My most fundamental piece of theory

My editorial

I am returning to what seems to be my most fundamental piece of theory, namely the equilibrium between population, food and energy, or N = A*(E/N)µ*(F/N)1-µ, where N represents the headcount of local population, E/N stands for the consumption of energy per capita, F/N is the intake of food per capita, whilst ‘A’ and ‘µ’ are parameters. I am taking on two cases: United Kingdom, and Saudi Arabia. In United Kingdom, the issue of population, and more specifically that of immigration, has recently become a much disputed one, in the context of what is commonly called ‘Brexit’. In Table 1, below, you can find, first of all, the two types of ‘model population’ computed with the equation specified in my article ‘Settlement by Energy – Can Renewable Energies Sustain Our Civilisation?’. Thus, columns [2] and [3] provide that model size of population, in millions of people, computed on the grounds of constant alimentary intake equal to F/N = 1 219 100 kcal per person per year. More specifically, this particular variable was used in mega-calories per person year, thus F/N = 1219,1 Mcal per person per year. We have here one of the best fed populations on Earth. This factor is being combined with the current consumption of energy per capita, in tons of oil equivalent per person per year, as published by the World Bank. Column [2] provides the model size of population calculated as model(N) = (Energy consumption per person per year)0,52*(1219,1)1-0,52=0,48. For the sake of presentational convenience, let’s call it ‘Energy-based population’. Column [3] takes on the same logic, but introduces, as an estimate of the (E/N) variable, just the consumption of renewable energy per person per year, once again in tons of oil equivalent, and using the equation model(N) = (Renewable energy consumption per person per year)0,3*(1219,1)1-0,3=0,7.  This type of model population is going to be labelled ‘Renewables-based population’. Column [4] provides the real, current headcount of British population each year, and column [5] gives the estimation of net migration (immigration minus emigration), in a snapshot every five years. The ‘energy-based population’ starts, in 1990, slightly above the real one, with 3,597 tons of oil equivalent being consumed, on average, by one resident, per year, in the beautiful homeland of Shakespeare and The Beatles. That model population follows ascending trend, just as the real one, until 2003. Over that period of time, i.e. between 1990 and all through 2003, energy use per capita had been climbing, in a slightly hesitant manner, up to 3,732 tons of oil equivalent. The real headcount increased, during that period, by 2,58 millions of people, whilst the ‘energy-based’, model population climbed by 1,14 million. Starting from 2004, the British population starts saving energy. In 2013, its average consumption was of 2,978 tons of oil equivalent per capita. The real population has increased, since the last checkpoint in 2003, by 5,25 millions of people. Yet, the ‘energy-based’ population has decreased by 7,1 million people, conformingly to its underlying equation. Saving on the final consumption of energy, which really took place in United Kingdom, reduces the theoretically sustainable demographic base. The reader could say: this is not an equilibrium, if the model population matches the actual one just in a few years over the whole period since 1990 through 2013. Still, if you compute the average proportion (i.e. average over 1990 – 2013) between the real population, and the ‘energy based population’, like ‘real one divided by the energy-based one’, that average proportion is equal to A = 1,028560563. Quite a close match on the long run, isn’t it? This close match decomposes into two distinct phases. The first phase is that of increasing, energy-based sustainability of the population. The second one is the process of growing discrepancy between the real headcount, on the one hand, and what is sustainable in ‘energy-based’ terms, on the other hand.

Now, let’s have a look at column [3], thus at the model population based just on the consumption of renewable energy, alimentary intake held constant. This model population follows a different trend. In 1990, when my observation starts, and when the average resident of United Kingdom consumes, on average, just 0,02 tons of oil equivalent in renewable energy per year. At the time, the ‘renewables-based population’ is way below the real one, more specifically 10,37 million below. At my second checkpoint, in 2003, consumption of renewable energy in the UK doubles, up to 0,04 tons of oil equivalent per year per person. The ‘renewable-based’ population, in 2003, with 53,4 million people, is still below the real one by 6,45 million. In 2013, at my final checkpoint, the situation reverses. With 0,18 tons of oil equivalent per capita per year, in terms of renewable energy consumed, the ‘renewables-based’, model population of Britain makes 85,83 million, 21,5 million more than the real one. Interestingly, the ‘renewables-based’, model population started soaring up by 2007 – 2008, precisely when the global consumption of renewable energies started to grow really fast. Once again, some readers could have the legitimate doubt whether a model yielding that much difference is any kind of equilibrium. I had the same doubts when doing these maths, and the result surprised me. Over the whole period of 1990 – 2013, the ratio of real population divided by the ‘renewables-based’ one was A = 1,028817158, i.e. up to the third decimal point it is the same proportion as the one between the ‘energy-based’ population and the real one. I know that, at this point, it would be very easy to enter the tempting world of metaphysics. If the proportion between my femur and my humerus is X, and I find a piece of driftwood, which, compared to my femur, makes the same proportion, that piece of wood can easily become the fossilized bone of my distant ancestor etc. What holds me (relatively) close to real life is the fact that the recurrent proportion in question is the outcome of two equations with different input data and different values in parameters, and still with the same essential structure. This, in turn, makes me think that what I have found out are two processes, which make some kind of undertow in the country under scrutiny, i.e. United Kingdom in this precise occurrence. Being more and more profuse on the overall consumption of energy made the sustainable demographic base of UK swell, up to 2003, and then the fact of getting meaner on energy per capita contributed to make this demographic base less and less sustainable. In parallel, the systematic increase in the consumption of renewable energies consistently pumped up the demographic sustainability of the UK. Why am I talking about two distinct processes? Well, saving energy per capita means, essentially, more efficiency in using engines of all kinds, as well as high-power electronics (like big servers). On the other hand, shifting towards renewable energies is, respectively, one step and two steps upstream, in the chain of transformation. This type of change pertains essentially to trading combustion engines for electric ones, and switching the generation of electricity from fossil fuels to wind, water, sun etc.

At this point, my theoretical stance fundamentally differs from what the reader could find, for example, with the Club of Rome (see, for example: Meadows et al. 1972[1]). I develop a theoretical approach, where we, humans, are inherently prone to maximized our total intake of energy from environment. Those local equilibriums between population, food and energy mean that any such local population can be represented as a super-organism, absorbing energy, like one of those Australian, saltwater crocodiles, which grow up to the limits offered by their habitat, and there is no question of stopping before reaching those limits. The otherwise highly respectable, intellectual stance of the Club of Rome amounts to saying that we have to save energy in order to survive. I say that if this is the only way for us, humans, to survive, we can just as well start packing. The simple, straightforward saving of energy is simply not what we do. You could ask a white shark to turn vegan. Guess the result. On the other hand, what we can do is to change our technological base so as to have the same or greater an amount of directly consumable energy (motor power, heat, and functionality in our electronics) out of less burdening a basket of primary energies. The reader could object: “But the average resident of United Kingdom did save energy between 2003 and 2013”. Yes, they did, and their sustainable demographic shrunk accordingly. The robustness of any reasoning about demographics can be verified with data on net migration. Whatever I could calculate as the ‘demographic base’ of a country, the net inflow (or net outflow) of people in a given time and place is a sure indicator of how attractive said place is. Column [5] in table 1 provides the data published by the World Bank. These are snapshots, taken every five years: 1992, 1997, 2002, 2007, and 2012. At each of these checkpoints, net migration is way above the net increase in population. It means that immigrants are filling a space left by the otherwise shrinking domestic population. The place is becoming so attractive for newcomers that an effect of demographic crowding out is to notice.

As we move to the right, in table 1, column [6] introduces the ratio of fixed capital stock per one resident patent application. The reader can notice an almost continuous growth in this variable between 1990 and 2013. In terms of the theoretical stance I am developing in my research, that growth means an almost continuous change in the evolutionary function of selection between the incoming, new technologies. We can see a case of fixed capital accumulating faster than the capacity to create patentable invention. The female capitalist structures in the economy of United Kingdom are systematically increasing their capacity to absorb and recombine inventions. That means stronger incentives to invest in the development of new, technologically advanced businesses (the female, capitalistic function), which, in turn, creates an absorptive process: the capitalist structures are, in a sense, hungry for innovation. As the process unfolds, the growing, average amount of fixed assets per one patent application alleviates the pressure, on each individual invention, to be the toughest and the meanest dog in the pack. This, in turn, can be interpreted as lesser a pressure towards hierarchy-forming, in patentable invention, and stronger a pressure towards networking between inventions. One more step to the right side of table 1 brings into our focus the data on aggregate depreciation in fixed assets, as a fraction of the Gross Domestic Product; this is column [7]. We can observe some sort of waving cycle there: increase between 1990 and 1995, then a swing down the scale, between 1996 and 2003, just to give rise another surge, between 2004 and 2013. Growing values in the ratio of physical capital per one patent application seem to produce a cyclical stir in the depreciation of fixed assets. It is reasonable to assume that the pace of physical wear and tear is pretty constant over time, and the changing burden of amortizing fixed assets comes from moral obsolescence, thus from the pace of technological change. That pace of obsolescence, although displaying a tendency to cyclical change, follows an overall ascending trend. The more capital per one patent application, thus the less hierarchy and the more networking among patentable inventions, the greater the burden of technological change on the current aggregate income. A last step to the right, in table 1, leads to column [8], which provides information about the supply of money in the British economy, as a % of the GDP. Another wavy cycle can be noticed, which eventually leads to very high a supply of money, and very low a velocity in said money. Quick pace of technological change brings about the necessity, in the monetary system, to produce a growing number of alternative algorithms of response. That period between 1990 and 2013 shows quite well, how monetary systems can very literally learn to respond. At first, between 1990 and 1993, the monetary system responds, to an accelerating obsolescence in established technologies, by increasing the velocity of money. Starting from 1994, a different mechanism turns on: instead of increasing the velocity of circulation, the monetary system just accumulates monetary balances. It is accumulating monetary resources in reserve, or, in the lines of the Keynesian theory, it is accumulating speculative positions. In the presence of increasing uncertainty as for the actual lifecycle of our average technology, we build up the capacity to react pretty quickly (money allows such quick reaction) to any further technological change.

Table 1 – Selected data regarding United Kingdom

Year Model population, millions, based on energy consumption in general Model population, millions, based on the consumption of renewable energy Real population, millions Net migration, headcount Capital stock per one patent application, at current PPPs (in mil. 2011US$ Aggregate depreciation of fixed assets, as % of the GDP Supply of broad money, as % of the GDP
[1] [2] [3] [4] [5] [6] [7] [8]
1990 58,94 46,89 57,26   185,48 0,116 0,85
1991 59,88 46,37 57,42   191,39 0,124 0,821
1992 59,68 51,00 57,58 205443 201,54 0,13 0,565
1993 59,92 49,89 57,74   213,04 0,135 0,561
1994 60,08 54,27 57,90   232,57 0,145 0,574
1995 60,05 54,87 58,08   246,71 0,148 0,615
1996 61,30 53,62 58,26   270,95 0,147 0,66
1997 60,32 54,51 58,46 498998 281,41 0,139 0,788
1998 60,54 54,62 58,66   261,31 0,133 0,912
1999 60,51 53,28 58,87   236,04 0,124 0,914
2000 60,53 53,51 59,08   232,87 0,116 0,959
2001 60,52 51,98 59,30   242,77 0,113 1,006
2002 59,69 53,64 59,55 968350 251,42 0,109 1,01
2003 60,07 53,40 59,85   260,60 0,107 1,046
2004 59,76 56,35 60,21   302,57 0,109 1,094
2005 59,69 59,43 60,65   368,38 0,114 1,178
2006 58,95 61,36 61,15   407,57 0,119 1,274
2007 57,60 63,74 61,69 2030075 433,89 0,124 1,403
2008 56,89 68,72 62,22   512,68 0,137 1,617
2009 54,96 71,41 62,72   565,24 0,156 1,664
2010 55,68 76,37 63,16   643,84 0,173 1,672
2011 53,32 78,96 63,57   635,67 0,167 1,543
2012 53,89 81,20 63,96 990000 690,89 0,174 1,512
2013 53,42 85,83 64,33   777,86 0,178 1,486

Source: World Bank, Penn Tables 9.0

The case of United Kingdom is that of a relatively well fed society, which increases its demographic sustainability by shifting its technological base towards renewable energies. Presently, we can have a look at completely different a socio-economic environment: Saudi Arabia. Saudi Arabia is one of those countries, which seem to present a huge potential for socio-economic change, at the condition of increasing the use of renewable energies. In terms of the evolutionary selection function regarding new technologies, Saudi Arabia is a land of peace: the ratio of physical capital per one resident patent application is counted in dozens of billions of US dollars. Still, there seems to be more and more agitation in the backstage: this ratio, although very high, had been cut by seven between 1990 and 2013. There is a sneaky snake in that Eden garden. On the top of that, Saudi Arabia is one of those interesting societies with just a slight food deficit per capita: enough to make people alert, not enough to push them into the apathy of deep, chronical hunger. The average alimentary intake per capita, in Saudi Arabia, from 1990 through 2013, had been of F/N = 1087,7 mega calories per year. Table 2, below, provides the same type of quantitative profiling regarding Saudi Arabia as has been presented for United Kingdom. Whilst in the latter case, we deal with a population that had increased its headcount by some 11% between 1990 and 2013, Saudi Arabia presents completely different a calibre of demographic change: plus 83% during the same period. With this magnitude of demographic growth, the social structure in 2013 was likely to be very different from that in 1990. Interestingly, the final consumption of energy per capita per year had increased almost by the same gradient as population, i.e. by 79,5%. Even more interestingly, the ‘energy-based’, model population in Saudi Arabia, calculated with the empirical function model(N) = (Energy consumption per capita)0,72*(1087,7)1-0,72=0,38, never reaches that magnitude, although, on the long run, it is matched by the real population by the scale factor A = 1,026310231. The ‘energy-based’ population grows, over the whole window of observation, just by 52,4%. It is a good example of how the alimentary base of a society works. In comparison to United Kingdom, this base is just 10,8% thinner, and, in spite of almost doubling the absorption of non-edible energy, Saudi Arabia has trouble to develop a sustainable demographic base.

Saudi Arabia is one of those countries, where the absorption of renewable energies per capita had been consistently shrinking in our window of observation, from 1,35 kilograms of oil equivalent per year per capita, in 1990, to barely 0,41 kilograms in 2013.   The second version of model population, the ‘renewables-based’ one, computed as model(N) = (Renewable energy consumption per capita)0,27*(1087,7)1-0,27=0,73, had shrunk from 27,64 million in 1990, to 19,99 million in 2013. Let’s rephrase it, in order to grasp the phenomenon under scrutiny. With the amount of energy that the average Saudi resident consumed per capita in 1990, the country had a sustainable demographic base. Still, with the long-run alimentary intake at 1087,7 mega calories per year per person, the present population, exceeding 30 million people, is hardly sustainable, even with the soaring consumption of energy. Going back to 1990, once again, the amount of renewable energies consumed at the time, other variables held constant, could sustain a population much larger than the 16,89 million recorded in 1990. With the present consumption of renewables, the present population of Saudi Arabia looks anything but sustainable. As we have a look at net migration in Saudi Arabia (column [5] in table 2), a puzzling tendency appears: as long as the local population was robustly sustained by its energy consumption, the balance on migration was negative. When the local population started to drop wheels off its sustainable base, the balance on migration turned positive. Illogical? Maybe, and this is precisely why it is an intellectual challenge, and why I am trying to sort out my first puzzlement, regarding local equilibriums between population, food, and energy. A quick comparison with United Kingdom shows two, completely different paradigms of social change. In United Kingdom, the abundance of food allowed smooth shift towards renewable energies, so as to keep the place highly attractive in spite of saving on the overall energy consumption. In Saudi Arabia, with just slightly lower an alimentary intake, and highly problematic sustainability in population, domestic demographic growth stays way above the net migratory inflow.

Let’s have a look at technological change in Saudi Arabia. First, by having a look at column [7] in table 2, we can see that the relative burden of depreciation, i.e. of obsolescence in established technologies, is close to what is observable in United Kingdom. Thus, the basic pace of technological change can be assumed as nearly identical. Still, the economic system reacts to that change exactly in the opposite way to that observable in United Kingdom. At the starting point of our observation, in 1990, the Saudi economy is extremely abundant in physical capital, when denominated in resident patent applications (column [6]), and rather mean on money. In terms of my theory, it means very little competition between patentable inventions, very little hierarchy among them, and very little algorithms of response in the monetary system. As time passes, and as technological change speeds up (the share of depreciation in the GDP grows), the amount of physical capital per one patent application dramatically shrinks. It means increased effort in research and development, and quickly growing a competition, as well as quickly forming a hierarchy, between all those new inventions. Still, by comparison to the British monetary system, the Saudi one is far from being profuse. Not much is happening in terms of algorithms of response, as well as in terms of speculative positions, as regards the supply of money. In the presence of very nearly the same pace of technological change, and similar gradient of change in that pace, those two economic systems – United Kingdom and Saudi Arabia – develop completely different responses. United Kingdom gives some loose to its hierarchy of inventions, and to the competition between them, and adds a lot of liquidity in its monetary system. Saudi Arabia spurs competition between inventions, and barely adds to the supply of money. Of course, a lot of factors make the difference between those two societies: religion, institutions, historical track, natural resources, climate etc. Still, in terms of the theory I am forming, one difference is sharp like a razor: the difference in food base. United Kingdom has a secure, slightly superfluous alimentary regime, whilst Saudi Arabia is just below satiety. Can this single factor be the ultimate distinction, explaining all the other economic differences? My empirical findings strongly suggest that the answer is ‘yes’, and what I am trying to do now is to go more in depth of that distinction.

Table 2 Selected data regarding Saudi Arabia

Year Model population, millions, based on energy consumption in general Model population, millions, based on the consumption of renewable energy Real population, millions Net migration, headcount Capital stock per one patent application, at current PPPs (in mil. 2011US$ Aggregate depreciation of fixed assets, as % of the GDP Supply of broad money, as % of the GDP
[1] [2] [3] [4] [5] [6] [7] [8]
1990  17,62  27,64  16,89  75 767,78  0,13  0,43
1991  19,21  28,29  17,40    45 179,69  0,13  0,44
1992  20,66  25,37  17,89 -110000  58 512,83  0,12  0,43
1993  20,80  23,10  18,37    60 291,97  0,13  0,46
1994  21,16  27,96  18,85  39 192,54  0,14  0,46
1995  20,86  26,55  19,33    47 465,66  0,14  0,45
1996  21,52  20,58  19,81  49 895,93  0,13  0,44
1997  20,43  19,83  20,30 -350000  24 239,44  0,13  0,44
1998  21,01  20,44  20,83  31 785,39  0,14  0,52
1999  20,90  20,22  21,39    20 603,36  0,13  0,50
2000  21,17  20,14  22,01  20 231,88  0,12  0,45
2001  21,13  20,89  22,67    34 545,11  0,13  0,48
2002  22,27  20,79  23,36 730000  26 811,98  0,13  0,54
2003  21,98  20,44  24,06    30 481,69  0,13  0,51
2004  22,50  20,36  24,75  22 634,09  0,13  0,50
2005  22,41  20,07  25,42    16 913,35  0,12  0,45
2006  23,67  20,78  26,08  19 550,01  0,13  0,47
2007  23,79  20,30  26,74 995000  20 713,69  0,15  0,51
2008  25,28  20,24  27,41  n.a.  0,14  0,48
2009  25,98  20,29  28,09    n.a.  0,18  0,65
2010  27,57  20,09  28,79  12 904,10  0,17  0,55
2011  26,31  20,22  29,50    12 386,98  0,16  0,49
2012  28,14  20,42  30,20 1590000  n.a.  0,16  0,52
2013  26,85  19,99  30,89    10 065,90  0,18  0,56

Source: World Bank, Penn Tables 9.0

I am consistently delivering good, almost new science to my readers, and love doing it, and I am working on crowdfunding this activity of mine. You can consider going to my Patreon page and become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

[1] Donella H. Meadows, Dennis L. Meadows, Jorgen Randers, William W. Behrens III, 1972, The Limits to Growth. A report for The Club of Rome’s Project on the Predicament of Mankind, Published in the United States of America in 1972 by Universe Books, 381 Park Avenue South, New York, New York 10016, © 1972 by Dennis L. Meadows, ISBN 0-87663-165-0

My individual square of land, 9 meters on 9

My editorial

And so I am building something with a strategy. Last year, 365 days ago, I was just beginning to play with scientific blogging. Now, I have pretty clear a vision of how I want to grow over the next 365 days. My internal bulldog is sniffing around two juicy bones: putting up a method of and pitching a product, relevant to the teaching of social sciences by participation in the actual doing of research, and, on the other hand, putting together an investment project in the domain of smart cities. In this update, I start developing more specifically on that second one, and I focus on two things. Firstly, I perceive smart cities as both technological and social a change, which develops through diffusion of innovation. Very nearly axiomatically, the phenomenon of diffusion in innovations is represented as a process tending towards saturation. I want to find a method, and, hopefully, the metrics relevant to measuring the compound size of the market in the phenomenon called ‘Smart Cities’, mostly in Europe. In the same time, I want to test the tending-towards-saturation approach in forecasting the size of this market.

The emergence of smart cities, as both an urban concept and a business model, is made of smaller parts. There is investment in the remodelling and rebuilding of infrastructure. On the other hand, there is the issue of energy, both in terms of efficiency in its use, and in terms of its renewable sourcing. Finally, there is the huge field of digital technologies, and, looming somehow at the horizon, the issue of Fintech: the use of digital technologies to create local, flexible monetary systems. I am collecting data, step by step, to acquire a really sharp view of the situation, and so my internal curious ape comes by that report ‘The State of European Cities’ , as well as by that article ‘Smart Cities in Europe’ , and finally it swings to that interesting website: ‘Organicity’ . There seem to be two common denominators to all the reports and websites on this topic: experimentation and teaming up. Cities build their smart cities in consortiums rather than single-handedly. Each project is an experiment, to the extent that ‘established technologies’ are essentially the opposite of what business people expect to invest in when they invest in a smart city.

When I teach my students the fundamentals of business planning, I ask them frequently to look at the business concept from two sides: that of the enthusiastic founder, and that of a conservative investor. The balance sheet of the new business is likely to take shape at the intersection of those two approaches. I am adopting the same approach with my business concept. If I were a truly conservative an investor, I would ask, among other questions, what type of business am I supposed to put capital into, and what is the workable business model. The main types of business that come to my mind, regarding smart cities, are: development of real estate, construction, and technical services. However smart a city is becoming, it is made of architectural structures: buildings, roads, rails etc. Someone owns them before the smart city starts burgeoning, and someone owns them when the smart city is already running. Question: are the someones who own those structures afterwards the same someones who owned them beforehand, or are they different someones? What does the transfer of property in real estate look like in those smart cities? Another thing that I teach my students is ‘When you know nearly nothing about a market or a business, look at the prices and the demographics in the first place. Is the market conflating with people, is it stationary, or is it deflating? Are there any prices, which you can qualify as equilibrium prices, i.e. prices virtually exogenous to the bargaining power of individual market players, and clearly sensitive to other economic variables? If you can spot such prices, what trends do they display?’. Right, so now, I am applying my wisdom for sale to my own plans, and I try to figure out those things for selected cases of smart cities, just to make my hand.

I have recently read a lot about a project of smart city, namely the ‘Confluence’ project in Lyon, France. The place is dear to my heart, as I spent quite a chunk of my youth in Lyon, and I am glad to return there, whenever I can. The Confluence Project is located in the 2nd district of Lyon, at what the locals call ‘Presqu’Ile’, i.e. ‘Nearly an Island’, and the confluence of two rivers: Rhone and Saone. From the bird’s view, it is like an irregular, triangular wedge, with its top pointing South at the exact confluence of the two rivers, and its base resting, more or less, on the Perrache rail station. I am having a look at the local prices of real estate. As I visit the website ‘Meilleurs Agents’  , I can see an almost uninterrupted growth in the price per 1 m2, since 1994. Surprisingly, even the burst of the housing bubble in 2007 – 2009 didn’t curb much that trend. Over the last 10 years, it means almost 31% more in the average price of square meter. I focus on the prices of flats. Right now, the average price in Lyon is 3 690 € per square meter, and that average is expected in a general span from 2 767 € to 5 535 €. Against this general background, I take a few snapshots at different addresses. First, I have a glance at a long street – Cours Charlemagne – which almost makes the longitudinal backbone of the Confluence wedge. The average price per 1 m2 is 3 783 €, in a range from 2 664 € to 5 040 €. That average is slightly higher than the whole city, but the range of prices has slightly lower extremities.

Cours Charlemagne connects the posh neighbourhood of Perrache, in the North, to really industrial a place, at the Southern junction of the two rivers. Thus, I take a closer focus, and I target those different environments. Angle of Quai Rambaud and Rue Suchet, a truly posh place in the Northern part of Confluence, displays an average price of 4 725 € per 1 m2, in a range from 3 186 € to 6 207 €. Yes, baby, it just rockets up. Now, I take a little stroll to the South, apparently advancing towards lower prices, and I call by Rue Paul Montrochet. It should be cheaper than up North, and yet it is not: the average price is 5 144 € per square meter, in a range from 3 461 € to 6 483 €.

As usually, observing reality has been of some value. Provisional hypothesis, based on the case of Lyon-Confluence: smart cities grow where the prices of real estate grow. Now, a bit of a bow to reverend Malthus: I check the demographics, with The World Population Review , and I show those numbers in Table 1, below. There has been, and there still is, quite a consistent demographic growth. Basically, if you calculate the annual average growth rates in, respectively, the price of 1 m2 in residential space, and the local population, those two rates look almost like twins: around 3% a year. My provisional hypothesis puts on some ornamentation: smart cities grow where the prices of real estate grow, and where population grows.

Table 1 The population of Lyon, France (urban area)

Year  Population Growth Rate (%) Growth
2030  1 814 000 3,72%  65 000
2025  1 749 000 3,98%  67 000
2020  1 682 000 2,81%  46 000
2017  1 636 000 1,68%  27 000
2015  1 609 000 3,74%  58 000
2010  1 551 000 3,68%  55 000
2005  1 496 000 3,67%  53 000
2000  1 443 000 2,78%  39 000
1995  1 404 000 2,48%  34 000
1990  1 370 000 2,54%  34 000
1985  1 336 000 4,54%  58 000
1980  1 278 000 8,49%  100 000
1975  1 178 000 5,56%  62 000
1970  1 116 000 8,67%  89 000
1965  1 027 000 13,61%  123 000
1960  904 17,71%  136 000
1955  768 5,06%  37 000
1950  731 0,00%  –

source: , last accessed January 11th 2018

The decision makers of the Lyon-Confluence project claim they are in some sort of agreement with two other initiatives: Vienna and Munich. I quickly perform the same check for Vienna as I did for Lyon. In this case, the initiative of smart city seems to be city-wide, and not confined to just one district. As for the prices of apartments, I start with the Global Property Guide . Apparently, the last six years brought a sharp rise in prices (plus 39%), still those prices started curbing down a bit, recently. A quick glance at Numbeo shows an average price of 7 017,18 € per 1 m2 in the city centre, in a range from 4 800 € to 10 000 €, and further out of the centre it makes like 3 613,40 € per square meter on average, comprised between 3 000 € and 5 000 €. On the whole, Vienna looks a shade more expensive than Lyon. Let’s check the demographics, once again with The World Population Review (Table 2, below). Quite similar to Lyon, maybe with a bit more bumps on the way. Interestingly, both initiatives of smart cities started to take shape around 2015, when both cities started to flirt with more or less 1,5 million people in the urban area. Looks like some sort of critical mass, at least for now.

Table 2 The population of Vienna, Austria (urban area)

Year Population Growth Rate (%) Growth
2030 1 548 000 0,98% 15 000
2025 1 533 000 2,06% 31 000
2020 1 502 000 2,32% 34 000
2017 1 468 000 2,09% 30 000
2015 1 438 000 6,28% 85 000
2010 1 353 000 7,89% 99 000
2005 1 254 000 4,33% 52 000
2000 1 202 000 -3,14% (39 000)
1995 1 241 000 1,89% 23 000
1990 1 218 000 -3,87% (49 000)
1985 1 267 000 -2,46% (32 000)
1980 1 299 000 0,23% 3 000
1975 1 296 000 0,15% 2 000
1970 1 294 000 10,13% 119 000
1965 1 175 000 10,85% 115 000
1960 1 060 000 13,25% 124 000
1955 936 12,64% 105 000
1950 831 0,00%

source: , last accessed January 11th, 2018

Good. As my internal curious ape turns and returns those coconuts, ideas start taking shape. At least one type of socio-economic environment, where that curious new species called ‘smart cities’ seem to dwell, is an environment where them growth rates in housing prices, and in population, are like 3% or more. One million and a half people living in a more or less continuous urban area seem to make like a decent size, in terms of feeding grounds for a smart city. Prices of residential real estate, associated with the emergence of smart cities in Europe, seem hitting like 4 500 € or more. This is probably just one type of environment, but one is already better than saying ‘any environment’. The longer I do social sciences, the more I am persuaded that we, humans, are very simple and schematic in our social structures. Theoretically, with the individual flexibility we are capable of, the science we have, and with Twitter, we could form an indefinitely diverse catalogue of social structures. Yet, it is more like in a chess game: there are just a few structures that work, and others just don’t, and we don’t even full comprehend the reasons for them not working at all. When we talk business and investment, there are some contexts that allow the deployment of a business model, whilst it just doesn’t work in other contexts. Same thing here: the type of environment I am casually sketching is the one where smart cities work in terms of business and investment.

My business plan for investing in smart cities has certainly one cornerstone, namely that of gains in the market value of real estate involved. One cornerstone is not bad at all, and now I am thinking about putting some stones under the remaining three corners. In that report which I mentioned earlier, namely report ‘The State of European Cities’ , I have already spotted two interesting pieces of information. Firstly, the sustainable density of population for a smart city is generally the same as for sustainable public transport: 3000 people per km2 or more. Secondly, the dominant trend in the European urbanisation is the growth of suburbs and towns, rather than cities strictly spoken. It pertains to my home country, Poland, as well. Thus, what we have as market, is a network of urban units moderate in size, but big in connections with other similar units. Two classes of business prospects emerge, then, regarding the investment in smart cities. Following my maths classes at school, I call those prospects, respectively, the necessary context, and the favourable context. The necessary is based on the density of population: the more we are per square kilometre, the more fun we are having, and the special kind of fun we can have in a smart city requires at least 3000 people per km2, or, in other words, each individual person having for their personal use no more than a square of 18 meters on 18. The favourable is made of real estate prices, and demographic growth, the former hitting above 4 500 € per 1 m2, and growing at 3% per annum, on average; the latter needs to make the same 3% a year.

By the way, I made a quick calculation for my family and our house. We live in a terraced house, located on a plot of land of 250 m2. We are three, which makes 83,6 m2 per capita, which, in turn, means that each capita has an individual square of land the size of 9,14 meters on 9,14. We are double the density of population required for a smart city. There is no other way: I have to go for it.

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

[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 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 ( ), and the share of renewable energies in that overall consumption ( ). 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

Stratégie fin 17ème , stratégie fin 18ème

Mon éditorial

Je suis en train de revoir mes notes de recherche (donc ce que j’avais écrit sur mon blog) et de les compiler en un livre. Voilà donc que je revoie deux mises à jour récentes (Quite abundant a walk of life et Countries never behave as they should ) et voilà (seconde fois) que je tombe sur quelque chose d’intéressant : la connexion entre la croissance du marché et l’opportunité pour innover. Je compare deux traités : « Le parfait négociant » de Jacques Savary, de 1675, et « La richesse des nations » d’Adam Smith, datant d’un siècle plus tard. Adam Smith, au milieu de la seconde moitié du 18ème siècle, dit fermement que les meilleures opportunités pour ce qu’il appelait « la division du travail » – et qui aujourd’hui voudrait dire l’innovation – se présentent dans les marchés qui croissent à une cadence relativement rapide. En revanche, Maître Savary, au milieu de la seconde moitié du 17ème siècle, était beaucoup plus enclin à voir des bonnes opportunités dans des marchés bien stables. Qu’est-ce qui eût changé le contexte de l’innovation si profondément in l’espace d’un siècle ?

Trois facteurs de différence viennent à mon esprit : la croissance démographique, la standardisation des systèmes monétaires, et la diversification des technologies. Les années 1670, c’était le temps quand une récession démographique profonde commençait à se faire remarquer un peu partout en Europe. Il avait fallu attendre les années 1760 pour voir un rebond dans la population. Vous pouvez trouver une description fascinante de ce processus de plusieurs décennies – quoi que c’est une histoire froide comme la finance dont elle parle – dans « La théorie de l’impôt » (1760) par Victor Riqueti, marquis de Mirabeau (oui, le même Mirabeau).

Donc, lorsque Jacques Savary écrivait, en 1675, que « cest une chose bien importante que dentreprendre des Manufactures, car il ny va pas moins que de la ruine des entrepreneurs, si elle nest pas conduite avec prudence et jugement », il faisait un croquis sur un fond de teint fait d’une population en déclin. Cette différence cardinale de contexte démographique se mariait d’une façon intéressante avec la diversité technologique. Durant la seconde moitié du 17ème siècle, l’industrie textile semble avoir été le secteur dominant, et de loin, en ce qui concerne l’innovation. Apparemment, à l’époque, inventer un tissu nouveau était l’équivalent de l’invention informatique aujourd’hui : un vrai cerveau, ça inventait un nouveau draguet pour les gens pauvres ou un nouveau ruban décoratif pour les riches. Notre guide dans les aléas de cette époque, Maître Savary, se vante lui-même d’avoir inventé, ainsi qu’avoir mis en marché, trois produits textiles différents, dont un – et voilà un petit bijou historique – était un ruban tissé en fil d’or et d’argent. En revanche, à la fin du 18ème , l’innovation prenait place un peu partout et, ce qui est un phénomène intéressant, elle prenait place dans le secteur financier, tout en contribuant à la standardisation financière. A l’époque, la finance, c’était en train d’inventer sa Ford Modèle T.

Voilà donc que j’arrive à ce troisième facteur : le pognon. Lorsque Maître Savary décrit les différentes stratégies de ce qu’il appelait « La Manufacture » – donc l’industrie – il préconise très clairement de se concentrer sur les étoffes bien établies dans le marché, qui ont « un cours ordinaire ». Cette notion de cours ordinaire reflète bien le fonctionnement des systèmes monétaires de l’époque : extrêmement diversifiés, basés très largement sur la circulation, par l’endossage, de la dette privée décentralisée. La plupart du monde d’affaires était basée sur un système des prix qui se croisait constamment avec le système des taux de change très fluide, y compris les taux de change des dettes privées provenant des sources diverses. Aussi bien dans le marché de vente que dans le marché d’achat, ce qu’on appelle aujourd’hui la politique de prix, dans le marketing mix, ressemblait plutôt au marché Forex moderne, mais avec plus de risque et avec une absence quasi-totale de ce que nous appelons, de nos jours, les valeurs-refuge (le franc suisse, tiens). La seconde moitié du 18ème siècle – les temps d’Adam Smith – c’était presque ennuyeux, par comparaison.

Voilà donc que nous arrivons à deux types de stratégies différentes en ce qui concerne l’innovation et le changement technologique. La stratégie « Fin 17ème » est celle qu’on pratique dans des marchés en déclin démographique, où la perte de vitesse en termes de population se traduit par un rétrécissement dramatique de la palette d’innovations possibles, ainsi que par un système monétaire où personne n’a vraiment d’intérêt à créer une circulation prévisible et à réduire le risque financier. D’autre part, je définis la stratégie « Fin 18ème », où une croissance démographique marquée, une innovation florissante et des systèmes monétaires qui croissent par standardisation. Bon, maintenant j’applique ça à ma petite obsession : les énergies renouvelables. Dans cet article que je viens de terminer , j’ai découvert un équilibre entre la population et la quantité d’énergies renouvelables par tête d’habitant. Il y a des pays, où l’importance des renouvelables pour l’équilibre démographique est extrêmement importante. Ce sont des cas aussi divers que l’Arabie Saoudite, Turkménistan, Botswana, Finlande ou la Lettonie. Là-bas, la population, ça semble être étroitement lié au marché d’énergies renouvelables. Par coïncidence, ce sont des pays avec des populations relativement stables et pas vraiment les plus grandes du monde. Intuitivement, j’associe leurs marchés d’énergies renouvelables avec la stratégie « Fin 17ème ». A l’extrémité opposée de l’échelle vous trouverez des pays comme la Chine ou l’Inde (mais aussi l’Ethiopie ou le Japon), où le marché des renouvelables semble avoir relativement peu de connexion avec le facteur population. Je pourrais être tenté de les associer avec la stratégie type « Fin 18ème » et en plus ça pourrait tenir pour les pays comme la Chine ou l’Inde, mais l’Ethiopie… Pas évident du tout. Là, je me sens comme dans un cul de sac. On va bien voir.

Ma formule magique marche dans certains cas, et pas tout à fait dans des cas autres que certains

Mon éditorial

Hier, dans ma mise à jour en anglais (consultez “Core and periphery” ), j’ai creusé un peu le modèle de différentiation spatiale d’une économie, plume Paul Krugman (Krugman 1991[1]). J’avais pris l’équation (1) de son modèle original – U = CMµ*CA1-µ – où U est l’utilité agrégée, CM est la production manufacturière, CA correspond à la production agriculturale et µ est la part prise par la production manufacturière dans la demande finale. Sur cette base, j’ai développé ma propre équation U(AE) = Wµ*F1-µ  µ < 1, où U(AE) est l’utilité agrégée dérivée de la consommation de l’énergie sous toutes ses formes possibles, W correspond à la consommation finale de l’énergie, F est la consommation de nourriture et µ est la part de la demande finale dépensée sur l’énergie. Cette transmutation de ma part avait été très intuitive et en y regardant de près, après fait, j’avais remarqué que les deux équations – l’originale de Paul Krugman et la transformée façon Wasniewski – suivent la même logique de base, celle de la fonction de production de Charles W. Cobb et Paul H. Douglas[2]. J’ai revu leur article et j’ai essayé d’appliquer leur méthode originale pour donner un peu de fond et de gravitas à ma transformation.

Vu l’hypothèse que je suis en train de vérifier – « la structure spatiale de la civilisation humaine s’adapte et se regroupe en vue de l’absorption maximale d’énergie » – je me suis dit que l’utilité agrégée de la consommation de l’énergie c’est tout simplement qu’il y ait du monde en un endroit donné, donc qu’il y ait une population sur un territoire. J’ai donc mis la variable de population sur le côté gauche de l’équation en posant formellement U(AE) = Pop. Ensuite, j’ai commencé à expérimenter avec le côté droit de l’équation : je prenais de différentes variables pertinentes à la consommation de l’énergie ainsi que celles qui correspondent à l’alimentation et je les testais façon Cobb – Douglas, donc « Population = a * (Energie, pouvoir µ) * (absorption alimentaire, pouvoir 1 – µ». Après maints essais, j’ai commencé à trouver une logique qui consiste, tout d’abord à utiliser, sur le côté gauche, la population en millions (donc 36 millions était juste 36). Sur le côté droit j’avais mis la consommation finale d’énergie par tête d’habitant, par an, mesurée tonnes d’équivalent pétrole, comme ma variable « Energie ». Je la symbolise, dans ce qui suit, comme « W/Pop ». Je l’avais élevée au pouvoir 0,75, donc je l’avais traitée exactement de la même façon que Charles W. Cobb et Paul H. Douglas eût traitée leur variable dominante. Comme variable correspondante à l’absorption alimentaire, donc la variable secondaire élevée au pouvoir 1 – 0,75 = 0.25,  j’ai utilisé une métrique publiée par FAO : l’absorption annuelle de nourriture en mégacalories par personne par an, moyenne sur la période 1990 – 2008, ou « A/Pop » dans ma notation de travail. Dans Table 1, ci-dessous, je présente les résultats du test de cette fonction « Pop = (W/Pop)0,75 * (A/Pop)0,25 » dans le cas de l’Argentine. Pourquoi Argentine ? Je n’en sais rien. Pourquoi pas ? Probablement c’est juste parce que l’Argentine est au tout début des listes alphabétiques.

Table 1 – Modèle « Pop = (W/Pop)0,75 * (A/Pop)0,25 » testé pour Argentine

Année Population modèle Population réelle Population réelle divisée par population modèle
1990 16,94515987 32,72974 1,931509662
1991 17,15400412 33,19392 1,93505375
1992 17,63123882 33,655149 1,908836319
1993 17,49698756 34,110912 1,949530563
1994 18,1568104 34,558114 1,903314142
1995 18,17673406 34,994818 1,925253343
1996 18,50330199 35,419683 1,914235795
1997 18,77977444 35,833965 1,908114771
1998 19,09688338 36,241578 1,897774484
1999 19,18104255 36,648054 1,910639315
2000 19,19068218 37,057453 1,931012803
2001 18,33116134 37,471535 2,044144084
2002 17,79285682 37,889443 2,129474957
2003 18,56300544 38,309475 2,063753907
2004 19,67676644 38,728778 1,968249108
2005 19,61545345 39,145491 1,995645479
2006 20,73285834 39,55875 1,908022008
2007 20,77463916 39,969903 1,9239758
2008 21,42453224 40,38186 1,884842084
2009 20,82006283 40,798641 1,959582991
2010 21,30211457 41,222875 1,935154131
2011 21,37553072 41,655616 1,948752363
2012 21,27620936 42,095224 1,978511458
2013 21,17559846 42,538304 2,008835976

Alors, vous demanderez, qu’est-ce qu’il y a de si spécial au sujet de Table 1 ? Si vous regardez la dernière colonne, donc celle où je présente le quotient de la population réelle de l’Argentine, divisée par celle modelée avec l’équation, vous pouvez voir un quotient étonnamment stable : avec une moyenne de 1.952675804, cette proportion a une variance de 0,003343958, donc trois fois rien avec cette moyenne. Je suis donc arrivé, dans le cas de l’Argentine, à une proportion très stable entre le produit (W/Pop)0,75 * (A/Pop)0,25 et la population réelle. C’est exactement de cette façon que Charles W. Cobb et Paul H. Douglas avaient démontré la robustesse de leur fonction de production : ils avaient trouvé une proportion stable (a = 1,01) entre le produit K0,25 * L0,75 et le PIB des Etats-Unis.

Bon, alors si ça a marché pour Argentine, je teste pour un autre pays. Pour devancer des reproches d’alphabétisme ou de continentalisme, je saute jusqu’à la République Tchèque. Je présente les résultats dans Table 2, ci-dessous. Il y a deux trucs qui frappent. Premièrement, le quotient « population réelle divisée par la population modèle » est d’un ordre de grandeur plus petit que celui calculé pour Argentine, mais tout aussi stable. Avec une moyenne de 0.254871929, ce quotient présente une variance de      9,54914E-05 : presque rien.

Table 2 – Modèle « Pop = (W/Pop)0,75 * (A/Pop)0,25 » testé pour la République Tchèque

Année Population modèle Population réelle Population réelle divisée par population modèle
1990 42,01901303 10,32844 0,245803965
1991 41,09669593 10,33393 0,251454035
1992 40,12189819 10,338381 0,257674274
1993 39,19042449 10,339439 0,263825645
1994 39,60863068 10,335556 0,260942018
1995 40,58847225 10,326682 0,254424013
1996 40,82241752 10,313836 0,252651279
1997 39,88617912 10,297977 0,258184094
1998 37,84459093 10,280525 0,271651106
1999 39,37364352 10,26301 0,260656853
2000 40,28179246 10,244261 0,254314924
2001 40,66550053 10,225198 0,251446505
2002 42,07940371 10,211846 0,242680388
2003 42,82094284 10,212088 0,238483492
2004 42,39265377 10,230877 0,241336083
2005 43,04580379 10,271476 0,238617359
2006 42,88357419 10,330487 0,240896129
2007 41,88719031 10,397984 0,248237801
2008 39,71897639 10,460022 0,263350744
2009 41,20964533 10,506617 0,254955288
2010 40,03317891 10,533985 0,263131365
2011 39,8616928 10,545161 0,264543733
2012 39,38759924 10,545314 0,267731829
2013 39,0565498 10,542666 0,269933367

J’ai donc trouvé une fonction que, faute de pouvoir trouver mieux sur le champ, je peux appeler « fonction de population-énergie », produit un agrégat que je peux interpréter comme population potentielle possible sur la base de l’absorption agrégée de l’énergie. Je l’ai testé un peu au hasard, pour un pays-ci, un pays-là. D’une manière générale, la population modèle sur la base de l’absorption de l’énergie est plus grande que la population réelle, plutôt type République Tchèque, avec ce quotient « population réelle divisée par la population modèle » solide comme du béton armé. Encore, il y a des exceptions intéressantes. Tenez l’Indonésie. Je présente son cas dans Table 3, ci-dessous. Voilà une population réelle plusieurs fois plus élevée que la population modelée sur la base de l’absorption locale d’énergie. En plus, le quotient « population réelle divisée par la population modèle » dans le cas Indonésien est beaucoup moins stable : avec une valeur moyenne de 25.18571988, il présente une variance de 0.390129622, donc beaucoup plus respectable que chez les Tchèques et les Argentins. Conclusion : ma formule magique marche dans certains cas, et pas tout à fait dans des cas autres que certains. Chouette ! Je vois une bonne recherche à l’horizon.

Table 3 – Modèle « Pop = (W/Pop)0,75 * (A/Pop)0,25 » testé pour l’Indonésie

Année Population modèle Population réelle Population réelle divisée par population modèle
1990 6,910456897 182,177052 26,36251911
1991 7,07024969 185,379624 26,21967146
1992 7,20208569 188,554943 26,18060255
1993 7,632690336 191,693719 25,11482984
1994 7,549393699 194,782664 25,80110029
1995 8,031643459 197,814284 24,62936571
1996 8,157250449 200,786111 24,61443501
1997 8,271624937 203,707717 24,62729132
1998 8,049718606 206,598599 25,66531939
1999 8,248410897 208,644079 25,29506369
2000 8,672234316 211,540428 24,39284045
2001 8,734987683 214,448301 24,55049838
2002 8,88687902 217,369087 24,45955284
2003 8,816998424 220,307809 24,98671298
2004 9,158320367 223,268606 24,3787722
2005 9,188094507 226,254703 24,62476881
2006 9,257872076 229,26398 24,76421991
2007 9,135126017 232,29683 25,42896831
2008 9,180058336 235,360765 25,63826464
2009 9,567339213 238,465165 24,92492005
2010 9,806815912 241,613126 24,63726537
2011 9,56672306 244,808254 25,58956212
2012 9,698388916 248,037853 25,57516049
2013 9,665810563 251,268276 25,99557216

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

[2] 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