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"# Lecture Notes: Introduction to Economic History: Understanding the Ancient Economy \n",
"## 1: The Biggest-Picture Perspective \n",
"### 1.1: The Old and Middle Stone Ages \n",
"\n",
"70,000 years ago, back in the old stone age, there were perhaps 100,000 of *us*—100,000 east African plains apes who looked like us, moved like us, acted like us, talked like us, and from whom the overwhelming proportion of all of our heredity is derived. Yes, we have small admixtures (5%?) from other groups and subspecies and may be even species, but overwhelmingly we are those proto-hundred-thousand's children, and we are all all of their children: it is overwhelmingly likely that each of those who still has living descendants today has a place—has an astronomical number of places—on our family tree.\n",
"\n",
"Back then we were very smart herd animals. We gathered, we hunted (some), we protected ourselves, we made stone and wood tools, we understood our environment, we manipulated our environment, we communicated with each other, we cooperated and we fought, we talked, and we did the things that humans. Our standard of living? If we had to slot it into emerging-markets standards of living in the world today, we might call it 3.25 dollars a day. Poverty, but not what the United Nations calls extreme poverty: natural resources were not scarce, our knowledge of our east African environment was profound, and we probably had to spend a little more than one-third of our waking hours collecting 2000 calories plus essential nutrients each day, plus enough shelter and fire and clothing that we were not unduly wet or cold. We were buff: life was strenuous. We were shortlived: a life expectancy at birth of perhaps 25-30, for hauling around a family in our then-seminomadic lifestyle was dangerous: life was strenuous.\n",
"\n",
">###### References: \n",
">###### Slides: \n",
"\n",
" "
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"### 1.2: An Index of Human Technological and Organizational Capabilities \n",
"There are things that are objective and can be measured: five bushels of properly-threshed barley kernels, or three gallons of water. There are things that are subjective that can nevertheless be accurately measured in an objective form: the feeling of heat, for example: this northern California hot tub here in the fog feels hot, and, indeed, is at a temperature of 105F: its molecules have thermal kinetic energy above that of absolute zero by 565/180 times the difference in thermal kinetic energy between water on the edge of boiling and water on the edge of freezing. There are things that are subjective that cannot be measured: anger, rage, and sorrow. Economists start with objetively measured prices and quantities of goods and services exchanged in markets, and then go on to construct quantitative measures of subjective things like willingnesses-to-pay and willingnesses-to-substitute and values and so forth. Mid-twentieth century British economist John Maynard Keynes warned us against carrying this too far:\n",
"\n",
">Approximate statistical comparisons depending on some broad element of judgment rather than of strict calculation… may possess significance and validity within certain limits. But the proper place for such things... lies within the field of historical and statistical description, and their purpose should be to satisfy historical or social curiosity... of a similar character to the statement that Queen Victoria was a better queen but not a happier woman than Queen Elizabeth—a proposition not without meaning and not without interest, but unsuitable as material for the differential calculus. Our precision will be a mock precision if we try to use such partly vague and non-quantitative concepts as the basis of a quantitative analysis...\n",
"\n",
"Neverthless we do carry it far. For example, we have our estimates of how many people there were—100-thousand 70-thousand years ago, 3-million ten-thousand years ago—and we have our estimates of what their standard of living was on average—3.25 dollars per day. We can then make the truly heroic assumptions that underpin a more-or-less standard Solow-Malthus growth model like the one found here: . We can then construct a quantitative index $ H $ of the _value_ of the useful ideas about how to cooperate and manipulate the environment in order to provide one another with what we need, find convenient, and simply want. Set that index $ H_{-68000} $—the index of the level of human technological and organizational knowledge 70-thousand years ago, in 68-thousand BC by the common calendar—to 1. \n",
"\n",
"Flash-forward 60,000 years, to 10,000 years ago, on the very eve of the invention/discovery of agriculture and of animal domestication. Things were much the same, save that there were then not one-hundred thousand of us in East Africa but rather perhaps two-and-a-half million of us, well, pretty much everywhere. Our living standards were much the same as they had been. We had better tools, but they were of stone and wood, plus fur and fiber, and not yet metal: it was still the Middle Stone Age. Our knowledge of our environment—or rather environments—was more profound, and so was our power to manipulate them. But in each environment we lived in we found ourselves in rough ecological balance. As of 8000 BC the index $ H_{-8000} $ stands at 5. \n",
"\n",
" \n",
"\n",
"#### The Big Picture: Summary Table \n",
"\n",
"\n",
"\n",
">###### Source: \n",
"\n",
">###### References: \n",
"\n",
" "
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"### 1.3: The Neolithic Revolution, and After \n",
"\n",
"Then, at the end of the gatherer-hunter age, comes the upward leap (or was it an upward leap) of the neolithic—new stone¸—revolution: 2000 years after 8000 BC we are (poor) agriculturalists and (unsophisticated) herders of barely domesticated animals, with a human population of perhaps 7 million, but a lower living standard of perhaps 2.50 dollars a day, with an index $ H_{-6000} = 6.5 $. \n",
"\n",
"Why a near-tripling of population? Because living was easier when you were sedentary or semi-sedentary: you no longer had to carry babies substantial distances, and you could accumulate more useful stuff than you could personally carry. Plus even early agriculture and herding were very productive relative to what had come before. Since life was easier, more babies survived to grow up and themselves reproduce? \n",
"\n",
"Why a fall in the standard of living? Because population grew until humanity was once again in ecological balance, with population expanded to the environment's carrying capacity given technology and organization. But what keeps population from growing further? The fact that life has become harder again. But it became harder in a different way: agriculturalists are shorter—figure about three inches, 7.5 centimeters—malnourished, prone to endemic diseases, and vulnerable to plagues relative to gatherer-hunters. Biologically, it would seem much better to be a typical person in the gatherer-hunter than in the neolithic age: your life expectancy is no less, your daily life presents you with more interesting and less boring cognitive problems, and you are much more buff and swole.\n",
"\n",
"Jared Diamond believes—or at least whoever wrote the title of his article believes—that the invention of agriculture was, as the title says, a bad mistaker: humans would be better-off had we remained gatherer-hunters. \n",
"\n",
"Then comes further development of agriculture, craftwork, organization, literacy, civilization: by year 1 the index $ H_{1} = 31 $. By year 1500 we have $ H_{1500} = 53 $. By 1500 we have 500 million humans compared to the 7 million of 6000 BC. But typical standards of living seem much the same: still 2.5 dollars a day. This is a _Malthusian Equilibrium_: vast improvements in technological and organizational capabilities, from 6.5 to 53; but all of that improvement going to support a 70-fold increase in human population; and with only 1/70 the potential natural resources at their disposal, the typical peasant or craftsman in 1500 was able to use that technology to eak out roughly the same standard of living as their predecessors 7.5 millennia before.\n",
"\n",
"There is definitely a spurious precision here. And even if we could gain universal assent as to technological capability in, say, ceramics and each of the other aspects of human productivity and creativity, squashing multi-dimensional objects down into a single one-dimensional index simply cannot be done. All we can say is that _if_ there were an economy simple enough for such an index to be accurate, and _if_ its levels of productivity corresponded to those we assign to the real history, _then_ its index of human technological and organizational capabilities would be our H. Nevertheless, I find such a framework very useful as a metaphor in organizing my thoughts. \n",
"\n",
"Queen Victoria does not appear to have been a much better queen than Queen Elizabeth. But, from all historical accounts, Gloriana appears to have been perhaps four times as happy as happy a woman as the Widow of Windsor.\n",
"\n",
"And the statements that $ H_{-8000} = 5 $, $H_1 = 31$, and $H_{1500} = 53 $ do carry meaning: look at pottery in 8000 BC, in year 1, and in 1500:\n",
"\n",
" \n",
"\n",
"#### Technology in Ceramics, -8000 to 1500: Jomon, Roman, Ming \n",
"\n",
"\n",
"\n",
" \n",
"\n",
">(How certain are we of all this? For what we think we know—and how we think we know it—dive deeper into the _Malthusian Economy_: .)\n",
"\n",
">###### **Jared Diamond** (1987): _The Invention of Agriculture: The Worst Mistake In the History of the Human Race_ \n",
"\n",
" "
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"### 1.4: After the Ancient Economy: Speedup and Explosion \n",
"\n",
"Then comes a speedup: from 1500 to 1770 to 1870—over, first, the Commercial Revolution and, second, the Industrial Revolution eras—our quantitative index H grows from 53 to 79 to 125. This time there was some increase in typical standards of living: figure a world in 1870 with 3.5 dollars a day per person, albeit much more unevently distributed. But, still, the overwhelming bulk of improvements in human technology and organization went to supporting a larger population: the 500 million of 1500 had grown to 1.3 billion by 1800, as better living standards lowered death rates worldwide. (And you can dive deeper into the _Commercial Revolution_ <> and the _Industrial Revolution_ <>.)\n",
"\n",
"Then came the explosion: from 1870 to today, in our era of Modern Economic Growth, our H has risen from 125 to 2720. Our population has risen from 1.3 to 7.6 billion. And our resources from 3.5 to 32 dollars a day. (And you can dive deeper into _Modern Economic Growth_: <>.)\n",
"\n",
" \n",
"\n",
"### 1.5: Rates of Growth \n",
"\n",
"Over the Paleolithic Era of stone and the Mesolithic Era of stone plus some pottery and textiles from 70 to 10 thousand years ago, the rate at which the stock of useful ideas about technology and organization was growing was 0.0027% per year—and, with standards of living stagnant at an average of 3.5 dollars a day or so, the rate of growth of human populations was twice that: 0.0054% per year, or 0.135% per generation: a typical generation would see, an average, 1000 people turn into 1001 and a bit more. What if growth over the generations had been much faster? Then, given the—very slow, 0.0027% per year—rate of growth in useful ideas H, the population finds itself without sufficient resources too sustain itself and drops. What if growth over the generations had been much slower? The population would find itself better-nourished, with children's immune systems less compromised and women ovulating more regularly, and population growth would have accelerated. Malthusian equilibrium thus kept population growing along with useful ideas, and the rate of growth of useful ideas was very slow.\n",
"\n",
"The rate of growth of ideas jumped up, to 0.011% per year, during the 8000-6000 BC Neolithic Revolution: herding and agriculture were really good ideas. And progress continued at 0.013% per year from 6000-3000 BC. Agriculture, craftwork, organization, literacy, and more advance civilization: from 3000-1000 BC and 1000 BC-1 we see H rise at first 0.03% per year, and then 0.06% per year, with a year-1 human population of 170 million, at least half of which was collected in three great empires—Roman, Parthian, and Han—enforcing imperial peace and spanning Eurasia.\n",
"\n",
"Then from 1 to 1500 it looks like a definite not pause but slowdown in the progress of civilization and human knowledge: an ideas growth rate back to the 0.03% per year of 3000-1000 BC.\n",
"\n",
"And, last, comes the breakout:\n",
"\n",
"* a growth rate of useful ideas of 0.15% per year during the 1500-1770 Commercial Revolution.\n",
"* a growth rate of useful ideas of 0.44% per year during the 1770-1870 Industrial Revolution.\n",
"* a growth rate of useful ideas of 2.06% per year during the post-1870 Modern Economic Growth era.\n",
"* a population explosion, and then a slowdown toward zero population growth as prosperity brings female education, female education brings greater female autonomy, and literate women with rights to own property find that there are other ways to gain and maintain social power than to try as hard as possible to become the mohter of many sons and daughters.\n",
"\n",
"From this perspective, there are two big questions in post-Neolithic Revolution global economic history:\n",
"\n",
"1. Why was there and what determined the pace of the triple accelerations in growth to 0.15% and then 0.44% and now 2.06% per year?\n",
"2. Why was there and what determined the—much, much, much slower—pace of growth of 0.03% per year (with a 1000 BC-1 temporary jump up) from the invention of writing to 1500?\n",
"\n",
"Right now we are studying the ancient economy. The first of these questions is thus well outside our field of vision. But keep it in the back of your mind.\n",
"\n",
" \n",
"\n",
"----"
]
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"## 2: The Solow-Malthus Model \n",
"\n",
"### 2.1: The Basic Solow Setup \n",
"\n",
"Here, as always, we do what economists do: ruthlessly simplify. People control resources, and use this resources in ways that respond to incentives, and so the societal system moves forward. Economists write down very simple equations describing this: behavioral relationships (how people act), equilibrium conditions (what people's interactions entail), and identities (adding-up conditions. \n",
"From those they derive how the societal system _should_ have behaved or be behaving. It goes wrong. So economists then go back and complicate the model, and see what the complication entails. They then iterate, until they believe that they have gotten close enough to say that the final-stage model is a good-enough one. \n",
"\n",
"In economic growth, the basic setup model is the Solow Growth Model. It has total society income (and production) $ Y $ as a function of the capital stock $ K $, the labor force $ L $, the efficiency of labor $ E $, and a decreasing-returns parameter $ \\alpha $:\n",
"\n",
">(2.1) $ Y = K^{\\alpha}(EL)^{1-\\alpha} $ :: income and output\n",
"\n",
">(2.2) $ \\ln(Y) = \\alpha\\ln(K) + (1-\\alpha)\\left(\\ln(E)+\\ln(L)\\right) $ :: log form\n",
"\n",
"Growth rates of the capital stock, the labor force, the efficiency of labor, and of production as functions of the savings-investment rate $ s $, the population and labor force growth rate $ n $, the efficiency-of-labor growth rate $ g $, and the depreciation rate $ \\delta $:\n",
"\n",
">(2.3) $ \\frac{dK/dt}{K} = \\frac{d\\ln(K)}{dt} = g_k = \\frac{sY}{K} - \\delta $ :: the proportional rate of growth of the capital stock\n",
"\n",
">(2.4) $ \\frac{dL/dt}{L} = \\frac{d\\ln(L)}{dt} = n $ :: the proportional rate of growth of the labor force and population\n",
"\n",
">(2.5) $ \\frac{dE/dt}{E} = \\frac{d\\ln(E)}{dt} = g $ :: the proportional rate of growth of the efficiency of labor\n",
"\n",
">(2.6) $ \\frac{d\\ln(Y)}{dt} = g_{n+y} = \\alpha g_k + (1-\\alpha)n + (1-\\alpha)g $ :: the proportional rate of growth of total production\n",
"\n",
"And define the capital-output ratio:\n",
"\n",
">(2.7) $ \\kappa = \\frac{K}{Y} $\n",
"\n",
">(2.8) $ \\ln(\\kappa) = \\ln(K) - \\ln(Y) $\n",
"\n",
">(2.9) $ \\frac{d\\ln(\\kappa)}{dt} = g_\\kappa = g_k - g_y $ :: proportional growth rate of the capital-output ratio\n",
"\n",
" \n",
"\n",
"### 2.2 Determining the Equilibrium Capital-Output Ratio $ \\kappa^* $ \n",
"\n",
"Look for a situation in which $ g_\\kappa = 0 $: in which the capital stock $ K $ and production $ Y $ are growing at the same rate so that the capital-output ratio $ g_\\kappa $ is constant.\n",
"\n",
"Starting from (2.9) and substituting:\n",
"\n",
">(2.10) $ g_\\kappa = g_k - \\left( \\alpha g_k + (1-\\alpha)n + (1-\\alpha)g \\right) $\n",
"\n",
">(2.11) $ g_\\kappa = (1-\\alpha)\\left( \\frac{sY}{K} - \\delta - n - g \\right) $\n",
"\n",
">(2.12) $ \\kappa^* = \\frac{K}{Y} = \\frac{s}{n + g + \\delta} $ whenever $ g_\\kappa = 0 $\n",
"\n",
"We define $ \\kappa^* $ as the _steady-state growth equilibrium_ capital-output ratio:\n",
"\n",
" \n",
"\n",
"### 2.3: Determining Steady-State Growth-Path Production per Worker \n",
"\n",
"From (2.2) derive:\n",
"\n",
">(2.13) $ \\ln(Y) = \\alpha\\left(\\ln(\\kappa) + \\ln(Y) \\right) + (1-\\alpha)\\left(\\ln(E)+\\ln(L)\\right) $\n",
"\n",
">(2.14) $ \\ln \\left( \\frac{Y}{L} \\right) = \\left( \\frac{\\alpha}{1-\\alpha} \\right)\\ln(\\kappa) + \\ln(E) $\n",
"\n",
"These $ \\alpha/(1-\\alpha) $ terms are getting annoying:\n",
"\n",
">(2.15) $ \\theta = \\frac{\\alpha}{1-\\alpha} $\n",
"\n",
"And so we define steady-state growth-path production-per-worker as:\n",
"\n",
">(2.16) $ \\ln \\left( \\frac{Y}{L} \\right)^* = \\theta \\ln(\\kappa^*) =+ \\ln(E) $ \n",
"\n",
">(2.17) $ \\frac{d}{dt} \\left(\\frac{Y}{L}\\right)^* = g $\n",
"\n",
"Along the steady-state growth path, production per worker $ Y/L $, capital per worker $ K/L $, and the efficiency of labor $ E $ both grow at the proportional rate $ g $; the population and labor force $ L $ grows at the proportional rate $ n $; total production $ Y $ and the capital stock $ K $ grow at the proportional rate $ n + g $; and the capital-output ratio $ \\kappa = K/Y $ is constant.\n",
"\n",
"An economy well-modeled by this Solow Growth Model heads for a balanced-growth equilibrium path on which there is a constant balanced-growth capital-output ratio $ \\kappa^* = s/(n+g+\\delta) $, a constant growth rate $ g $ of income (and production) and the capital stock per worker, a constant growth rate $ n $ of the labor force, and a constant growth rate $ n + g $ of total societal income (and production) and of the total capital stock.\n",
"\n",
"But this is not the ancient economy. In the ancient economy $ g = 0 $, or is very close. The model is unsatisfactory in that it does not provide an explanation for why $ g $ is near zero. Hence we complicate the model by introducing _Malthusian_ elements.\n",
"\n",
" "
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"### 2.4: Malthus: Population, Resource Scarcity, and the Efficiency of Labor \n",
"\n",
"Now let's make efficiency of labor growth a function of the rate $ h $ at which economically useful ideas are generated, but also of the rate of population and labor force growth $ n $ because a higher population makes resources per capita scarce, as determined by an effect-of-resource scarcity parameter $ \\gamma $:\n",
"\n",
">(2.18) $ \\frac{dE/dt}{E} = \\frac{d\\ln(E)}{dt} = g = h - \\frac{n}{\\gamma} $\n",
"\n",
"Thus:\n",
"\n",
">(2.19) $ \\frac{d}{dt} \\left(\\frac{Y}{L}\\right)^* = 0 $ whenever $ h - \\frac{n}{\\gamma} = 0 $\n",
"\n",
">(2.20) $ n^{*mal} = \\gamma h $ \n",
"\n",
"is the population growth rate at which $ \\frac{d}{dt} \\left(\\frac{Y}{L}\\right)^* = 0 $\n",
"\n",
"When population is growing at the rate $ n^{*mal} $, the efficiency of labor—and thus the steady-state growth-path level of production per worker $ Y/L $—is constant.\n",
"\n",
" "
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"### 2.5: Determinants of Population and Labor Force Growth \n",
"\n",
"Now let's make the rate of growth of the population and labor force depend on the level of prosperity $ y = Y/L $; on the \"subsistence\" standard of living for necessities $y^{sub} $; and also on the fraction $ 1/\\phi $ of production that is devoted to necessities, not conveniences and luxuries, and thus enters into reproductive and survival fitness:\n",
"\n",
">(2.21) $ \\frac{dL/dt}{L} = \\frac{d\\ln(L)}{dt} = n = \\beta \\left( \\frac{y}{\\phi y^{sub}}-1 \\right) $\n",
"\n",
"Then for population to be growing at its Malthusian rate:\n",
"\n",
">(2.22) $ \\gamma h = \\beta \\left(\\frac{1}{\\phi}\\right) \\left( \\frac{y}{y^{sub}}- \\phi \\right) $\n",
"\n",
">(2.23) $ y^{*mal} = \\phi y^{sub} \\left( 1 + \\frac{ n^{*mal}}{\\beta}\\right) = \\phi y^{sub} \\left( 1 + \\frac{ \\gamma h}{\\beta}\\right) $\n",
"\n",
" \n",
"\n",
"### 2.6: The Full Equilibrium \n",
"\n",
"We can determine the log level $ E $ of the efficiency of labor:\n",
"\n",
">(2.24) $ \\ln(E) = \\ln(H) - \\frac{\\ln(L)}{\\gamma} $\n",
"\n",
"Then since:\n",
"\n",
">(2.25) $ y^{*mal} = \\left( \\frac{s}{\\gamma h +\\delta} \\right)^\\theta E $\n",
"\n",
">(2.26) $ \\ln(\\phi) + \\ln\\left( y^{sub} \\right) + \\ln\\left(1 + \\frac{\\gamma h}{\\beta} \\right) = \\theta \\ln(s) - \\theta \\ln(\\gamma h +\\delta) + \\ln(E) $\n",
"\n",
"The population and labor force in the full Malthusian equilibrium will be:\n",
"\n",
">(2.27) $ \\ln(L_t^{*mal}) = \\gamma \\left[ \\ln(H_t) - \\ln( y^{sub}) \\right] + \\gamma \\theta \\left( \\ln(s) - \\ln(\\delta) \\right) - \\gamma \\ln(\\phi) + \\left( - \\gamma \\theta \\ln(1 + \\gamma h/\\delta) -\\gamma ln\\left(1 + \\frac{\\gamma h}{\\beta} \\right) \\right) $"
]
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"Or:\n",
"\n",
">(2.28) $ L_t^{*mal} = \\left[ \\left( \\frac{H_t}{y^{sub}} \\right) \\left( \\frac{s}{\\delta} \\right)^\\theta \\left( \\frac{1}{\\phi} \\right) \\left[ \\frac{1}{(1+\\gamma h/\\delta)^\\theta} \\frac{1}{(1+\\gamma h/\\beta)} \\right] \\right]^\\gamma $ "
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" \n",
"\n",
"### 2.7: Interpretation and Analysis \n",
"\n",
"Thus to analyze the pre-industrial Malthusian economy, at least in its equilibrium configuration:\n",
"\n",
"* Start with the rate $ h $ at which new economically-useful ideas are being generated and with the responsiveness $ \\beta $ of population growth to increased prosperity.\n",
"\n",
"* From those derive the Malthusian rate of population growth: $ n^{*mal} = \\gamma h $\n",
"\n",
"* Then the Malthusian standard of living is: $ y^{*mal} = \\phi y^{sub} \\left( 1 + \\frac{ \\gamma h}{\\beta}\\right) $\n",
"\n",
"Thus at any date t, the Malthusian-equilibrium population is:\n",
"\n",
"1. the current level $ H_t $ of the valuable ideas stock divided by the (sociologically determined, by, for example western European delayed female marriage patterns, or lineage-family control of reproduction by clan heads) Malthusian-subsistence income level $ y^{sub} $ consistent with a stable population on average, times\n",
"\n",
"2. the ratio between the savings-investment rate $ s $ and the depreciation rate $ \\delta $, raised to the parameter $ \\theta $ which governs how much an increase in the capital-output ratio raises income—with a higher $ \\theta $ the rule of law, imperial peace, and a culture of thrift and invetment matter more, and can generate \"efflorescences\"—times\n",
"\n",
"3. one over the conveniences-and-luxuries parameter $ \\phi $—it drives a wedge between prosperity and subsistence as spending is diverted categories that do not affect reproduction, such as middle-class luxuries, upper-class luxuries, but also the \"luxury\" of having an upper class, and the additional conveniences of living in cities and having trade networks that can spread plagues—times\n",
"\n",
"4. two nuisance terms near zero, which depend on how much the level of population must fall below the true subsistence level at which population growth averages zero to generate the (small) average population growth rate that produces growing resource scarcity that offsets the (small) rate of growth of useful ideas. all this\n",
"\n",
"5. raised to the power $ \\gamma $ that describes how much more important ideas are than resources in generating human income and production.\n",
"\n",
"(1) is the level of the stock of _useful ideas_ relative to the requirements for subsistence. (2) depends on how the rule of law and the rewards to thrift and entrepeneurship drive savings and investment, and thus the divisio of labor. (3) depends on how society diverts itself from nutrition and related activities that aim at boosting reproductive fitness and, instead, devotes itself to conveniences and luxuries—including the \"luxury\" of having an upper class, and all the conveniences of urban life. (4) are constant, and are small. And (5) governs how productive potential is translated into resource scarcity-generating population under Malthusian conditions.\n",
"\n",
"And recall the full Malthusian equilibrium standard of living:\n",
"\n",
">(2.23) $ y^{*mal} = \\phi y^{sub} \\left( 1 + \\frac{ \\gamma h}{\\beta}\\right) $\n",
"\n",
"The level of income is:\n",
"\n",
"1. The luxuries-and-conveniences parameter $ \\phi $, times\n",
"2. The level of subsistence $ y^{sub} $, times\n",
"3. The (small and constant) nuisance parameter $ 1 + \\gamma h/\\beta $ needed to generate average population growth $ n^{*mal} = \\gamma h $.\n",
"\n",
" \n",
"\n",
"Production per worker and thus prosperity are thus primarily determined by (a) true subsistence, (b) the wedge between prosperity and reproductive fitness produced by spending on conveniences and luxuries that do not impact reproductive success, plus a minor contribution by (c) the wedge above subsistence needed to generate population growth consonant with the advance of knowledge and population pressure's generation of resource scarcity.\n",
"\n",
"With this model, we can investigate broader questions about the Malthusian Economy—or at least about the Malthusian model, with respect to its equilibrium:\n",
"\n",
"* How much does the system compromise productivity, both static and dynamic, to generate inequality?\n",
"* How would one rise in this world—or avoid losing status relative to your ancestors?\n",
"* How does the system react to shocks?:\n",
" * like a sudden major plague—like the Antonine plague of 165, the St. Cyprian plague of 249, or the Justinian plague of 542—that suddenly and discontinuously pushes population down sharply...\n",
" * like the rise of a civilization that carries with it norms of property and law and commerce, and thus a rise in the savings-investment rate $ s $...\n",
" * like the rise of an empire that both creates an imperial peace, and thus a rise in the savings-investment rate $ s $, and that also creates a rise in the taste for luxuries $ \\phi $ (and possibly reduces biological subsistence $ y^{sub} $...\n",
" * like the fall of an empire that destroys imperial peace, and thus a fall in the savings-investment rate $ s $, and in the taste for luxuries $ \\phi $ (and possibly reduces biological subsistence $ y^{sub} $ as looting barbarians stock the land...\n",
" * a shift in the rate of ideas growth...\n",
" * a shift in sociology that alters subsistence...\n",
"\n",
"The fall of an empire, for example, would see a sharp decline in the savings-investment share $ s $, as the imperial peace collapsed, a fall in the \"luxuries\" parameter $ \\phi $, as the taste for urbanization and the ability to maintain gross inequality declined, and possibly a rise in $ y^{sub} $, if barbarian invasions and wars significantly raised mortality from violent death.\n",
"\n",
"This model provides an adequate framework—or I at least, think it is an adequate framework—for thinking about the post-Neolithic Revolution pre-Industrial Revolution economy.\n",
"\n",
" "
]
},
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"cell_type": "markdown",
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"### 2.8: Model Simulation Experiments \n",
"\n",
"\n",
"And, with respect to its dynamics, in Python:\n",
"\n",
" delong_classes.malthusian\n",
" \n",
"at:\n",
"\n",
"> \n",
"\n",
" \n",
"we can examine how the simulated model behaves dynamically.\n",
"\n",
">###### A Solow Malthus Model for Ancient Economies will be maintained at: <>\n",
">###### Digression on Malthusian Convergence will be maintained at: \n",
"\n",
" \n",
"\n",
"----"
]
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"# DEFINING CLASS MALTHUSIAN\n",
"#\n",
"# kept in delong_classes\n",
"# \n",
"# in general use:\n",
"# import delong_classes\n",
"#\n",
"# m = delong_classes.malthusian\n",
"#\n",
"# .__init__ :: initialize\n",
"# .update :: calculate the next year's values\n",
"# .gen_seq :: return time series of selected variable\n",
"# .steady_state ::calculate the steady state\n",
"\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline \n",
"\n",
"import numpy as np\n",
"\n",
"class malthusian:\n",
" \n",
" \"\"\"\n",
" Implements the Malthusian Model with:\n",
" \n",
" 1. population growth \n",
" n = β*(y/(ϕ ysub)-1)\n",
" \n",
" 2. growth of efficiency-of-labor \n",
" g = h-n/γ\n",
" \"\"\"\n",
" def __init__(self,\n",
" L = 1, # initial labor force\n",
" E = 1/3, # initial efficiency of labor\n",
" K = 3.0, # initial capital stock\n",
" \n",
" # determinants of n (population growth):\n",
" β = 0.025, # responsiveness of population growth to increased prosperity.\n",
" ϕ = 1, # luxuries parameter\n",
" ysub = 1, # subsistence level\n",
" \n",
" # determinants of g(efficiency-of-labor growth):\n",
" h = 0, # rate at which useful ideas are generated\n",
" γ = 2.0, # effect-of-resource scarcity parameter \n",
" \n",
" s = 0.15, # savings-investment rate\n",
" α = 0.5, # orientation-of-growth-toward-capital parameter\n",
" δ = 0.05, # deprecation rate on capital parameter\n",
" ):\n",
" self.L, self.E, self.K, self.h, self.γ, self.s, self.α, self.δ = L, E, K, h, γ, s, α, δ \n",
" self.β, self.ϕ, self.ysub = β, ϕ, ysub\n",
" \n",
" # production (or output)\n",
" self.Y = self.K**self.α*(self.E*self.L)**(1-self.α) \n",
" self.y = self.Y/self.L\n",
" \n",
" # capital-output ratio \n",
" self.κ = self.K/self.Y \n",
" \n",
" # population growth \n",
" self.n = self.β*((self.y/(self.ϕ*self.ysub)) - 1)\n",
" \n",
" # growth rate of efficiency-of-labor\n",
" self.g = self.h-self.n/self.γ\n",
" \n",
" # store initial data\n",
" self.initdata = vars(self).copy()\n",
" \n",
" def update(self):\n",
" # unpack parameters\n",
" K, s, Y, δ, L, n, E, g, α =self.K, self.s, self.Y, self.δ, self.L, self.n, self.E, self.g, self.α\n",
" β, ϕ, ysub, h, γ = self.β, self.ϕ, self.ysub, self.h, self.γ\n",
" \n",
" #update variables \n",
" K = s*Y + (1-δ)*K\n",
" L = L*np.exp(n)\n",
" E = E*np.exp(g)\n",
" Y = K**α*(E*L)**(1-α)\n",
" y = Y/L\n",
" κ = K/Y\n",
" n = β*(y/(ϕ*ysub)-1)\n",
" g = h-n/γ\n",
" \n",
" #store variables\n",
" self.K, self.s, self.Y, self.δ, self.L, self.n, self.E, self.g, self.α = K, s, Y, δ, L, n, E, g, α\n",
" self.κ, self.y = κ, y\n",
" \n",
" def gen_seq(self, t, var = 'κ', init = True, log = False):\n",
" \"Generate and return time series of selected variable. Variable is κ by default.\"\n",
" \n",
" path = []\n",
" \n",
" # initialize data \n",
" if init == True:\n",
" for para in self.initdata:\n",
" setattr(self, para, self.initdata[para])\n",
"\n",
" for i in range(t):\n",
" path.append(vars(self)[var])\n",
" self.update()\n",
" \n",
" if log == False:\n",
" return path\n",
" else:\n",
" return np.log(np.asarray(path))\n",
"\n",
" def steady_state(self, disp = True):\n",
" \"Calculate variable values in the steady state\"\n",
" #unpack parameters\n",
" s, γ, h, δ, ϕ, ysub, β, α= self.s, self.γ, self.h, self.δ, self.ϕ, self.ysub, self.β, self.α\n",
" \n",
" self.mal_κ = s/(γ*h+δ)\n",
" # malthusian rate of population growth\n",
" self.mal_n = γ*h\n",
" # malthusian standard of living\n",
" self.mal_y = ϕ*(ysub+γ*h/β)\n",
" self.mal_E = self.mal_y*((γ*h+δ)/s)**(α/(1-α))\n",
" \n",
" if display == True:\n",
" return(f'steady-state capital-output ratio κ: {self.mal_κ:.2f}')\n",
" return(f'Malthusian rate of population growth n: {self.mal_n: .2f}')\n",
" return(f'Malthusian standard of living y: {self.mal_y:.2f}')\n",
" return(f'steady-state efficiency-of-labor E: {self.mal_E:.2f}') \n",
" else: \n",
" return(self.mal_κ,self.mal_n,self.mal_y,self.mal_E)"
]
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" \n",
"\n",
"----\n",
"\n",
"## 3: Using the Framework "
]
},
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"metadata": {},
"source": [
"### 3.1: Slow Growth of Technology "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 3.1.1: The Solow-Malthus Framework \n",
"\n",
"The Solow-Malthus model predicts that a pre-Commercial Revolution economy will have a slowly growing population and labor force at a rate:\n",
"\n",
">(3.1) $ n^{*mal} = \\gamma h $\n",
"\n",
"where $ h $ is the proportional growth rate of the stock of useful human ideas and $ \\gamma $ is the relative importance of technology and organization vis-a-vis resources in production. \n",
"\n",
"The Solow-Malthus model predicts that a pre-Commercial Revolution economy, on its Malthusian steady-state growth path, will have a living standard close to \"subsistence\" $ y^{sub} $ multiplied by a factor $ \\phi $ determined by the diversion of resources into \"luxuries\" that do not boost reproduction and survival: civilization, urbanization, and those luxuries-for-some that are inequality:\n",
"\n",
">(3.2) $ y^{*mal} = \\phi y^{sub} \\left( 1 + \\frac{ \\gamma h}{\\beta}\\right) $\n",
"\n",
"plus a small nuisance term $ \\gamma h/\\beta $ proportional to the Malthusian trend population growth rate.\n",
"\n",
"The Solow-Malthus model predicts that a pre-Commercial Revolution economy, on its Malthusian steady-state growth path, will have a population level determined by the balance between the stock of useful human ideas $ H $ and the requirements of a stable-population standard of living at sociological \"subsistence\" $ y^{sub} $\n",
"\n",
">(3.3) $ \\ln(L_t^{*mal}) = \\gamma \\left[ \\ln(H_t) - \\ln( y^{sub}) \\right] + \\gamma \\theta \\left( \\ln(s) - \\ln(\\delta) \\right) - \\gamma \\ln(\\phi) + \\left( - \\gamma \\theta \\ln(1 + \\gamma h/\\delta) -\\gamma ln\\left(1 + \\frac{\\gamma h}{\\beta} \\right) \\right) $\n",
"\n",
"with population being boosted by things—an imperial peace or a culture of thrift—that boost savings and investment, with population being reduced by a desire for \"luxuries\"—comforts, upper-class consumption, and urbanization—and by two small nuisance terms depending on depreciation and what the Malthusian trend is in population growth.\n",
"\n",
"This then gives us a framework within which we can discuss the slow growth of humanity's capabilities, \"efflorescences\" and dark ages—the rise and fall of empires and civilizations—and other topics.\n",
"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 3.1.2: Competing Theories \n",
"\n",
"Recall the relevant entries in our big-picture summary table: from the coming of literacy around 3000 BC up to 1500, the average proportional rate of growth of the stock of human ideas useful for technology and organization grew at an average rate of 0.039% per year—and that is 1% per 25-year generation:\n",
"\n",
" \n",
"\n",
"#### The Big Picture: Summary Table \n",
"\n",
"\n",
"\n",
">###### Source: \n",
"\n",
" "
]
},
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"That is, admittedly, better than the 0.4% per 25-year generation that came in the illiterate post-Mesolithic economy, and better than the 0.07% per 25-year generation that came in the pre-agricultural gatherer-hunter age. But we today get proportional growth in the useful-ideas stock 50 times as fast: what they got in a generation in the ancient economy, we get in six months in today's world.\n",
"\n",
"**3.1.2.1: The Two-Heads Theory**\n",
"**3.1.2.2: Culture Theory**\n",
"**3.1.2.3: Incentives Theory**\n",
"**3.1.2.4: Unlucky Theory**\n",
"\n",
"\n",
" "
]
},
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"source": [
"#### 3.1.2.1: The Two-Heads Theory \n",
"\n",
"One explanation is the two-heads-are-better-than-one explanation of thinkers like **Jared Diamond**: _Guns, Germs, and Steel: The Fates of Human Societies_ and **Michael Kremer**: _Population Growth and Technological Change: One Million B.C. to 1990_ . We have 50 times as many people alive today as were alive then, and we can and do communicate and broadcast ideas much faster and wider. With 50 times the brains thinking up useful ideas, and with a considerable amount of \"standing on the shoulders of giants\" in the idea-generation process, is it any surprise that technological and organizational progress today is 50 times as fast?\n",
"\n",
"Yet we do not appear to see economic growth pressures building up at an increasing pace in the post-literacy pre-commercial revolution years from 3000 BC to 1500. We see the proportional rate of growth of the worldwide useful-ideas stock bounce around at about 0.9% per 25-year generation for 4.5 millennia, with one excursion up to 1.5% per generation during the 1000 BC-1 \"classical\" age. It is only after 1500 and the coming of the Commercial Revolution era that, globally, two heads seem genuinely better than one over time, and the average pace of idea-stock growth accelerates to nearly 4% per generation, and then to 16% per generation, and now to 67% per generation.\n",
"\n",
"In addition to \"two-heads-are-better-than-one\" theories, there are \"culture\" theories and \"incentive\" theories—and they shade into one another. And there are also \"humanity-was-just-unlucky\" theories: that there were a number of times when we might have broken through to sustained commercial growth and then non-human power sources, automatic machinery, and true metallurgy—and thus attained an earlier and an alternative Industrial Revolution.\n",
"\n",
" "
]
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"Moses Finley wrote: **Moses Finley**: _Technical Progress and Economic Innovation in the Ancient World_ : \"It is a commonplace that the Greeks and Romans together added little to the world's store of technical knowledge and equipment. The Neolithic and Bronze Ages between them invented or discovered, and then developed, the essential processes of agriculture, metallurgy, pottery, and textile-making. With these the Greeks and Romans built a high civilization, full of power and intellect and beauty, but they transmitted to their successors few new inventions. The gear and the screw, the rotary mill and the water-mill, the direct screw- press, glass-blowing and concrete, hollow bronze-casting, the dioptra for surveying, the torsion catapult, the water-clock and water organ, automata (mechanical toys) driven by water and wind and steam-this short list is fairly exhaustive, and it adds up to not very much for a great civilization over fifteen hundred years...\n",
"\n",
">...Paradoxically, there was both more and less technical progress in the ancient world than the standard picture reveals. There was more, provided we avoid the mistake of hunting solely for great radical inventions and we also look at developments within the limits of the traditional techniques. There was less—far less—if we avoid the reverse mistake and look not merely for the appearance of an invention, but also for the extent of its employment.... Painted pottery is the best instance, one which takes on special significance from the fact that it is the only ancient industry whose history we can write (or will some day be able to write). The potter's wheel is a very ancient invention, and the Aegean world of the Bronze Age already knew all about the properties of clays, how to fashion a variety of pleasing shapes, how to colour and fire and produce a sheen. The heights to which the Greeks then carried this art is evident in museums all over the world. Yet these advances were all accomplished without any technical innovation, by greater mastery of the already known processes and materials, and, above all, by greater artistry. \n",
"\n",
">Then, in the course of the fourth century B.C., the taste for fine painted pottery disappeared, almost abruptly, and at once there was a sharp decline in quality. But people continued to need pots, and rich Greeks and Romans continued to demand better pots with some sort of decoration. Moulded decorations replaced painting and therefore a new technique was introduced in the industry, the only one in its history throughout classical antiquity. That is to say, the long-familiar technique of casting in a mould was adapted from metal to clay in order to produce commodities in the new style. Experts seem to be agreed that neither the speed nor the cost of production was significantly changed as a result. A new fashion was met by the transfer of an old technique. Fourth-century Greeks were not Neanderthal men and we need not hail this particular step as a brilliant accomplishment...\n",
"\n",
"It is not clear to me that Moses Finley's distinction between \"technical innovation\" and \"greater mastery... and... greater artistry\" can be maintained:\n",
"\n",
" \n",
"\n",
"#### Technology in Ceramics, -8000 to 1500: Jomon, Roman, Ming \n",
"\n",
"\n",
"\n",
" "
]
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{
"data": {
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991Gu2bqT8bExZmZn2bxxPRvOW3O830aSFqUuZwQXALuq6uGqeha4Cbj0sDGXAp/uP74FeEuSHM8i9uw7wDVbd/LMzCxPHzjIMzOzXL11pzMDSerrMgjWALsH2lP9vjnHVNVB4LvAysNfKMmVSXYk2TE9PX1MRUzt3c/42HN/zPGxMab27j+m15Gkk1WXQTDXX/b1AsZQVVuqarKqJlevXn1MRUysWMbM7Oxz+mZmZ5lYseyYXkeSTlZdBsEUcOZAewJ4bL4xSZYAPwR853gWsXL5UjZvXM9p42OcvnQJp42PsXnjelYuX3o830aSFq3ODhYDdwHrkpwNPApcBvz0YWO2Ae8Fvgq8E/j9qnrejOAHteG8NVx4ziqm9u5nYsUyQ0CSBnQWBFV1MMlVwG3AKcAnq+r+JB8BdlTVNuA3gd9KsoveTOCyrupZuXypASBJc+hyRkBVbQe2H9Z33cDjZ4B3dVmDJOnIPLNYkhpnEEhS4wwCSWqcQSBJjTMIJKlxBoEkNS4dnL/VqSTTwJ+8wKevAr59HMtZrFwPPa6HHtfD953M6+IVVTXnNXoWXRD8IJLsqKrJUdcxaq6HHtdDj+vh+1pdF+4akqTGGQSS1LjWgmDLqAs4QbgeelwPPa6H72tyXTR1jECS9HytzQgkSYcxCCSpcc0EQZKLkzyUZFeSa0ddz7AkOTPJ7UkeTHJ/kl/o9780yf9M8o3+9xWjrnUYkpyS5J4kn++3z05yZ389fDbJqaOusWtJzkhyS5L/298uXtfi9pDkH/d/J76e5MYkp7W4PUAjQZDkFOB64BLgXGBTknNHW9XQHAQ+VFU/BrwW+Pn+z34t8IWqWgd8od9uwS8ADw60Pwb8Sn897AWuGElVw/UfgP9RVX8FeDW99dHU9pBkDfABYLKqXkXv5lmX0eb20EYQABcAu6rq4ap6FrgJuHTENQ1FVT1eVX/Yf/w0vV/6NfR+/k/3h30a+InRVDg8SSaAvw18ot8O8Gbglv6Qk349JHkJ8EZ6dwekqp6tqidpcHugd2OuZf37pb8IeJzGtodDWgmCNcDugfZUv68pSdYC5wN3An+pqh6HXlgAPzy6yobm3wNXA7P99krgyao62G+3sF38CDANfKq/i+wTSV5MY9tDVT0K/BvgT+kFwHeBu2lvewDaCYLM0dfU52aTLAe2Av+oqp4adT3DluTHgSeq6u7B7jmGnuzbxRLgNcCvV9X5wJ9zku8Gmkv/GMilwNnAy4EX09t1fLiTfXsA2gmCKeDMgfYE8NiIahm6JOP0QuC/VtXn+t3fSvKy/vKXAU+Mqr4huRDYkOSb9HYNvpneDOGM/q4BaGO7mAKmqurOfvsWesHQ2vbwVuCRqpquqhngc8DraW97ANoJgruAdf1PBJxK76DQthHXNBT9/eC/CTxYVf9uYNE24L39x+8Fbh12bcNUVb9YVRNVtZbev//vV9V7gNuBd/aHtbAe/gzYneSV/a63AA/Q2PZAb5fQa5O8qP87cmg9NLU9HNLMmcVJ3k7vL8BTgE9W1b8ecUlDkeQNwJeBr/H9feP/jN5xgpuBs+j9Uryrqr4zkiKHLMlFwD+pqh9P8iP0ZggvBe4BLq+qA6Osr2tJzqN3wPxU4GHgffT+KGxqe0jyS8C76X2y7h7g/fSOCTS1PUBDQSBJmlsru4YkSfMwCCSpcQaBJDXOIJCkxhkEktQ4g0CSGmcQSFLjDAJpgZKs7V/D/9NJdvav6f+iJG/pX8Dta0k+mWRpf/w3k3wsyf/pf50z6p9BmotBIB2bVwJbqmo98BTwQeAG4N1V9VfpXdTt7w+Mf6qqLgB+ld6Z7dIJxyCQjs3uqvpK//Fv07tGzSNV9Uf9vk/Tu97/ITcOfH/dcEqUjo1BIB2bY70mS83zWDphGATSsTkryaG/7DcB/wtYO7D//2eALw6Mf/fA968Op0Tp2Cw5+hBJAx4E3pvkN4Bv0LsH8h3A7/SvY38X8PGB8UuT3Envj65Nwy5WWgivPiotUP9Wn5/v3+x8IeO/Se/m6N/usCzpB+auIUlqnDMCSWqcMwJJapxBIEmNMwgkqXEGgSQ1ziCQpMb9f7rYhS0CZkQ/AAAAAElFTkSuQmCC\n",
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