Core and periphery

My editorial

And so I am officially starting to prepare a manuscript for my book, which I provisionally give the title ‘Good at Energy’.  I am exploring the same general hypothesis I have already turned and returned many times on this blog, namely that technological change in our human civilisation is functionally oriented on maximising the absorption of energy from the environment. I articulate this general line of thinking into four more specific hypotheses, which are supposed to drive the writing of four distinct sections in my book. One, the spatial structure of the human civilisation adapts and rearranges so as to maximise the absorption of energy. Two, the pace of technological change is functionally connected to the food deficit the given society experiences, and reaches its peak in societies with a food deficit between zero and 90 kilocalories per day per person. Three, technological change follows an evolutionary function of selection and hierarchizing, where social entities specialise, respectively, in the male function of transmission and conception, or in the female function of recombination and reproduction, which creates a hierarchy of male entities according to their capacity of meeting the expectations of the female entities. Four, technological change in the absorption of energy is functionally connected to the development of communication systems, with the supply of money acting as a communication system among others and the velocity of money being inversely proportional to the pace of technological change.

Yesterday, as I formulated those hypotheses in my update in French (see Les implications de ce que je viens d’écrire), I started reviewing the literature regarding the first specific hypothesis, the one about the spatial structure of the human civilisation. Quite naturally, being an economist, I called by Paul Krugman and the so-called ‘new economic geography’ (Krugman 1991[1];  Krugman 1998[2]). The basic logic I could derive from these readings is that of differentiation inside a territory: geographical structures differentiate internally into specialized parts, and this differentiation follows a pattern of core different from periphery. I think I can take on the model proposed by Paul Krugman, and replace the maximisation of utility, in the original version, by the maximisation of energy absorbed. As I think about it, with this precise orientation in my hypothesis, I can take any economic model that implies the maximisation of utility, transform it so as it maximises the absorption of energy, and see what happens.

Now, the tricky part is the ‘I can’. Can I? Let’s see. I take on the equations from the original model by Paul Krugman (Krugman 1991[3]). I start with equation (1). With CM standing, for the consumption of the manufacturing aggregate, and CA corresponding to the consumption of agricultural goods, the former receives always a share µ of the aggregate expenditure, the given society maximizes its aggregate utility ‘U’ so as to satisfy U = CMµ*CA1-µ. Here comes the first big question from my point of view: whilst it is simple to replace aggregate utility by the aggregate absorption of energy – let’s call it ‘AE’ (could also stand for ‘Attractive Expectations’, mind you) – it is more delicate to rephrase the right side of my equation. In economics, utility is a blissful category, as it has no definite unit of measurement. Utility can be cardinal or ordinal, can be expressed in money or in equivalent units of any economic good. Utility is cool and relax, even when it maximizes itself. Now, the absorption of energy is stricter a category: there are always joules under the bottom line. They can gang up into kilojoules or mega joules, or even dress into calories or watts, but at the end of the day, I have to sum my calculations up with a unit of energy. Logically, on the right side of the equation, I have to put aggregates that sum up into joules, watts or related.

We absorb energy in two ways: we eat it in kilocalories and we use it in various units. All that stuff is convertible into watt-hours, fortunately. I assign the symbol ‘F’ to the aggregate absorption of energy through eating (comes from ‘food’, but you have probably guessed this one already), and I designate the aggregate use of energy as ‘W’, or something measured directly in watts. As I am having my first go at transforming the original equation by Paul Krugman, I’m saying AE = Fp*Wq. The next stop is by that ‘p’ and that ‘q’. What are they? They can be anything, but as I look at it, I have to transform this transformation a bit. I mean, if I literally take the absorption of food and the final use of energy, express them both in an aggregate of watts, I get straight to the left side, namely to the aggregate absorption of energy, without any powers. I know, I could make it look like AE = F1*W1, but: a) it looks stupid b) it does not make sense. The final absorption of energy is the sum total of food eaten and energy used in other forms, not their product, whatever power I raise them to. Thus, I should say AE = F + W, but this is an accounting identity, not a functional model. Master Paul, I humbly apologize for having doubted in your insightfulness, when you used that aggregate utility thingy. Now I can see the depth of your wisdom, and I humbly return to the path of enlightenment, and I know it is better to use U(AE), so the utility derived from aggregate absorption of energy, than the plain AE.

Still I have a question: in your initial model, Master Paul, you raised the manufacturing output to the power ‘µ’, and agricultural goods to ‘1 – µ’. I guess it means that first we spend money on manufactures, and only after having done that, we scratch the bottom of our purse and get the last ‘1 – µ’ pennies to buy them pork loins and tomatoes. If you say so, Master… But what should I do? Should I assume that we spend money on food first, and only then we pour fuel into our cars (if we have any), or the opposite way round, namely petrol tank first, stomach next? Master? What? I have to think by myself, as I am a university professor? If you say so, Master… I am giving a try at thinking by myself, and I recollect my earlier research, and I remember that sharp difference between societies with officially recorded food deficit, on the one hand, and the satiate ones, on the other hand. I guess I should assume both options as possible, and say:

Equation (1), Class #1: U(AE) = Fµ*W1-µ        >> these people eat first, and turn their TV on next. Expenditures on energy are residual regarding expenditures on food. Roughly speaking, this class covers all the cases of societies with the food deficit being kind of official.

Equation (1) Class #2: U(AE) = Wµ*F1-µ            >> of course, those people eat, too, and they have to, and probably they eat better and more than Class #1, and yet, as they don’t have any official food deficit displayed on their doorstep, they mostly forget that food can go scarce. They spend most of their revenue on other forms of energy use, and leave a reasonable residual for caviar and Champagne.

According to Paul Krugman, that ‘µ’ parameter is one of the main bearings in his original model. It determines whether regions converge or diverge. Anyway, I am skipping to equation (2) in the original model, which basically details the way we compute the consumption CM of manufactures, and which I can generalize as the way of computing the aggregate endowed raised to power µ in equation (1). Before I go further, an old reminder: I am writing this precise content for my blog, and neither of my blogging environments, namely neither Blogger nor Word Press, is at home with equations. Hence, I do my best to express the original scientific equations as text. So I say {F; W} = [∑(i = 1 -> N; ci(π-1)/π)]π/(π-1) , where ∑(i = 1 -> N) means sum total over the interval from i = 1 to N, ‘ci’is the i-th consumable in the lot, and π > 1 is the elasticity of substitution between those consumables. That ‘π’ parameter is the second anchor of the equilibrium in the model.

As I am quickly wrapping my mind around equation (2), I think that substitution between various foods is an abyssal topic, especially if I want to treat global data, with all the local specificities in alimentary regimes. In class #1, with food coming first, the aggregate F = [∑(i = 1 -> N; ci(π-1)/π)]π/(π-1) would be quite foggy. Conversely, there are sharp distinctions as for the use of energy. I can sharply divide electricity used in houseware from fuel burnt in cars etc. Intuitively, I would go for class #2 when applying this Paul Krugman’s model. I could even invent some kind of intellectual parkour in order to jump over the food deficit. Actually, I don’t even need parkour: common observation comes handy. This summer, in China, I had the occasion to observe people who have s***load of technology to their disposition and still are officially starving, by some 74 kilocalories per day per person, on average. In other words, a paradigm where money is spent on the use of energy first, and only then on the energy consumed via food, is not really confined to the wealthy and satiate societies. After reflection, I go for class #1, and so I state my rephrased model as follows:

Equation (1) U(AE) = Wµ*F1-µ      µ < 1

Equation (2) W = [∑(i = 1 -> N; ci(π-1)/π)]π/(π-1)     π > 1

As I understand the original reasoning by Paul Krugman, the internal, spatial differentiation of a territory into a core and a periphery depends, among others, on those two parameters: µ and π. I guess that the greater are the values of µ and π, the greater the potential for such differentiation. I will slowly drift towards rephrasing that original model so as to show, how does the working of equations (1) and (2) impact the density of population.

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

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

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

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