 1987 movie Wall Street – “Greed is good” – it was a theme that ancient Greek poets and dramatists dealt with as hubris, the drunken arrogance of wealth and power. The very word “greed” was coined to describe something sinful. It was a word of condemnation, not praise of the sort found in such recent texts as C. B. McConnell’s Economics (1984:16): “The principal task of the economy is to attain the maximum fulfillment of society’s unlimited material wants.”
Utilitarianism since Jeremy Bentham and Stanley Jevons has deemed satiety to be the guiding principle of human psychology. Schoolbook economic models assume that each added unit of consumption goods yields less and less pleasure (“utility”). This theory of diminishing marginal utility holds that people tend to reduce their economic drives as they grow richer. Instead of wanting to consume more and more, they save more of their income or simply choose leisure. Left out of account is the insatiable drive on which ancient societies placed such great emphasis – the drive to accumulate property, most typically through the dynamics of usury. Modern utilitarian theory views wealth is ultimately as something to be consumed, much like food or clothing – an amassing of the means of consumption rather than as the means of production or, ultimately, a social power relationship.
A repertory of mathematical economic functions, real and imaginary
Four types of mathematical curves describe how economies grow and, sometimes, collapse (Illustration 2).
Straight-line growth (y = bx) represents constant returns to scale, as in Mesopotamian exercises in calculating the amount of labor needed to perform everyday tasks, including the cultivation of land. It is short-term and microeconomic in that it relates to an economic context in which factor proportions and productivity remain unchanged.
An exponential curve (y = erx) describes growth with time x of a sum starting with a value of 1 at compound interest r. When plotted on log paper, this growth appears as a straight line. When the growth due to compound interest is modeled by y = erx, this describes the growth when accrued interest is added continually to the loan. But the typical way of compounding interest is to add accrued interest after a fixed interval, for example a year, as already discussed. Then the growth equation changes to y = (1+r)x. This is also exponential growth, just as dramatic as in the continuous case. In this case with discrete and equal time intervals, exponential growth is also called geometric growth. Rates of growth are often expressed in terms of doubling times. The doubling time is ln2 / ln(1+r). Here “ln” is the natural logarithm.
An S-curve describes most biological growth. It is characterized by an accelerating upswing that tapers off as it reaches an asymptotic limit. Economies tend to grow exponentially as they recover, as long as under-utilized capital or land is available to employ labor. The typical business cycle, for instance, tapers off as capacity and debt-servicing limits are reached. Business upswings are brought to an end suddenly, by financial tightness caused by over-borrowing, that is, over-indebtedness. Defaults occur, and a crash follows. The ensuing business downturn occurs much more quickly than the upswing.
The characteristic shape of most business “cycles” is thus scalloped and ratchet-like. An upsweeping log curve encounters financial constraints and collapses rapidly. Actually, this shape represents a combination of two curves intersecting. The upswing (y = a + bx + cx2) is intersected by the exponential growth in debt (y = x2). Something has to give at the point of intersection. A financial collapse ensues, often with political overtones and institutional changes.
Most economists seek to explain the economy in terms of a single curve. Joseph Schumpeter used a smooth sine curve (y = sine x) as an analogy to describe the business cycle. This is especially attractive to theorists who postulate automatic stabilizers, such as Wesley Clair Mitchell and the program of leading and lagging indicators he pioneered in America at the National Bureau of Economic Research. Yet this does not acknowledge the extent to which the world’s financial overhead has multiplied over the past century.
.
.
.
.
.
.
.
.
.
.
.
Ancient economic thought did not endorse the ideal of accumulating wealth and riches. Rather than praising ambition as the mainspring of progress, Mesopotamian religion condemned the amassing of property. Excess was held to be the primary cause of injustice, and it was characteristic above all of creditors abusing the weak and poor and foreclosing on their lands. It was to avenge the economic injustice done by the rich and strong against the weak that the Sumerian goddess Nanshe moved, as would the Greek goddess Nemesis in classical antiquity.
Nearly every ancient society recognized that physical consumption might bring satiety, but that financial riches and property did not. The biblical prophets described how the selfish principle of insatiability led to hubris, a form of wealth addiction whose exponential upsweep in greed was akin to the growth of money at compound interest. When Isaiah declaimed “Woe to you who add house to house and join field to field till no space is left and you live alone in the land,” he was condemning not only the greed of creditors but the inexorability of interest-bearing debt that gave them the power to amass property at the expense of the society around them
.
.
.
.
.
The hubristic spirit of evil was that of insatiability, a wealth addiction that led its prey to victimize the rest of society – what Martin Luther depicted the drive for usury as the all-consuming monster, Cacus. Today’s world seems to be embracing this spirit, viewing moderation as uneconomic behavior. In its place is being put a self-referential economics of moral obesity. Ivan Boesky is reported to have announced in 1986 to a seminar convened at Stanford University that “There is nothing wrong with greed.” If the fictional corporate raider Gordon Gekko elaborated this passage more overtly in the 1987 movie Wall Street – “Greed is good” – it was a theme that ancient Greek poets and dramatists dealt with as hubris, the drunken arrogance of wealth and power. The very word “greed” was coined to describe something sinful. It was a word of condemnation, not praise of the sort found in such recent texts as C. B. McConnell’s Economics (1984:16): “The principal task of the economy is to attain the maximum fulfillment of society’s unlimited material wants.”
Utilitarianism since Jeremy Bentham and Stanley Jevons has deemed satiety to be the guiding principle of human psychology. Schoolbook economic models assume that each added unit of consumption goods yields less and less pleasure (“utility”). This theory of diminishing marginal utility holds that people tend to reduce their economic drives as they grow richer. Instead of wanting to consume more and more, they save more of their income or simply choose leisure. Left out of account is the insatiable drive on which ancient societies placed such great emphasis – the drive to accumulate property, most typically through the dynamics of usury. Modern utilitarian theory views wealth is ultimately as something to be consumed, much like food or clothing – an amassing of the means of consumption rather than as the means of production or, ultimately, a social power relationship.
A repertory of mathematical economic functions, real and imaginary
Four types of mathematical curves describe how economies grow and, sometimes, collapse (Illustration 2).
Straight-line growth (y = bx) represents constant returns to scale, as in Mesopotamian exercises in calculating the amount of labor needed to perform everyday tasks, including the cultivation of land. It is short-term and microeconomic in that it relates to an economic context in which factor proportions and productivity remain unchanged.
An exponential curve (y = erx) describes growth with time x of a sum starting with a value of 1 at compound interest r. When plotted on log paper, this growth appears as a straight line. When the growth due to compound interest is modeled by y = erx, this describes the growth when accrued interest is added continually to the loan. But the typical way of compounding interest is to add accrued interest after a fixed interval, for example a year, as already discussed. Then the growth equation changes to y = (1+r)x. This is also exponential growth, just as dramatic as in the continuous case. In this case with discrete and equal time intervals, exponential growth is also called geometric growth. Rates of growth are often expressed in terms of doubling times. The doubling time is ln2 / ln(1+r). Here “ln” is the natural logarithm.
An S-curve describes most biological growth. It is characterized by an accelerating upswing that tapers off as it reaches an asymptotic limit. Economies tend to grow exponentially as they recover, as long as under-utilized capital or land is available to employ labor. The typical business cycle, for instance, tapers off as capacity and debt-servicing limits are reached. Business upswings are brought to an end suddenly, by financial tightness caused by over-borrowing, that is, over-indebtedness. Defaults occur, and a crash follows. The ensuing business downturn occurs much more quickly than the upswing.
The characteristic shape of most business “cycles” is thus scalloped and ratchet-like. An upsweeping log curve encounters financial constraints and collapses rapidly. Actually, this shape represents a combination of two curves intersecting. The upswing (y = a + bx + cx2) is intersected by the exponential growth in debt (y = x2). Something has to give at the point of intersection. A financial collapse ensues, often with political overtones and institutional changes.
Most economists seek to explain the economy in terms of a single curve. Joseph Schumpeter used a smooth sine curve (y = sine x) as an analogy to describe the business cycle. This is especially attractive to theorists who postulate automatic stabilizers, such as Wesley Clair Mitchell and the program of leading and lagging indicators he pioneered in America at the National Bureau of Economic Research. Yet this does not acknowledge the extent to which the world’s financial overhead has multiplied over the past century.
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.
.
.
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