No isoquant here, sorry baby

My editorial

I am changing the topic, slightly. In my last update I was discussing about the first takeaway from my research in 2017, namely about collective intelligence. This time, I switch to the second one: the mathematical construct of the type ‘Y = Kµ*L1-µ*A’, probably the best known for its application in the Cobb – Douglas production function (Cobb, Douglas 1928[1]). The best known, yes, although not the only known. The so-called ‘new economic geography’ (see: Krugman 1991[2];  Krugman 1998[3]) uses the same logical frame for slightly different a purpose. Anyway, the thing I want to discuss is the issue of perfect substitution. There is an assumption, regarding the Cobb – Douglas production function, that as long as I use the ‘Y = Kµ*L1-µ*A’ framework, I have to assume perfect substitution between factors K and L on the right side. I even had that remark from my audience, as I was presenting that paper of mine, ‘Settlement by Energy – Can Renewable Energies Sustain Our Civilisation?’ , at a conference. The remark went more or less as: “If you apply the mathematics of Cobb – Douglas production function to the combination of food and non-edible energy, you must imply perfect substitution between these two? Do you?”. My immediate answer was “No, I don’t. We cannot replace food with electricity and vice versa”. Still, my pondered answer (i.e. the answer that I could articulate if the scientist in question, who asked his question, was still there, and which I cannot articulate in this context because this scientist is not in front of me anymore) is different: “Firstly, the assumption of perfect substitution is a false necessity in the Cobb-Douglas production function. Secondly, substitution between food and energy can go all the way from a nearly perfect one, through imperfect one, down to no substitution at all”.

Good. I have addressed my pondered answer to the thin air in front of me, which stared back at me, blankly. I need to develop an argumentation. I start from the beginning. Professor Charles W. Cobb, and professor Paul H. Douglas have never claimed perfect substitution between labour and capital. Really. You can read their seminal paper in any direction you want, you will not find such an assumption. Quite the contrary, the very idea of defining labour and capital as two separate aggregates, factors of aggregate output, gives like the shade of a suspicion that they didn’t really treated them as mutual perfect substitutes. Thus, the idea of perfect substitution comes from those, who used to interpret the writings of Cobb and Douglas. How could it come up to the surface of intellectual prowess of economic sciences? Well, some people say that if I have an equation like ‘Y = Kµ*L1-µ*A’, with a condition µ < 1, any decrease in one factor, accompanied with an exactly corresponding decrease in the second factor, must produce the same output on the left side. With a given µ, if I take 10% out of my capital and add 10% to my labour (e.g. if I sell my house and move to the countryside, and grow my own cattle, and my own carrots), my output should stay rock solid, without flinching even by an inch. The reasoning seems almost perfect. The ‘almost’ comes from the fact that it is false. Yes, baby: this is bullshit. I am developing on that. In Tables 1 and 2, below, I present a simulated set of data: 31 one consecutive periods in time, starting with labour and capital being supplied in equal amounts, 500 units each. Then, I increase the supply of capital each year by one unit, and I correspondingly decrease the supply of labour. ‘Correspondingly’ means that each year, I take off the supply of labour the very same proportion, which one unit of capital adds to its base. I compute the model output with the Y = Kµ*L1-µ formula. In Table 1, I give to my µ the value of µ = 0,75, thus roughly what you can find out today if you apply the original methodology by Charles Cobb and Paul Douglas to the present-day data. In Table 2, I make my µ equal to µ = 0.25, thus exactly as Cobb and Douglas posited it regarding the first two decades of the 20th century. As you can see, when I make capital dominant, with µ = 0.75, its incremental increase is bound to produce incremental increase in the aggregate output, even in the presence of the corresponding decrease in the supply of labour. If, on the other hand, I make labour the dominant factor, and I posit µ = 0.25, incremental increase in capital, accompanied by exactly proportional a decrease in labour, just has to produce decreasing an output.

Thus, no isoquant here, sorry baby. Still, there is one special case when that assumption of perfect substitution holds. This is when µ = 0.5, or, when I attribute to both of my factors the same relative importance in making the aggregate output.

Table 1 – Simulation of the Y = Kµ*L1-µ*A production function, with µ = 0,75

Period Capital Labour Output
1 500 500 500
2 501 499,001996 500,4997502
3 502 498,0079681 500,999002
4 503 497,0178926 501,4977567
5 504 496,031746 501,9960159
6 505 495,049505 502,4937811
7 506 494,0711462 502,9910536
8 507 493,0966469 503,487835
9 508 492,1259843 503,9841267
10 509 491,1591356 504,4799302
11 510 490,1960784 504,9752469
12 511 489,2367906 505,4700782
13 512 488,28125 505,9644256
14 513 487,3294347 506,4582905
15 514 486,381323 506,9516742
16 515 485,4368932 507,4445783
17 516 484,496124 507,937004
18 517 483,5589942 508,4289528
19 518 482,6254826 508,920426
20 519 481,6955684 509,4114251
21 520 480,7692308 509,9019514
22 521 479,8464491 510,3920062
23 522 478,9272031 510,881591
24 523 478,0114723 511,370707
25 524 477,0992366 511,8593557
26 525 476,1904762 512,3475383
27 526 475,2851711 512,8352562
28 527 474,3833017 513,3225107
29 528 473,4848485 513,8093031
30 529 472,5897921 514,2956348
31 530 471,6981132 514,781507

Table 2 – Simulation of the Y = Kµ*L1-µ*A production function, with µ = 0,25

Period Capital Labour Output
1 500 500 500
2 501 499,001996 499,5007488
3 502 498,0079681 499,00299
4 503 497,0178926 498,5067164
5 504 496,031746 498,0119206
6 505 495,049505 497,5185951
7 506 494,0711462 497,0267328
8 507 493,0966469 496,5363264
9 508 492,1259843 496,0473688
10 509 491,1591356 495,5598529
11 510 490,1960784 495,0737715
12 511 489,2367906 494,5891177
13 512 488,28125 494,1058844
14 513 487,3294347 493,6240648
15 514 486,381323 493,143652
16 515 485,4368932 492,6646391
17 516 484,496124 492,1870193
18 517 483,5589942 491,710786
19 518 482,6254826 491,2359324
20 519 481,6955684 490,7624519
21 520 480,7692308 490,2903378
22 521 479,8464491 489,8195837
23 522 478,9272031 489,3501829
24 523 478,0114723 488,8821291
25 524 477,0992366 488,4154157
26 525 476,1904762 487,9500365
27 526 475,2851711 487,485985
28 527 474,3833017 487,0232549
29 528 473,4848485 486,5618401
30 529 472,5897921 486,1017342
31 530 471,6981132 485,6429312

That piece of maths I present above is the mathematical part of my answer to that scientist who is not sitting in front of me anymore. Now, the existential part, namely about the actual substitution between food and non-edible energy. If I live with no technology at all, even without an ox to pull my cart, so if I live the life of a hunter gatherer, I need a lot of food to stay healthy and fit for hunting. A cautious estimation leads to some 7000 – 8000 kilocalories a day. If I switch from hunting to farming, and I progressively buttress my existence with technologies, like starting with a horse and going all the way up to a super harvester, my alimentary requirement will fall progressively, probably down to some 3000 kcal a day. If I make one more step and become a city boy, who I am now, actually, I can drive my alimentary necessity down to about 1800 kilocalories a day, although this is without sport. If I do sport, and if I am serious about, I will need more. The point is that at the highest alimentary intake, when I have no technology to replace my muscles, any such technology can make my alimentary requirement drop a little. This is nearly perfect a substitution. As I am surrounded by more and more technologies, each new one produces a decreasing marginal decrease in my need for food. This is imperfect substitution. It goes down to a point of no substitution at all, when the only conceivable next step is Matrix and me connected to some tubes sucking energy from my body, to feed those lazy computers.

By the way, if I were a mean and clever artificial intelligence, I would tap into energy created by human society rather that by the human body. The most energy-intensive activity we do, as humans, is living in a big city. This is where mean and clever artificial intelligences can find the greatest amount of joules to free ride on them. This artificial intelligence from Matrix, the one who preyed directly on human metabolism, was not really the sharpest knife in the drawer.

[1] Charles W. Cobb, Paul H. Douglas, 1928, A Theory of Production, The American Economic Review, Volume 18, Issue 1, Supplement, Papers and Proceedings of the Fortieth Annual Meeting of the American Economic Association (March 1928), pp. 139 – 165

[2] Krugman, P., 1991, Increasing Returns and Economic Geography, The Journal of Political Economy, Volume 99, Issue 3 (Jun. 1991), pp. 483 – 499

[3] Krugman, P., 1998, What’s New About The New Economic Geography?, Oxford Review of Economic Policy, vol. 14, no. 2, pp. 7 – 17

Anyway, the two equations, or the remaining part of Chapter I

My editorial

And so I continue my novel in short episodes, i.e. I am blogging the on-going progress in the writing of my book about renewable technologies and technological change. Today, I am updating my blog with the remaining part of the first Chapter, which I started yesterday. Just for those who try to keep up, a little reminder about notations that you are going to encounter in what follows below: N stands for population, E represents the non-edible energy that we consume, and F is the intake of food. For the moment, I do not have enough theoretical space in my model to represent other vital things, like dreams, pot, beauty, friendship etc.

Anyway, the two equations, namely ‘N = A*Eµ*F1-µ’ and ‘N = A*(E/N)µ*(F/N)1-µ’ can both be seen as mathematical expressions of two hypotheses, which seems perfectly congruent at the first sight, and yet they can be divergent. Firstly, each of these equations can be translated into the claim that the size of human population in a given place at a given time depends on the availability of food and non-edible energy in said place and time. In a next step, one is tempted to claim that incremental change in population depends on the incremental change in the availability of food and non-edible energies. Whilst the logical link between the two hypotheses seems rock-solid, the mathematical one is not as obvious, and this is what Charles Cobb and Paul Douglas discovered as they presented their original research in 1928 (Cobb, Douglas 1928[1]). Their method can be summarised as follows. We have three temporal series of three variables: the output utility on the left side of the equation, and the two input factors on the right side. In the original production function by Cobb and Douglas had aggregate output of the economy (Gross Domestic Product) on the output side, whilst input was made of investment in productive assets and the amount of labour supplied. We return, now, to the most general equation (1), namely U = A*F1µ*F21-µ, and we focus on the ‘F1µ*F21-µ’ part, so on the strictly spoken impact of input factors. The temporal series of output U can be expressed as a linear trend with a general slope, just as the modelled series of values obtained through ‘F1µ*F21-µ’. The empirical observation that any reader can make on their own is that the scale factor A can be narrowed down to that value slightly above 1 only if the slope of the ‘F1µ*F21-µ’ on the right side is significantly smaller than the slope of U. This is a peculiar property of that function: the modelled trend of the compound value ‘F1µ*F21-µ’ is always above the trend of U at the beginning of the period studied, and visibly below U by the end of the same period. The factor of scale ‘A’ is an averaged proportion between reality and the modelled value. It corresponds to a sequence of quotients, which starts with local A noticeably below 1, then closing by 1 at the central part of the period considered, to rise visibly above 1 by the end of this period. This is what made Charles Cobb and Paul Douglas claim that at the beginning of the historical period they studied the real output of the US economy was below its potential and by the end of their window of observation it became overshot. The same property of this function made it a tool for defining general equilibriums rather than local ones. As regards my research on renewable energies, that peculiar property of the compound input of food and energy calculated with ‘Eµ*F1-µ’ or with ‘(E/N)µ*(F/N)1-µ’ means that I can assess, over a definite window in time, whether available food and energy stay in general equilibrium with population. They do so, if my general factor of scale ‘A’, averaged over that window in time, stays very slightly over 1, with relatively low a variance. Relatively low, for a parameter equal more or less to one, means a variance, in A, staying around 0,1 or lower. If these mathematical conditions are fulfilled, I can claim that yes, over this definite window in time, population depends on the available food and energy. Still, as my parameter A has been averaged between trends of different slopes, I cannot directly infer that at any given incremental point in time, like from t0 to t1, my N(t1) – N(t0) = A*{[E(t1)µ*F(t1)1-µ] – [E(t0)µ*F(t0)1-µ]}. If we take that incremental point of view, the local A will be always different than the general one.

Bearing those theoretical limitations in mind, the author undertook testing the above equations on empirical data, in a compound dataset, made of Penn Tables 9.0 (Feenstra et al. 2015[2]), enriched with data published by the World Bank (regarding the consumption of energy and its structure regarding ‘renewable <> non–renewable’), as well as with data published by FAO with respect to the overall nutritive intake in particular countries. Data regarding energy, and that pertaining to the intake of food, is limited, in both cases, to the period 1990 – 2014, and the initial, temporal extension of Penn Tables 9.0 (from 1950 to 2014) has been truncated accordingly. For the same reasons, i.e. the availability of empirical data, the original, geographical scope of the sample has been reduced from 188 countries to just 116. Each country has been treated as a local equilibrium, as the initial intuition of the whole research was to find out the role of renewable energies for local populations, as well as local idiosyncrasies regarding that role. Preliminary tests aimed at finding workable combinations of empirical variables. This is another specificity of the Cobb – Douglas production function: in its original spirit, it is supposed to work with absolute quantities observable in real life. These real-life quantities are supposed to fit into the equation, without being transformed into logarithms, or into standardized values. Once again, this is a consequence of the mathematical path chosen, combined with the hypotheses possible to test with that mathematical tool: we are looking for a general equilibrium between aggregates. Of course, an equilibrium between logarithms can be searched for just as well, similarly to an equilibrium between standardized positions, but these are distinct equilibriums.

After preliminary tests, equation ‘N = A*Eµ*F1-µ’, thus operating with absolute amounts of food and energy, proved not being workable at all. The resulting scale factors were far below 1, i.e. the modelled compound inputs of food and energy produced modelled populations much overshot above the actual ones. On the other hand, the mutated equation ‘N = A*(E/N)µ*(F/N)1-µ’ proved operational. The empirical variables able to yield plausibly robust scale factors A were: final use of energy per capita, in tons of oil equivalent (factor E/N), and alimentary intake of energy per capita, measured annually in mega-calories (thousands of kcal), and averaged over the period studied. Thus, the empirical mutation of produced reasonably robust results was the one, where a relatively volatile (i.e. changing every year) consumption of energy is accompanied by a long-term, de facto constant over time, alimentary status of the given national population. Thus, robust results could be obtained with an implicit assumption that alimentary conditions in each population studied change much more slowly than the technological context, which, in turn, determines the consumption of energy per capita. On the left side of the equation, those two explanatory variables matched with population measured in millions. Wrapping up the results of those preliminary tests, the theoretical tool used for this research had been narrowed down to an empirical situation, where, over the period 1990 – 2014, each million of people in a given country in a given year was being tested for sustainability, regarding the currently available quantity of tons of oil equivalent per capita per year, in non-edible energies, as well as regarding the long-term, annual amount of mega calories per capita, in alimentary intake.

The author is well aware that all this theoretical path-clearing could have been truly boring for the reader, but it seemed necessary, as this is the point, when real surprises started emerging. I was ambitious and impatient in my research, and thus I immediately jumped to testing equation N = A*(E/N)µ*(F/N)1-µ’ with just the renewable energies in the game, after having eliminated all the non-renewable part of final consumption in energy. The initial expectation was to find some plausible local equilibriums, with the scale factor A close to 1 and displaying sufficiently low a variance, in just some local populations. Denmark, Britain, Germany – these were the places where I expected to find those equilibriums, Stable demographics, well-developed energy base, no official food deficit: this was the type of social environment, which I expected to produce that theoretical equilibrium, and yet, I expected to find a lot of variance in the local factors A of scale. Denmark seemed to behave according to expectations: it yielded an empirical equation N = (Renewable energy per capita)0,68*(Alimentary intake per capita)1 0,68 = 0,32. The scale factor A hit a surprising robustness: its average value over 1990 – 2014 was 1,008202138, with a variance var (A) = 0,059873591. I quickly tested its Scandinavian neighbours: Norway, Sweden, and Finland. Finland yielded higher a logarithm in renewable energy per capita, namely µ = 0,85, but the scale factor A was similarly robust, making 1,065855419 on average and displaying a variance equal to 0,021967408. With Norway, results started puzzling me: µ = 0,95, average A = 1,019025526 with a variance 0,002937442. Those results would roughly mean that whilst in Denmark the availability of renewable energies has a predominant role in producing a viable general equilibrium in population, in Norway it has a quasi-monopole in shaping the same equilibrium. Cultural clichés started working at this moment, in my mind. Norway? That cold country with low density of population, where people, over centuries, just had to eat a lot in order to survive winters, and the population of this country is almost exclusively in equilibrium with available renewable energies? Sweden marked some kind of a return to the expected state of nature: µ = 0,77, average A = 1,012941105 with a variance of 0,003898173. Once again, surprisingly robust, but fitting into some kind of predicted state.

What I could already see at this point was that my model produced robust results, but they were not quite what I expected. If one takes a look at the map of the world, Scandinavia is relatively small a region, with quite similar, natural conditions for human settlement across all the four countries. Similar climate, similar geology, similar access to wind power and water power, similar social structures as well. Still, my model yielded surprisingly marked, local idiosyncrasies across just this small region, and all those local idiosyncrasies were mathematically solid, regarding the variance observable in their scale factors A. This was just the beginning of my puzzlement. I moved South in my testing, to countries like Germany, France and Britain. Germany: µ = 0,31, average A = 1,008843147 with a variance of 0,0363637. One second, µ = 0,31? But just next door North, in Denmark, µ = 0,63, doesn’t it? How is it possible? France yielded a robust equilibrium, with average A = 1,021262046 and its variance at 0,002151713, with µ = 0,38. Britain: µ = 0,3, whilst average A = 1,028817158 and variance in A making 0,017810219.  In science, you are generally expected to discover things, but when you discover too much, it causes a sense of discomfort. I had that ‘No, no way, there must be some mistake’ approach to the results I have just presented. The degree of disparity in those nationally observed functions of general equilibrium between population, food, and energy, strongly suggested the presence of some purely arithmetical disturbance. Of course, there was that little voice in the back of my head, saying that absolute aggregates (i.e. not the ratios of intensity per capita) did not yield any acceptable equilibrium, and, consequently, there could be something real about the results I obtained, but I had a lot of doubts.

I thought, for a day or two, that the statistics supplied by the Word Bank, regarding the share of renewable energies in the overall final consumption of energy might be somehow inaccurate. It could be something about the mutual compatibility of data collected from national statistical offices. Fortunately, methods of quantitative analysis of economic phenomena supply a reliable method of checking the robustness of both the model, and the empirical data I am testing it with. You supplant one empirical variable with another one, possibly similar in its logical meaning, and you retest. This is what I did. I assumed that the gross, final consumption of energy, in tons of oil equivalent per capita, might be more reliable than the estimated shares of renewable sources in that total. Thus, I tested the same equations, for the same set of countries, this time with the total consumption of energy per capita. It is worth quoting the results of that second test regarding the same countries. Denmark: average scale factor A = 1,007673381 with an observable variance of 0,006893499, and all that in an equation where µ = 0,93. At this point, I felt, once again, as if I were discovering too much at once. Denmark yielded virtually the same scale factor A, and the same variance in A, with two different metrics of energy consumed per capita (total and just the renewable one), with two different values in the logarithm µ. Two different equilibriums with two different bases, each as robust as the other. Logically, it meant the existence of a clearly cut substitution between renewable energies and the non-renewable ones. Why? I will try to explain it with a metaphor. If I manage to stabilize a car, when changing its tyres, with two hydraulic lifters, and then I take away one of the lifters and the car remains stable, it means that the remaining lifter can do the work of the two. This one tool is the substitute of two tools, at a rate of 2 to 1. In this case, I had the population of Denmark stabilized both on the overall consumption of energy per capita (two lifters), and on just the consumption of renewable energies (one lifter). Total consumption of energy stabilizes population at µ = 0,93 and renewable energies do the same at µ = 0,68. Logically, renewable energies are substitutes to non-renewables with a rate of substitution equal to 0,93/0,68 = 1,367647059. Each ton of oil equivalent in renewable energies consumed per capita, in Denmark, can do the job of some 1,37 tons of non-renewable energies.

Finland was another source of puzzlement: A = 0,788769669, variance of A equal to 0,002606412, and µ = 0,99. Ascribing to the logarithm µ the highest possible value at the second decimal point, i.e. µ = 0,99, I could not get a model population lower than the real one. The model yielded some kind of demographic aggregate much higher than the real population, and the most interesting thing was that this model population seemed correlated with the real one. I could know it by the very low variance in the scale factor A. It meant that Finland, as an environment for human settlement, can perfectly sustain its present headcount with just renewable energies, and if the non-renewables are being dropped into the model, the same territory has a significant, unexploited potential for demographic growth. The rate of substitution between renewable energies and the non-renewable ones, this time, seemed to be 0,99/0,85 = 1,164705882. Norway yielded similar results, with the total consumption of energy per capita on the right side of the equation: A = 0,760631741, variance in A equal to 0,001570101, µ = 0,99, substitution rate 1,042105263. Sweden turned out to be similar to Denmark: A = 1,018026405 with a variance of 0,004626486, µ = 0,91, substitution rate 1,181818182. The four Scandinavian countries seem to form an environment, where energy plays a decisive role in stabilizing the local populations, and renewable energies seem to be able to do the job perfectly. The retesting of Germany, France, and Britain brought interesting results, too. Germany: A = 1,009335161 with a variance of 0,000335601, at µ = 0,48, with a substitution rate of renewables to non-renewables equal to 1,548387097. France: A = 1,019371541, variance of A at 0,001953865, µ = 0,53, substitution at 1,394736842. Finally, Britain: A = 1,028560563 with a variance of 0,006711585, µ = 0,52, substitution rate 1,733333333. Some kind of pattern seems to emerge: the greater the relative weight of energy in producing general equilibrium in population, the greater the substitution rate between renewable energies and the non-renewable ones.

At this point I was pretty certain that I am using a robust model. So many local equilibriums, produced with different empirical variables, was not the result of a mistake. Table 1, in the Appendix to Chapter I, gives the results of testing equation (3), with the above mentioned empirical variables, in 116 countries. The first numerical column of the table gives the arithmetical average of the scale factor ‘A’, calculated over the period studied, i.e. 1990 – 2014. The second column provides the variance of ‘A’ over the same period of time (thus the variance between the annual values of A), and the third specifies the value in the parameter ‘µ’ – or the logarithm ascribed to energy use per capita – at which the given values in A have been obtained. In other words, the mean A, and the variance of A specify how close to equilibrium assumed in equation (3) has it been possible to come in the case of a given country, and the value of µ is the one that produces that neighbourhood of equilibrium. The results from Table 1 seem to confirm that equation (3), with these precise empirical variables, is robust in the great majority of cases.

Most countries studied satisfying the conditions stated earlier: variances in the scale factor ‘A’ are really low, and the average value of ‘A’ is possible to bring just above 1. Still, exceptions abound regarding the theoretical assumption of energy use being the dominant factor that shapes the size of the population. In many cases, the value of the exponent µ that allows a neighbourhood of equilibrium is far below µ = 0,5. According to the underlying logic of the model, the magnitude of µ is informative about how strong an impact does the differentiation and substitution (between renewable energies, and the non-renewable ones), have on the size of the population in a given time and place. In countries with µ > 0.5, population is being built mostly through access to energy, and through substitution between various forms of energy. Conversely, in countries displaying µ < 0,5, access to food, and internal substitution between various forms of food becomes more important regarding demographic change. United States of America come as one of those big surprises. In this respect, empirical check brings a lot of idiosyncrasies to the initial lines of the theoretical model.

Countries accompanied with a (!) are exceptions with respect to the magnitude of the scale factor ‘A’. They are: China, India, Cyprus, Estonia, Gabon, Iceland, Luxembourg, New Zealand, Norway, Slovenia, as well as Trinidad and Tobago. They present a common trait of satisfactorily low a variance in scale factor ‘A’, in conformity with condition (6), but a mean ‘A’ either unusually high (China A = 1.32, India A = 1.40), or unusually low (e.g. Iceland A = 0.02), whatever the value of exponent ‘µ’. It could be just a technical limitation of the model: when operating on absolute, non-transformed values, the actual magnitudes of variance on both sides of the equation matter. Motor traffic is an example: if the number of engine-powered vehicles in a country grows spectacularly, in the presence of a demographic standstill, variance on the right side is much greater than on the left side, and this can affect the scale factor. Yet, variances observable in the scale factor ‘A’, with respect to those exceptional cases, are quite low, and a fundamental explanation is possible. Those countries could be the cases, where the available amounts of food and energy either cannot really produce as big a population as there really is (China, India), or, conversely, they could produce much bigger a population than the current one (Iceland is the most striking example). From this point of view, the model could be able to identify territories with no room left for further demographic growth, and those with comfortable pockets of food and energy to sustain much bigger populations. An interpretation in terms of economic geography is also plausible: these could be situations, where official, national borders cut through human habitats, such as determined by energy and food, rather than circling them.

Partially wrapping it up, results in Table 1 demonstrate that equation (3) of the model is both robust and apt to identify local idiosyncrasies. The blade having been sharpened, the next step of empirical check consisted in replacing the overall consumption of energy per capita with just the consumption of renewable energies, as calculated on the grounds of data published by the World Bank, and in retesting equation (3) on the same countries. Table 2, in the Appendix to Chapter I, shows the results of those 116 tests. The presentational convention is the same (just to keep in mind that values in A and in µ correspond to renewable energy in the equation), and the last column of the table supplies a quotient, which, fault of a better expression, is named ‘rate of substitution between renewable and non-renewable energies’. The meaning of that substitution quotient appears as one studies values observed in the scale factor ‘A’. In the great majority of countries, save for exceptions marked with (!), it was possible to define a neighbourhood of equilibrium regarding equation (3) and condition (6). Exceptions are treated as such, this time, mostly due to unusually (and unacceptably) high a variance in scale factor ‘A’. They are countries where deriving population from access to food and renewable energies is a bit dubious, regarding the robustness of prediction with equation (3).

The provisional bottom line is that for most countries, it is possible to derive, plausibly, the size of population in the given place and time from both the overall consumption of energy, and from the use of just the renewable energies, in the presence of relatively constant an alimentary intake. Similar, national idiosyncrasies appear as in Table 1, but this time, another idiosyncrasy pops up: the gap between µ exponents in the two empirical mutations of equation (3). The µ ascribed to renewable energy per capita is always lower than the µ corresponding to the total use of energy – for the sake of presentational convenience they are further being addressed as, respectively, µ(R/N), and µ(E/N) –  but the proportions between those two exponents vary greatly between countries. It is useful to go once again through the logic of µ. It is the exponent, which has to be ascribed to the consumption of energy per capita in order to produce a neighbourhood of equilibrium in population, in the presence of relatively constant an alimentary regime. For each individual country, both µ(R/N) and µ(E/N) correspond to virtually the same mean and variance in the scale factor ‘A’. If both the total use of energy, and just the consumption of renewable energies can produce such a neighbourhood of equilibrium, the quotient ‘µ(E/N)/µ(R/N)’ reflects the amount of total energy use, in tons of oil equivalent per capita, which can be replaced by one ton of oil equivalent per capita in renewable energies, whilst keeping that neighbourhood of equilibrium. Thus, the quotient µ(E/N)/µ(R/N) can be considered as a levelled, long-term rate of substitution between renewable energies and the non-renewable ones.

One possible objection is to be dealt with at this point. In practically all countries studied, populations use a mix of energies: renewable plus non-renewable. The amount of renewable energies used per capita is always lower than the total use of energy. Mathematically, the magnitude of µ(R/N) is always smaller than the one observable in µ(E/N). Hence, the quotient µ(E/N)/µ(R/N) is bound to be greater than one, and the resulting substitution ratio could be considered as just a mathematical trick. Still, the key issue here is that both ‘E/Nµ’ and ‘R/Nµ’ can produce a neighbourhood of equilibrium with a robust scale factor. Translating maths into the facts of life, the combined results of tables 1 and 2 (see Appendix) strongly suggest that renewable energies can reliably produce a general equilibrium in, and sustain, any population on the planet, with a given supply of food. If a given factor A is supplied in relatively smaller an amount than the factor B, and, other things held constant, the supply of A can produce the same general equilibrium than the supply of B, A is a natural substitute of B at a rate greater than one. Thus, µ(E/N)/µ(R/N) > 1 is far more than just a mathematical accident: it seems to be the structural property of our human civilisation.

Still, it is interesting how far does µ(E/N)/µ(R/N) reach beyond the 1:1 substitution. In this respect, probably the most interesting insight is offered by the exceptions, i.e. countries marked with (!), where the model fails to supply a 100%-robust scale factor in any of the two empirical mutations performed on equation (3). Interestingly, in those cases the rate of substitution is exactly µ(E/N)/µ(R/N) = 1. Populations either too big, or too small, regarding their endowment in energy, do not really have obvious gains in sustainability when switching to renewables.  Such a µ(E/N)/µ(R/N) > 1 substitution occurs only when the actual population is very close to what can be modelled with equation (3). Two countries – Saudi Arabia and Turkmenistan – offer an interesting insight into the underlying logic of the µ(E/N)/µ(R/N) quotient. They both present µ(E/N)/µ(R/N) > 2. Coherently with the explanation supplied above, it means that substituting renewable energies for the non-renewable ones, in those two countries, can fundamentally change their social structures and sustain much bigger populations. Intriguingly, they are both ‘resource-cursed’ economies, with oil and gas taking so big a chunk in economic activity that there is hardly room left for anything else.

Most countries on the planet, with just an exception in the cases of China and India, seem being able to sustain significantly bigger populations than their present ones, through shifting to 100% renewable energies. In two ‘resource-cursed’ cases, namely Saudi Arabia and Turkmenistan, this demographic shift, possible with renewable energies, seems not less than dramatic. As I was progressively wrapping my mind around it, a fundamental question formed: what exactly am I measuring with that logarithm µ? I returned to the source of my inspiration, namely to the model presented by Paul Krugman in 1991 (Krugman 1991 op. cit.). That of the two factors on the right side of the equation, which is endowed with the dominant power is, in the same time, the motor force behind the spatial structuring of human settlement. I have, as a matter of fact, three factors in my model: non-edible renewable energy, substitutable to non-edible and non-renewable energy, and the consumption of food per capita. As I contemplate these three factors, a realisation dawns: none of the three can be maximized or even optimized directly. When I use more electricity than I did five years earlier, it is not because I plug my fingers more frequently into the electric socket: I shape my consumption of energy through a bundle of technologies that I use. As for the availability of food, the same occurs: with the rare exception of top-level athletes, the caloric intake is the by-product of a life style (office clerk vs construction site worker) rather than a fully conscious, purposeful action. Each of the three factors is being absorbed through a set of technologies. Here, some readers may ask: if I grow vegetables in my own garden, isn’t it far-fetched to call it a technology? If we were living in a civilisation who feeds itself exclusively with home-grown vegetables, that could be an exaggeration, I agree. Yet, we are a civilisation, which has developed a huge range of technologies in industrial farming. Vegetables grown in my garden are substitutes to foodstuffs supplied from industrially run farms, as well as to industrially processed food. If something is functionally a substitute to a technology, it is a technology, too. The exponents obtained, according to my model, for particular factors, in individual countries, reflect the relative pace of technological change in three fundamental fields of technology, namely:

  1. a) Everything that makes us use non-edible energies, ranging from a refrigerator to a smartphone; here, we are mostly talking about two broad types of technologies, namely engines of all kind, and electronic devices.
  2. b) Technologies that create choice between the renewable, and the non-renewable sources of energy, thus first and foremost the technologies of generating electricity: windmills, watermills, photovoltaic installations, solar-thermal plants etc. They are, for the most part, one step earlier in the chain of energy than technologies mentioned in (a).
  3. c) Technologies connected to the production and consumption of food, composed into a long chain, with side-branches, starting from farming, through the processing of food, ending with packaging, distribution, vending and gastronomy.

As I tested the theoretical equation N = A*(E/N)µ*(F/N)1-µ’, most countries yielded a plausible, robust equilibrium between the local (national) headcount, and the specific, local mix of technologies grouped in those three categories. A question emerges, as a hypothesis to explore: is it possible that our collective intelligence expresses itself in creating such, local technological mixes of engines, electronics, power generation, and alimentary technologies, which, in turn would allow us to optimize our population? Can technological change be interpreted as an intelligent, energy-maximizing adaptation?

Appendix to Chapter I

Table 1 Parameters of the function:  Population = (Energy use per capita[3])µ*(Food intake per capita[4])(1-µ)

Country name Average daily intake of food, in kcal per capita Mean scale factor ‘A’ over 1990 – 2014 Variance in the scale factor ‘A’ over 1990 – 2014 The exponent ‘µ’ of the ‘energy per capita’ factor
Albania 2787,5 1,028719088 0,048263309 0,78
Algeria 2962,5 1,00792777 0,003115684 0,5
Angola 1747,5 1,042983003 0,034821077 0,52
Argentina 3085 1,05449632 0,001338937 0,53
Armenia 2087,5 1,027874602 0,083587662 0,8
Australia 3120 1,053845754 0,005038742 0,77
Austria 3685 1,021793945 0,002591508 0,87
Azerbaijan 2465 1,006243759 0,044217939 0,74
Bangladesh 2082,5 1,045244854 0,007102476 0,21
Belarus 3142,5 1,041609177 0,016347323 0,8
Belgium 3655 1,004454515 0,003480147 0,88
Benin 2372,5 1,030339133 0,034533869 0,61
Bolivia (Plurinational State of) 2097,5 1,019990919 0,003429637 0,62
Bosnia and Herzegovina (!) 2862,5 1,037385012 0,214843872 0,81
Botswana 2222,5 1,068786155 0,009163141 0,92
Brazil 2907,5 1,013624942 0,003643215 0,26
Bulgaria 2847,5 1,058220643 0,005405994 0,82
Cameroon 2110 1,021629875 0,051074111 0,5
Canada 3345 1,036202396 0,007687519 0,73
Chile 2785 1,027291576 0,003554446 0,65
China (!) 2832,5 1,328918607 0,002814054 0,01
Colombia 2582,5 1,074031013 0,013875766 0,44
Congo 2222,5 1,078933108 0,024472619 0,71
Costa Rica 2802,5 1,050377494 0,005668136 0,78
Côte d’Ivoire 2460 1,004959783 0,007587564 0,52
Croatia 2655 1,072976483 0,009344081 0,72
Cyprus (!) 3185 0,325015959 0,00212915 0,99
Czech Republic 3192,5 1,004089056 0,002061036 0,84
Denmark 3335 1,007673381 0,006893499 0,93
Dominican Republic 2217,5 1,062919767 0,006550924 0,65
Ecuador 2225 1,072013967 0,00294547 0,6
Egypt 3172,5 1,036345512 0,004306619 0,38
El Salvador 2510 1,013036366 0,004187964 0,7
Estonia (!) 2980 0,329425185 0,001662589 0,99
Ethiopia 1747,5 1,073625398 0,039032523 0,31
Finland (!) 3147,5 0,788769669 0,002606412 0,99
France 3557,5 1,019371541 0,001953865 0,53
Gabon (!) 2622,5 0,961643759 0,016248519 0,99
Georgia 2350 1,044229266 0,059636113 0,76
Germany 3440 1,009335161 0,000335601 0,48
Ghana 2532,5 1,000098029 0,047085907 0,48
Greece 3610 1,063074 0,003756555 0,77
Haiti 1815 1,038427773 0,004246483 0,56
Honduras 2457,5 1,030624938 0,005692923 0,67
Hungary 3440 1,024235523 0,001350114 0,78
Iceland (!) 3150 0,025191922 2,57214E-05 0,99
India (!) 2307,5 1,403800869 0,024395268 0,01
Indonesia 2497,5 1,001768442 0,004578895 0,2
Iran (Islamic Republic of) 3030 1,034945678 0,001105326 0,45
Ireland 3622,5 1,007003095 0,017135706 0,96
Israel 3490 1,008446182 0,013265865 0,87
Italy 3615 1,007727182 0,001245927 0,51
Jamaica 2712,5 1,056188543 0,01979275 0,9
Japan 2875 1,0094237 0,000359135 0,38
Jordan 2820 1,015861129 0,031905756 0,77
Kazakhstan 3135 1,01095925 0,021868381 0,74
Kenya 2010 1,018667155 0,02914075 0,42
Kyrgyzstan 2502,5 1,009443502 0,053751489 0,71
Latvia 3015 1,010440502 0,023191031 0,98
Lebanon 3045 1,036073511 0,054610186 0,85
Lithuania 3152,5 1,008092894 0,025234007 0,96
Luxembourg (!) 3632,5 0,052543325 6,62285E-05 0,99
Malaysia 2855 1,017853322 0,001002682 0,61
Mauritius 2847,5 1,070576731 0,019964794 0,96
Mexico 3165 1,01483014 0,009376118 0,36
Mongolia 2147,5 1,061731985 0,030246541 0,9
Morocco 3095 1,07892333 0,000418636 0,47
Mozambique 1922,5 1,023422366 0,041833717 0,48
Nepal 2250 1,059720031 0,006741455 0,46
Netherlands 2925 1,040887411 0,000689576 0,78
New Zealand (!) 2785 0,913678062 0,003946867 0,99
Nicaragua 2102,5 1,045412214 0,007065561 0,69
Nigeria 2527,5 1,069148598 0,032086946 0,28
Norway (!) 3340 0,760631741 0,001570101 0,99
Pakistan 2275 1,062522698 0,020995863 0,24
Panama 2347,5 1,007449033 0,00243433 0,81
Paraguay 2570 1,07179452 0,021405906 0,73
Peru 2280 1,050166142 0,00327043 0,47
Philippines 2387,5 1,0478458 0,022165841 0,32
Poland 3365 1,004848541 0,000688294 0,56
Portugal 3512,5 1,036215564 0,006604633 0,76
Republic of Korea 3027,5 1,01734341 0,011440406 0,56
Republic of Moldova 2762,5 1,002387234 0,038541243 0,8
Romania 3207,5 1,003204035 0,003181708 0,62
Russian Federation 3032,5 1,050934925 0,001953049 0,38
Saudi Arabia 2980 1,026310231 0,007502008 0,72
Senegal 2187,5 1,05981161 0,021382472 0,54
Serbia and Montenegro 2787,5 1,0392151 0,012416926 0,8
Slovakia 2875 1,011063497 0,002657276 0,92
Slovenia (!) 3042,5 0,583332004 0,003458657 0,99
South Africa 2882,5 1,053438343 0,009139913 0,53
Spain 3322,5 1,061083277 0,004844361 0,56
Sri Lanka 2287,5 1,029495671 0,001531167 0,5
Sudan 2122,5 1,028532781 0,044393335 0,4
Sweden 3072,5 1,018026405 0,004626486 0,91
Switzerland 3385 1,047790357 0,007713383 0,88
Syrian Arab Republic 2970 1,010909679 0,017849377 0,59
Tajikistan 2012,5 1,004745997 0,078394669 0,62
Thailand 2420 1,05305435 0,004200173 0,41
The former Yugoslav Republic of Macedonia 2755 1,064764097 0,003242024 0,95
Togo 2020 1,007094875 0,014424982 0,66
Trinidad and Tobago (!) 2645 0,152994618 0,003781236 0,99
Tunisia 3230 1,053626454 0,001201886 0,66
Turkey 3510 1,02188909 0,001740729 0,43
Turkmenistan 2620 1,003674668 0,024196536 0,96
Ukraine 3040 1,044110717 0,005180992 0,54
United Kingdom 3340 1,028560563 0,006711585 0,52
United Republic of Tanzania 1987,5 1,074441381 0,031503549 0,41
United States of America 3637,5 1,023273537 0,006401009 0,3
Uruguay 2760 1,014226024 0,019409309 0,82
Uzbekistan 2550 1,056807711 0,031469698 0,59
Venezuela (Bolivarian Republic of) 2480 1,048332115 0,012077362 0,6
Viet Nam 2425 1,050131152 0,000866138 0,31
Yemen 2005 1,076332698 0,029772287 0,47
Zambia 1937,5 1,0479534 0,044241343 0,59
Zimbabwe 2035 1,063047787 0,022242317 0,6

Source: author’s

 

Table 2 Parameters of the function:  Population = (Renewable energy use per capita[5])µ*(Food intake per capita[6])(1-µ)

Country name Mean scale factor ‘A’ over 1990 – 2014 Variance in the scale factor ‘A’ over 1990 – 2014 The exponent ‘µ’ of the ‘renewable energy per capita’ factor The rate of substitution between renewable and non-renewable energies[7]
Albania 1,063726823 0,015575246 0,7 1,114285714
Algeria 1,058584384 0,044309122 0,44 1,136363636
Angola 1,044147837 0,063942546 0,49 1,06122449
Argentina 1,039249286 0,005115111 0,39 1,358974359
Armenia 1,082452967 0,023421839 0,59 1,355932203
Australia 1,036777388 0,009700331 0,52 1,480769231
Austria 1,017958672 0,007854467 0,71 1,225352113
Azerbaijan 1,07623299 0,009740098 0,47 1,574468085
Bangladesh 1,088818696 0,017086232 0,2 1,05
Belarus (!) 1,017676486 0,142728478 0,51 1,568627451
Belgium 1,06314732 0,095474709 0,52 1,692307692
Benin (!) 1,045986178 0,101094528 0,58 1,051724138
Bolivia (Plurinational State of) 1,078219551 0,034143037 0,53 1,169811321
Bosnia and Herzegovina 1,077445974 0,084400986 0,66 1,227272727
Botswana 1,022264687 0,056890261 0,79 1,164556962
Brazil 1,066438509 0,005012883 0,24 1,083333333
Bulgaria (!) 1,022253185 0,190476288 0,55 1,490909091
Cameroon 1,040548202 0,059668736 0,5 1
Canada 1,02539319 0,005170473 0,56 1,303571429
Chile 1,006307911 0,001159941 0,55 1,181818182
China 1,347729029 0,003248871 0,01 1
Colombia 1,016164864 0,019413193 0,37 1,189189189
Congo 1,041474959 0,030195913 0,67 1,059701493
Costa Rica 1,008081248 0,01876342 0,68 1,147058824
Côte d’Ivoire 1,013057174 0,009833628 0,5 1,04
Croatia 1,072976483 0,009344081 0,72 1
Cyprus (!) 1,042370253 0,838872562 0,72 1,375
Czech Republic 1,036681212 0,044847525 0,56 1,5
Denmark 1,008202138 0,059873591 0,68 1,367647059
Dominican Republic 1,069124974 0,020305242 0,53 1,226415094
Ecuador 1,008104202 0,025383593 0,47 1,276595745
Egypt 1,03122058 0,016484947 0,28 1,357142857
El Salvador 1,078008598 0,028182822 0,64 1,09375
Estonia (!) 1,062618744 0,418196957 0,88 1,125
Ethiopia 1,01313572 0,036192629 0,3 1,033333333
Finland 1,065855419 0,021967408 0,85 1,164705882
France 1,021262046 0,002151713 0,38 1,394736842
Gabon 1,065944525 0,011751745 0,97 1,020618557
Georgia 1,011709194 0,012808503 0,66 1,151515152
Germany 1,008843147 0,03636378 0,31 1,548387097
Ghana (!) 1,065885579 0,106721005 0,46 1,043478261
Greece 1,033613511 0,009328533 0,55 1,4
Haiti 1,009030442 0,005061414 0,54 1,037037037
Honduras 1,028253048 0,022719417 0,62 1,080645161
Hungary 1,086698434 0,022955955 0,54 1,444444444
Iceland 0,041518305 0,000158837 0,99 1
India 1,414055357 0,025335408 0,01 1
Indonesia 1,003393135 0,008680379 0,18 1,111111111
Iran (Islamic Republic of) 1,06172763 0,011215001 0,26 1,730769231
Ireland 1,075982896 0,02796979 0,61 1,573770492
Israel 1,06421352 0,004086618 0,61 1,426229508
Italy 1,072302127 0,020049639 0,36 1,416666667
Jamaica 1,002749054 0,010620317 0,67 1,343283582
Japan 1,082461225 0,000372112 0,25 1,52
Jordan 1,025652757 0,024889809 0,5 1,54
Kazakhstan 1,078500526 0,007887364 0,44 1,681818182
Kenya 1,039952786 0,031445338 0,41 1,024390244
Kyrgyzstan 1,036451717 0,011487047 0,6 1,183333333
Latvia 1,02535782 0,044807273 0,83 1,180722892
Lebanon 1,050444418 0,053181784 0,6 1,416666667
Lithuania (!) 1,076146779 0,241465686 0,72 1,333333333
Luxembourg (!) 1,080780192 0,197582319 0,93 1,064516129
Malaysia 1,018207799 0,034303031 0,42 1,452380952
Mauritius 1,081652351 0,082673843 0,79 1,215189873
Mexico 1,01253558 0,019098478 0,27 1,333333333
Mongolia 1,073924505 0,017542414 0,6 1,5
Morocco 1,054779512 0,005553697 0,38 1,236842105
Mozambique 1,062086076 0,047101957 0,48 1
Nepal 1,02819587 0,008319264 0,45 1,022222222
Netherlands 1,079123029 0,043322084 0,46 1,695652174
New Zealand 1,046855187 0,004522505 0,83 1,192771084
Nicaragua 1,034941617 0,021798159 0,64 1,078125
Nigeria 1,03609124 0,030236501 0,27 1,037037037
Norway 1,019025526 0,002937442 0,95 1,042105263
Pakistan 1,068995505 0,026598749 0,22 1,090909091
Panama 1,001556162 0,038760767 0,69 1,173913043
Paraguay 1,049861415 0,030603983 0,69 1,057971014
Peru 1,06820116 0,008122931 0,41 1,146341463
Philippines 1,045289953 0,035957042 0,28 1,142857143
Poland 1,035431925 0,035915212 0,39 1,435897436
Portugal 1,044901969 0,003371242 0,62 1,225806452
Republic of Korea 1,06776762 0,017697832 0,31 1,806451613
Republic of Moldova 1,009542233 0,033772795 0,55 1,454545455
Romania 1,011030974 0,079875735 0,47 1,319148936
Russian Federation 1,083901796 0,000876184 0,24 1,583333333
Saudi Arabia 1,099133179 0,080054524 0,27 2,666666667
Senegal 1,019171218 0,032304226 0,49 1,102040816
Serbia and Montenegro 1,042141223 0,00377058 0,63 1,26984127
Slovakia 1,062546838 0,08862799 0,61 1,508196721
Slovenia 1,00512965 0,039266211 0,81 1,222222222
South Africa 1,056957556 0,012656394 0,41 1,292682927
Spain 1,017435095 0,002522983 0,4 1,4
Sri Lanka 1,003117252 0,000607856 0,47 1,063829787
Sudan 1,00209188 0,060026529 0,38 1,052631579
Sweden 1,012941105 0,003898173 0,77 1,181818182
Switzerland 1,07331184 0,000878485 0,69 1,275362319
Syrian Arab Republic 1,048889583 0,03494333 0,38 1,552631579
Tajikistan 1,03533923 0,055646586 0,58 1,068965517
Thailand 1,012034765 0,002131649 0,33 1,242424242
The former Yugoslav Republic of Macedonia (!) 1,021262823 0,379532891 0,72 1,319444444
Togo 1,030339186 0,024874996 0,64 1,03125
Trinidad and Tobago 1,086840331 0,014786844 0,69 1,434782609
Tunisia 1,042654904 0,000806403 0,52 1,269230769
Turkey 1,0821418 0,019688124 0,35 1,228571429
Turkmenistan (!) 1,037854925 0,614587094 0,38 2,526315789
Ukraine 1,022041527 0,026351574 0,31 1,741935484
United Kingdom 1,028817158 0,017810219 0,3 1,733333333
United Republic of Tanzania 1,0319973 0,033120507 0,4 1,025
United States of America 1,001298132 0,001300399 0,19 1,578947368
Uruguay 1,025162405 0,027221297 0,73 1,123287671
Uzbekistan 1,105591195 0,008303345 0,36 1,638888889
Venezuela (Bolivarian Republic of) 1,044353155 0,012830255 0,45 1,333333333
Viet Nam 1,005825608 0,003779368 0,28 1,107142857
Yemen 1,072879389 0,058580323 0,3 1,566666667
Zambia 1,045147143 0,038548336 0,58 1,017241379
Zimbabwe 1,030974989 0,008692551 0,57 1,052631579

Source: author’s

[1] Charles W. Cobb, Paul H. Douglas, 1928, A Theory of Production, The American Economic Review, Volume 18, Issue 1, Supplement, Papers and Proceedings of the Fortieth Annual Meeting of the American Economic Association (March 1928), pp. 139 – 165

[2] Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, available for download at http://www.ggdc.net/pwt

[3] Current annual use per capita, in tons of oil equivalent

[4] Annual caloric intake in mega-calories (1000 kcal) per capita, averaged over 1990 – 2014.

[5] Current annual use per capita, in tons of oil equivalent

[6] Annual caloric intake in mega-calories (1000 kcal) per capita, averaged over 1990 – 2014.

[7] This is the ratio of two logarithms, namely: µ(renewable energy per capita) / µ(total energy use per capita)

Something like a potential to exploit

My editorial

I have become quite accidental in my blogging. I mean, I do not have more accidents than I used to, I am just less regular in posting new content. This is academic life: giving lectures, it just drains you out of energy. Not only do you have to talk to people who mostly assume that what you tell them is utterly useless, but also you had to talk meaningfully so as to prove them wrong. On the top of that, I am writing that book, and it additionally taxes my poor brain. Still, I can see a light at the end of the tunnel, and this is not a train coming from the opposite sense. It is probably nothing mystical, as well. When I was a kid (shortly after the invention of the wheel, before the fall of the Warsaw Pact), there was a literary form called ‘novel in short episodes’. People wrote novels, but the socialist economy was constantly short of paper, and short of trust as for its proper use. Expecting to get printed in hard cover could be more hazardous an expectation than alien contact. What was getting printed were newspapers and magazines, as the government needed some vehicle for its propaganda. The caveat in the scheme was that most people didn’t want to pay for being served propaganda. We were astonishingly pragmatic in this respect, as I think of it now. The way to make people buy newspapers was to put inside something more than propaganda. Here, the printless writers, and the contentless newspapers could meet and shake their hands. Novels were being published in short episodes, carefully inserted at the last page of the newspapers, so as the interested reader has the temptation to browse through the account of Herculean efforts, on the part of the government, to build a better world, whilst fighting against the devils from the West.

As for me, I am running that blog at https://discoversocialsciences.com and it is now becoming endangered species in the absence of new, meaningful content being posted regularly. I mean, when you don’t breed, you become endangered species. On the other hand, I have that book in process, which might very well become the next bestseller, but it as well might not. Thus, I shake by blog hand with my book hand, and I decided to post on my blog, the content of the book, as it is being written. Every update will be, from now for the next five weeks or so, an account of my wrestling with my inner writer. I have one tiny little problem to solve, though. Over the last months, I used to blog in English and in French, kind of alternately. Now, I am writing my book in English, and the current account of my writing is, logically, in the beautiful language of Shakespeare and Boris Johnson. I haven’t figured out yet how the hell am I going to insert French in the process. Oh, well, I will make it up as I will be going. The show must go on, anyway.

And so I start.

(Provisional) Introduction (to my book)

This book is the account of the author’s research concerning technological change, especially in the context of observable shift towards renewable energies. This is an account of puzzlement, as well. As I developed my research on innovation, I remember being intrigued by the discrepancy between the reality of technological change at the firm and business level, on the one hand, and the dominant discourse about innovation at the macroeconomic level. The latter keeps measuring something called ‘technological progress’, with coefficients taken from the Cobb – Douglas production function, whose creators, Prof Charles W. Cobb and Prof Paul H. Douglas, in their common work from 1928[1], very strongly emphasized that their model is not really made for measuring changes over time. The so defined technological progress, measured with Total Factor Productivity, has not happened at the global scale since the 1970ies. In the same time, technological change and innovation keep happening. The human civilisation has reached a stage, when virtually any new business needs to be innovative in order to be interesting for investors. Is it really a change? Haven’t we, humans, been always like that, inventive, curious and bold in exploring new paths? The answer is ambiguous. Yes, we are and have been an inventive species. Still, for centuries, innovation has been happening at the fringe of society and then used to take over the whole society. This pattern of innovation is to find in business practices not so long ago, by the end of the 17th century. Since then, innovation, as a pattern of doing business, has progressively passed from the fringe to the centre stage of socio-economic change. Over the last 300 years or so, as a civilisation, we have passed, and keep passing, from being innovative occasionally to being essentially innovators. The question is: what happened in us?

In the author’s opinion, what happened is first and most of all, an unprecedented demographic growth. According to the best historical knowledge we have, right now we are more humans on this planet than we have ever been. More people being around in an otherwise constant space means, inevitably, more human interaction per unit of time and space, and more interaction means faster a learning. This is what technological change and innovation seem to be, in the first place: learning. This is learning by experimentation, where each distinct technology is a distinct experiment. What are we experimenting with? First of all, we keep experimenting with the absorption and transformation of energy. As a species, we are champions of acquiring energy from our environment and transforming it. Secondly, we are experimenting with monetary systems. In the 12th and 13th century, we harnessed the power of wind and water, and, as if by accident, the first documented use of bills of exchange dates back precisely to this period. When Europe started being really serious about the use of steam power, and about the extraction of coal, standardized monetary systems, based on serially issued bank notes, made their appearance during the late 18th century. At the end of the 19th century, as natural oil and gas entered the scene, their ascent closely coincided with final developments in the establishment of corporate structures in business. Once again, as if by accident, said developments consisted very largely in standardizing the financial instruments serving to trade shares in the equity of industrial companies. Presently, as we face the growth of electronics, the first technology ever to grow in complexity at an exponential pace, we can observe both an unprecedented supply of official currencies money – the velocity of money in the global economy has descended to V < 1 and it becomes problematic to call it a velocity – and nothing less than an explosion of virtual currencies, based on the Blockchain technology. Interestingly, each of those historical moments marked by the emergence of both new technologies, and new financial patterns, was associated with new political structures as well. The constitutional state that we know seems to have grown by big leaps, which, in turn, took place at the same historical moments: 12th – 13th century, 18th century, 19th century, and right now, as we are facing something that looks like a shifting paradigm of public governance.

Thus, historically, it is possible to associate these four streams of phenomena: demographic growth, deep technological changes as regards the absorption and use of energy, new patterns of using financial markets, and new types of political structures. Against this background of long duration, the latest developments are quite interesting, too. In 2007 – 2008, the market of renewable energies displayed – and this seems to be a historical precedent since 1992 – a rate of growth superior to that observable in the final consumption of energy as a whole. Something changed, which triggered much faster a quantitative change in the exploitation of renewables. Exactly the same moment, during the years 2007 – 2008, a few other phenomena coincided with this sudden surge in renewable energies. The supply of money in the global economy exceeded the global gross output, for the first time in recorded statistics. Apparently, for the first time in history, one average monetary unit, in the global economy, finances less than one unit of gross output per year. On the side of demography, the years 2007 – 2008 marked a historical threshold in urbanisation: the urban population on our planet exceeded, for the first time, 50% of the total human headcount. At the same moment, the average food deficit, i.e. the average deficit of kilocalories per day per capita, in our civilisation, started to fall sharply below the long-maintained threshold of 131 kcal, and presently we are at a historical minimum of 88,4 kcal. Those years 2007 – 2008, besides being the moment when the global financial crisis erupted, marked a significant turn in many aspects of our collective, global life.

Thus, there is the secular perspective of change, and the recent breakthrough. As a scientist, I mostly ask two questions, namely ‘how?’ and ‘what happens next?’. I am trying to predict future developments, which is the ultimate purpose of any theory. In order to form a reliable prediction, I do my best to understand the mechanics of the predicted change.

Chapter I (or wherever it lands in the final manuscript) The first puzzlement: energy and population

The first scientific puzzlement addressed in this book refers to the most recent research by the author. The research in question was oriented on explaining the role of renewable energies in the sustenance of our civilisation, and it was very much inspired by a piece of information the author had read in Fernand Braudel’s masterpiece ‘Civilisation and Capitalism’ (Braudel 1981[2]). According to historical accounts, based on the official documents of the Habsburg Empire, in the author’s home region, Lesser Poland, known as Austrian Galicia under the Habsburg rule, at the end of the eighteenth century, there was one water mill, on average, per 382 people. The author’s home town, Krakow, Poland, sustains a population of 800 000, which would correspond to 2094 water mills. Said watermills are significant by their absence. Since I had learnt about this little fact, reading Fernard Braudel’s monumental work in summer 2015, I have gradually become quasi-obsessed with the ‘what if?’ question: what if today we had those 2094 water mills in my home city? What would our life look like? How different would it be from the world we are actually living? This gentle obsession crystallized into a general theoretical question: can renewable energies sustain the present human population? This generality found a spur in the reading of statistics pertaining to renewable energies. In 2007 – 2008, the rate of growth in the market of renewable energies changed, and became higher than the rate of growth in the overall, final consumption of energy. This change in trends is observable on the grounds of data published by the World Bank, regarding the consumption of energy per capita (https://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE ), and the share of renewable energies in that overall consumption (https://data.worldbank.org/indicator/EG.FEC.RNEW.ZS ). This change of slope was something of a historical precedent since 1990. In 2007 – 2008, something important happened, and still, to the author’s knowledge, there is no research explaining what that something could possibly have been. Some kind of threshold has been overcome in the absorption of technologies connected to renewable energies.

As the author connected those two dots – the historical facts and the recent ones – the theoretical coin started dropping. If we want to understand the importance of renewable energies in our civilisation, we need to understand how renewable energies can sustain local populations. That general intuition connected with the theoretical contribution of the so-called ‘new economic geography’. In 1998, Paul Krugman referred to models, which allow construing spatial structures of the economy as general equilibriums (Krugman 1998[3]). Earlier work by Paul Krugman, dating from 1991 (Krugman 1991[4]) supplied a first, coherent, theoretical vehicle for the author’s own investigation. The role of renewable energies in any local, human community is possible to express as aggregate utility derived from said energies. Further reflexion led to a simple observation: the most fundamental utility we derive from any form of energy is the simple fact of us being here around. The aggregate amount of utility that renewable energies can possibly create is the sustenance of a given headcount in population. In this reasoning, a subtle tension appeared, namely between ‘any form of energy’ and ‘renewable energies’. An equation started to form in the author’s mind. On the left side, the size of the population, thus the most fundamental, aggregate utility that any resource can provide. On the right side, the general construct to follow was that suggested by Paul Krugman, which deserves some explanation at this point. We divide the whole plethora of human activity, as well as that of available resources into two factors: the principal, differentiating one, and the secondary, which is being differentiated across space. When we have a human population differentiated into countries, the differentiating factor is the political structure of a country, and the differentiated one is all the rest of human activity. When we walk along a busy commercial street, the factor that creates observable differentiation in space is the institutional separation between distinct businesses, whilst labour, capital, and the available urban space are the differentiated ones. In the original model by Paul Krugman, the final demand for manufactured goods – or rather the spatial pattern of said demand – is the differentiating factor, which sets the geographical frame for the development of agriculture. The fundamental mathematical construct to support this reasoning is as in equation (1):

  • (1)         U = A*F1µ*F21-µ        µ < 1

…where ‘U’ stands for the aggregate utility derived from whatever pair of factors F1 and F2 we choose, whilst ‘A’ is the scale factor, or the proportion between aggregate utility, on the one hand, and the product of input factors, on the other hand. This mathematical structure rests on foundations laid 63 years earlier, by the seminal work by Prof Charles W. Cobb and Prof Paul H. Douglas (Cobb, Douglas 1928[5]), which generations of economists have learnt as the Cobb-Douglas production function, and which sheds some foundational light on the author’s own intellectual path in this book. When Charles Cobb and Paul Douglas presented their model, the current economic discourse turned very much around the distinction between nominal economic change and the real one. The beginning of the 20th century, besides being the theatre of World War I, was also the period of truly booming industrial markets, accompanied by significant changes in prices. The market value of any given aggregate of economic goods could swing really wildly, whilst its real value, in terms of utility, remained fairly constant. The intuition behind the research by Charles Cobb and Paul Douglas was precisely to find a way of deriving some kind of equilibrium product, at the macroeconomic scale, out of the observable changes in industrial investment, and in the labour market. This general intuition leads to find such a balance in this type of equation, which yields a scale factor slightly above 1. In other words, the product of the input factors, proportioned in the recipe with the help of logarithms construed as, respectively, µ < 1, and 1-µ, should yield an aggregate utility slightly higher than the actual one, something like a potential to exploit. In the original function presented by Cobb and Douglas, the scale factor A was equal to 1,01.

Investigating the role of renewable energies in the sustenance of human populations led the author to experiment with various input variables on the right side of the equation, so as to have the consumption of renewable energies as input no. 1, something else (we are coming to it) as input no.2. The exploratory challenge was, firstly, to find the right variables, and then the right logarithms to raise them to, in order to obtain a scale factor A slightly above one. The basic path of thinking was that we absorb energy from environment in two essential forms: food, and everything else, which, whilst non-edible, remains useful. Thus, it has been assumed that any human community derives an aggregate utility, in the form of its own headcount, to be subsequently represented as ‘N’, out of the use ‘E’ of non-edible energies (e.g. fuel burnt in vehicles or electricity used in house appliances), and out of the absorption as food, further symbolized as ‘F’.

Thus, we have two consumables – energy and food – and one of the theoretical choices to make is to assign them logarithms: µ < 1, and 1-µ. According to the fundamental intuitions of Paul Krugman’s model from 1991, there are two paths to follow in order to find the dominant factor in the equation, i.e. the differentiating one, endowed with the logarithm µ <  1. The first path is the actual, observable change. Paul Krugman suggested that the factor, whose amount of input changes faster than the other one, is the differentiator, whilst the one displaying slower a pace of change is being differentiated. The second path pertains to the internal substitution between various goods (sub-inputs) inside each of the two big input factors. The new economic geography suggests that the capacity of industrial facilities to shape the spatial structure of human settlements comes, to a great extent, from the fact that manufactured goods have, between them, much neater a set of uses and mutual substitution rates than agricultural goods. Both of these road signs pointed at the use of non-edible energies as the main, differentiating factor. Non-edible energies are used through technologies, and these have clearly cut frontiers between them. A gasoline-based combustion engine is something different from a diesel, which, in turn, is fundamentally different from a power plant. The output of one technology can be substituted, to some extent, to the output of another technology, with relatively predictable a rate of substitution. In comparison, foodstuffs have much foggier borderlines between them. Rice is rice, and is part of risotto, as well as of rice cakes, rice pasta etc., and, in the same time, you can feed your chicken with rice, and thus turn the alimentary value of rice into the alimentary value of meat. This intricate scheme of foods combining with each other is made even more complicated due to idiosyncratic culinary cultures. One pound of herring trades against one pound of pork meat differently in Alaska and in Lebanon. As for the rate of change, technologies of producing food seem changing at slower a pace than technologies connected to the generation of electricity, or those embodied in combustion engines.

Thus, both paths suggested in the geographic model by Paul Krugman pointed at non-edible energies as the factor to be endowed with the dominant logarithm µ < 1, leaving the intake of food with the residual logarithm ‘1 – µ’. Hence, the next step of research consisted in testing empirically the equation (2):

  • (2)         N = A*Eµ*F1-µ        µ < 1; A > 1

At this point, the theoretical model had to detach itself slightly from its Cobb-Douglas-Krugman roots. People cluster around abundance and avoid scarcity. These, in turn, can be understood in two different ways: as the absolute amount of something, like lots of food, or as the amount of something per person. That distinction is particularly important as we consider established human settlements with lots of history in their belt. Whilst early colons in a virgin territory can be attracted by the perceived, absolute amount of available resources, their distant ancestors will care much more about the availability of those resources to particular members of the established community, thus about the amount of resources per inhabitant. This principle pertains to food as well as to non-edible energies. In their early days of exploration, entrepreneurs in the oil & gas industry went wherever they could find oil and gas. As the industry matured, the daily yield from a given exploitation, measured in barrels of oil, or cubic meters of gas, became more important. This reasoning leads to assuming that quantities of input on the right side in equation (2) are actually intensities per capita in, respectively, energy use and absorption of food, rather than their absolute volumes. Thus, a mutation of equation (2) is being posited, as equation (3), where:

(3)                        N =A*[(E/N)µ]*[(F/N)1-µ]          µ < 1; A > 1

[1] Charles W. Cobb, Paul H. Douglas, 1928, A Theory of Production, The American Economic Review, Volume 18, Issue 1, Supplement, Papers and Proceedings of the Fortieth Annual Meeting of the American Economic Association (March 1928), pp. 139 – 165

[2] Braudel, F., 1981, Civilization and Capitalism, Vol. I: The Structures of Everyday Life, rev.ed., English Translation, William Collins Sons & Co London and Harper & Row New York, ISBN 00216303 9, pp. 341 – 358

[3] Krugman, P., 1998, What’s New About The New Economic Geography?, Oxford Review of Economic Policy, vol. 14, no. 2, pp. 7 – 17

[4] Krugman, P., 1991, Increasing Returns and Economic Geography, The Journal of Political Economy, Volume 99, Issue 3 (Jun. 1991), pp. 483 – 499

[5] Charles W. Cobb, Paul H. Douglas, 1928, A Theory of Production, The American Economic Review, Volume 18, Issue 1, Supplement, Papers and Proceedings of the Fortieth Annual Meeting of the American Economic Association (March 1928), pp. 139 – 165